id	sid	tid	token	lemma	pos
fumecheng-7267	1	1	facta	facta	PROPN
fumecheng-7267	1	2	universitatis	universitatis	PROPN
fumecheng-7267	1	3	series	series	NOUN
fumecheng-7267	1	4	:	:	PUNCT
fumecheng-7267	1	5	mechanical	mechanical	ADJ
fumecheng-7267	1	6	engineering	engineering	NOUN
fumecheng-7267	1	7	vol	vol	NOUN
fumecheng-7267	1	8	.	.	PROPN
fumecheng-7267	2	1	19	19	NUM
fumecheng-7267	2	2	,	,	PUNCT
fumecheng-7267	2	3	no	no	DET
fumecheng-7267	2	4	2	2	NUM
fumecheng-7267	2	5	,	,	PUNCT
fumecheng-7267	2	6	2021	2021	NUM
fumecheng-7267	2	7	,	,	PUNCT
fumecheng-7267	2	8	pp	pp	ADV
fumecheng-7267	2	9	.	.	PUNCT
fumecheng-7267	3	1	253	253	NUM
fumecheng-7267	3	2	269	269	NUM
fumecheng-7267	3	3	https://doi.org/10.22190/fume210111044b	https://doi.org/10.22190/fume210111044b	PROPN
fumecheng-7267	3	4	©	©	PROPN
fumecheng-7267	3	5	2021	2021	NUM
fumecheng-7267	3	6	by	by	ADP
fumecheng-7267	3	7	university	university	PROPN
fumecheng-7267	3	8	of	of	ADP
fumecheng-7267	3	9	niš	niš	PROPN
fumecheng-7267	3	10	,	,	PUNCT
fumecheng-7267	3	11	serbia	serbia	PROPN
fumecheng-7267	3	12	|	|	ADV
fumecheng-7267	3	13	creative	creative	ADJ
fumecheng-7267	3	14	commons	common	NOUN
fumecheng-7267	3	15	license	license	NOUN
fumecheng-7267	3	16	:	:	PUNCT
fumecheng-7267	3	17	cc	cc	VERB
fumecheng-7267	3	18	by	by	ADP
fumecheng-7267	3	19	-	-	PUNCT
fumecheng-7267	3	20	nc	nc	PROPN
fumecheng-7267	3	21	-	-	PUNCT
fumecheng-7267	3	22	nd	nd	NOUN
fumecheng-7267	3	23	review	review	NOUN
fumecheng-7267	3	24	paper	paper	VERB
fumecheng-7267	3	25	excel	excel	PROPN
fumecheng-7267	3	26	vba	vba	NOUN
fumecheng-7267	3	27	-	-	PUNCT
fumecheng-7267	3	28	based	base	VERB
fumecheng-7267	3	29	user	user	NOUN
fumecheng-7267	3	30	defined	define	VERB
fumecheng-7267	3	31	functions	function	NOUN
fumecheng-7267	3	32	for	for	ADP
fumecheng-7267	3	33	highly	highly	ADV
fumecheng-7267	3	34	precise	precise	ADJ
fumecheng-7267	3	35	colebrook	colebrook	PROPN
fumecheng-7267	3	36	’s	’s	PART
fumecheng-7267	3	37	pipe	pipe	NOUN
fumecheng-7267	3	38	flow	flow	NOUN
fumecheng-7267	3	39	friction	friction	NOUN
fumecheng-7267	3	40	approximations	approximation	NOUN
fumecheng-7267	3	41	:	:	PUNCT
fumecheng-7267	3	42	a	a	DET
fumecheng-7267	3	43	comparative	comparative	ADJ
fumecheng-7267	3	44	overview	overview	NOUN
fumecheng-7267	3	45	dejan	dejan	NOUN
fumecheng-7267	3	46	brkić1	brkić1	NOUN
fumecheng-7267	3	47	,	,	PUNCT
fumecheng-7267	3	48	zoran	zoran	PROPN
fumecheng-7267	3	49	stajić2	stajić2	PROPN
fumecheng-7267	4	1	1it4innovations	1it4innovations	X
fumecheng-7267	4	2	,	,	PUNCT
fumecheng-7267	4	3	vsb	vsb	PROPN
fumecheng-7267	4	4	–	–	PUNCT
fumecheng-7267	4	5	technical	technical	ADJ
fumecheng-7267	4	6	university	university	PROPN
fumecheng-7267	4	7	of	of	ADP
fumecheng-7267	4	8	ostrava	ostrava	PROPN
fumecheng-7267	4	9	,	,	PUNCT
fumecheng-7267	4	10	ostrava	ostrava	PROPN
fumecheng-7267	4	11	,	,	PUNCT
fumecheng-7267	4	12	czech	czech	PROPN
fumecheng-7267	4	13	republic	republic	NOUN
fumecheng-7267	4	14	2research	2research	NUM
fumecheng-7267	4	15	and	and	CCONJ
fumecheng-7267	4	16	development	development	NOUN
fumecheng-7267	4	17	centre	centre	NOUN
fumecheng-7267	4	18	“	"	PUNCT
fumecheng-7267	4	19	irc	irc	PROPN
fumecheng-7267	4	20	alfatec	alfatec	ADJ
fumecheng-7267	4	21	”	"	PUNCT
fumecheng-7267	4	22	,	,	PUNCT
fumecheng-7267	4	23	niš	niš	NOUN
fumecheng-7267	4	24	,	,	PUNCT
fumecheng-7267	4	25	serbia	serbia	PROPN
fumecheng-7267	4	26	abstract	abstract	ADJ
fumecheng-7267	4	27	.	.	PUNCT
fumecheng-7267	5	1	this	this	DET
fumecheng-7267	5	2	review	review	NOUN
fumecheng-7267	5	3	paper	paper	NOUN
fumecheng-7267	5	4	gives	give	VERB
fumecheng-7267	5	5	excel	excel	NOUN
fumecheng-7267	5	6	functions	function	NOUN
fumecheng-7267	5	7	for	for	ADP
fumecheng-7267	5	8	highly	highly	ADV
fumecheng-7267	5	9	precise	precise	ADJ
fumecheng-7267	5	10	colebrook	colebrook	PROPN
fumecheng-7267	5	11	’s	’s	PART
fumecheng-7267	5	12	pipe	pipe	NOUN
fumecheng-7267	5	13	flow	flow	NOUN
fumecheng-7267	5	14	friction	friction	NOUN
fumecheng-7267	5	15	approximations	approximation	NOUN
fumecheng-7267	5	16	developed	develop	VERB
fumecheng-7267	5	17	by	by	ADP
fumecheng-7267	5	18	users	user	NOUN
fumecheng-7267	5	19	.	.	PUNCT
fumecheng-7267	6	1	all	all	PRON
fumecheng-7267	6	2	shown	show	VERB
fumecheng-7267	6	3	codes	code	NOUN
fumecheng-7267	6	4	are	be	AUX
fumecheng-7267	6	5	implemented	implement	VERB
fumecheng-7267	6	6	as	as	ADP
fumecheng-7267	6	7	user	user	NOUN
fumecheng-7267	6	8	defined	define	VERB
fumecheng-7267	6	9	functions	function	NOUN
fumecheng-7267	6	10	–	–	PUNCT
fumecheng-7267	6	11	udfs	udfs	NOUN
fumecheng-7267	6	12	written	write	VERB
fumecheng-7267	6	13	in	in	ADP
fumecheng-7267	6	14	visual	visual	ADJ
fumecheng-7267	6	15	basic	basic	ADJ
fumecheng-7267	6	16	for	for	ADP
fumecheng-7267	6	17	applications	application	NOUN
fumecheng-7267	6	18	–	–	PUNCT
fumecheng-7267	6	19	vba	vba	NOUN
fumecheng-7267	6	20	,	,	PUNCT
fumecheng-7267	6	21	a	a	DET
fumecheng-7267	6	22	common	common	ADJ
fumecheng-7267	6	23	programming	programming	NOUN
fumecheng-7267	6	24	language	language	NOUN
fumecheng-7267	6	25	for	for	ADP
fumecheng-7267	6	26	ms	ms	PROPN
fumecheng-7267	6	27	excel	excel	PROPN
fumecheng-7267	6	28	spreadsheet	spreadsheet	PROPN
fumecheng-7267	6	29	solver	solver	PROPN
fumecheng-7267	6	30	.	.	PUNCT
fumecheng-7267	7	1	accuracy	accuracy	NOUN
fumecheng-7267	7	2	of	of	ADP
fumecheng-7267	7	3	the	the	DET
fumecheng-7267	7	4	friction	friction	NOUN
fumecheng-7267	7	5	factor	factor	NOUN
fumecheng-7267	7	6	computed	compute	VERB
fumecheng-7267	7	7	using	use	VERB
fumecheng-7267	7	8	nine	nine	NUM
fumecheng-7267	7	9	to	to	ADP
fumecheng-7267	7	10	date	date	NOUN
fumecheng-7267	7	11	the	the	DET
fumecheng-7267	7	12	most	most	ADV
fumecheng-7267	7	13	accurate	accurate	ADJ
fumecheng-7267	7	14	explicit	explicit	ADJ
fumecheng-7267	7	15	approximations	approximation	NOUN
fumecheng-7267	7	16	is	be	AUX
fumecheng-7267	7	17	compared	compare	VERB
fumecheng-7267	7	18	with	with	ADP
fumecheng-7267	7	19	the	the	DET
fumecheng-7267	7	20	sufficiently	sufficiently	ADV
fumecheng-7267	7	21	accurate	accurate	ADJ
fumecheng-7267	7	22	solution	solution	NOUN
fumecheng-7267	7	23	obtained	obtain	VERB
fumecheng-7267	7	24	through	through	ADP
fumecheng-7267	7	25	an	an	DET
fumecheng-7267	7	26	iterative	iterative	NOUN
fumecheng-7267	7	27	scheme	scheme	NOUN
fumecheng-7267	7	28	which	which	PRON
fumecheng-7267	7	29	gives	give	VERB
fumecheng-7267	7	30	satisfying	satisfy	VERB
fumecheng-7267	7	31	results	result	NOUN
fumecheng-7267	7	32	after	after	ADP
fumecheng-7267	7	33	sufficient	sufficient	ADJ
fumecheng-7267	7	34	number	number	NOUN
fumecheng-7267	7	35	of	of	ADP
fumecheng-7267	7	36	iterations	iteration	NOUN
fumecheng-7267	7	37	.	.	PUNCT
fumecheng-7267	8	1	the	the	DET
fumecheng-7267	8	2	codes	code	NOUN
fumecheng-7267	8	3	are	be	AUX
fumecheng-7267	8	4	given	give	VERB
fumecheng-7267	8	5	for	for	ADP
fumecheng-7267	8	6	the	the	DET
fumecheng-7267	8	7	presented	present	VERB
fumecheng-7267	8	8	approximations	approximation	NOUN
fumecheng-7267	8	9	,	,	PUNCT
fumecheng-7267	8	10	for	for	ADP
fumecheng-7267	8	11	the	the	DET
fumecheng-7267	8	12	used	use	VERB
fumecheng-7267	8	13	iterative	iterative	NOUN
fumecheng-7267	8	14	scheme	scheme	NOUN
fumecheng-7267	8	15	and	and	CCONJ
fumecheng-7267	8	16	for	for	ADP
fumecheng-7267	8	17	the	the	DET
fumecheng-7267	8	18	colebrook	colebrook	PROPN
fumecheng-7267	8	19	equation	equation	NOUN
fumecheng-7267	8	20	expressed	express	VERB
fumecheng-7267	8	21	through	through	ADP
fumecheng-7267	8	22	the	the	DET
fumecheng-7267	8	23	lambert	lambert	PROPN
fumecheng-7267	8	24	w	w	PROPN
fumecheng-7267	8	25	-	-	PUNCT
fumecheng-7267	8	26	function	function	NOUN
fumecheng-7267	8	27	(	(	PUNCT
fumecheng-7267	8	28	including	include	VERB
fumecheng-7267	8	29	its	its	PRON
fumecheng-7267	8	30	cognate	cognate	NOUN
fumecheng-7267	8	31	wright	wright	PROPN
fumecheng-7267	8	32	ωfunction	ωfunction	NOUN
fumecheng-7267	8	33	)	)	PUNCT
fumecheng-7267	8	34	.	.	PUNCT
fumecheng-7267	9	1	the	the	DET
fumecheng-7267	9	2	developed	develop	VERB
fumecheng-7267	9	3	code	code	NOUN
fumecheng-7267	9	4	for	for	ADP
fumecheng-7267	9	5	the	the	DET
fumecheng-7267	9	6	principal	principal	ADJ
fumecheng-7267	9	7	branch	branch	NOUN
fumecheng-7267	9	8	of	of	ADP
fumecheng-7267	9	9	the	the	DET
fumecheng-7267	9	10	lambert	lambert	PROPN
fumecheng-7267	9	11	w	w	PROPN
fumecheng-7267	9	12	-	-	PUNCT
fumecheng-7267	9	13	function	function	NOUN
fumecheng-7267	9	14	has	have	VERB
fumecheng-7267	9	15	additional	additional	ADJ
fumecheng-7267	9	16	and	and	CCONJ
fumecheng-7267	9	17	more	more	ADV
fumecheng-7267	9	18	general	general	ADJ
fumecheng-7267	9	19	application	application	NOUN
fumecheng-7267	9	20	for	for	ADP
fumecheng-7267	9	21	solving	solve	VERB
fumecheng-7267	9	22	different	different	ADJ
fumecheng-7267	9	23	problems	problem	NOUN
fumecheng-7267	9	24	from	from	ADP
fumecheng-7267	9	25	variety	variety	NOUN
fumecheng-7267	9	26	branches	branch	NOUN
fumecheng-7267	9	27	of	of	ADP
fumecheng-7267	9	28	engineering	engineering	NOUN
fumecheng-7267	9	29	and	and	CCONJ
fumecheng-7267	9	30	physics	physics	NOUN
fumecheng-7267	9	31	.	.	PUNCT
fumecheng-7267	10	1	the	the	DET
fumecheng-7267	10	2	approach	approach	NOUN
fumecheng-7267	10	3	from	from	ADP
fumecheng-7267	10	4	this	this	DET
fumecheng-7267	10	5	review	review	NOUN
fumecheng-7267	10	6	paper	paper	NOUN
fumecheng-7267	10	7	automates	automate	VERB
fumecheng-7267	10	8	computational	computational	ADJ
fumecheng-7267	10	9	processes	process	NOUN
fumecheng-7267	10	10	and	and	CCONJ
fumecheng-7267	10	11	speeds	speed	VERB
fumecheng-7267	10	12	up	up	ADP
fumecheng-7267	10	13	manual	manual	ADJ
fumecheng-7267	10	14	tasks	task	NOUN
fumecheng-7267	10	15	.	.	PUNCT
fumecheng-7267	11	1	key	key	ADJ
fumecheng-7267	11	2	words	word	NOUN
fumecheng-7267	11	3	:	:	PUNCT
fumecheng-7267	11	4	hydraulic	hydraulic	ADJ
fumecheng-7267	11	5	resistance	resistance	NOUN
fumecheng-7267	11	6	,	,	PUNCT
fumecheng-7267	11	7	colebrook	colebrook	PROPN
fumecheng-7267	11	8	flow	flow	PROPN
fumecheng-7267	11	9	friction	friction	NOUN
fumecheng-7267	11	10	,	,	PUNCT
fumecheng-7267	11	11	lambert	lambert	PROPN
fumecheng-7267	11	12	w	w	PROPN
fumecheng-7267	11	13	-	-	PUNCT
fumecheng-7267	11	14	function	function	NOUN
fumecheng-7267	11	15	,	,	PUNCT
fumecheng-7267	11	16	excel	excel	VERB
fumecheng-7267	11	17	macro	macro	ADJ
fumecheng-7267	11	18	programming	programming	NOUN
fumecheng-7267	11	19	,	,	PUNCT
fumecheng-7267	11	20	visual	visual	ADJ
fumecheng-7267	11	21	basic	basic	ADJ
fumecheng-7267	11	22	for	for	ADP
fumecheng-7267	11	23	applications	application	NOUN
fumecheng-7267	11	24	(	(	PUNCT
fumecheng-7267	11	25	vba	vba	PROPN
fumecheng-7267	11	26	)	)	PUNCT
fumecheng-7267	11	27	,	,	PUNCT
fumecheng-7267	11	28	user	user	NOUN
fumecheng-7267	11	29	defined	define	VERB
fumecheng-7267	11	30	functions	function	NOUN
fumecheng-7267	11	31	(	(	PUNCT
fumecheng-7267	11	32	udfs	udfs	ADJ
fumecheng-7267	11	33	)	)	PUNCT
fumecheng-7267	11	34	1	1	NUM
fumecheng-7267	11	35	.	.	PUNCT
fumecheng-7267	11	36	introduction	introduction	NOUN
fumecheng-7267	11	37	the	the	DET
fumecheng-7267	11	38	colebrook	colebrook	PROPN
fumecheng-7267	11	39	equation	equation	NOUN
fumecheng-7267	11	40	from	from	ADP
fumecheng-7267	11	41	1939	1939	NUM
fumecheng-7267	12	1	[	[	X
fumecheng-7267	12	2	1	1	NUM
fumecheng-7267	12	3	]	]	PUNCT
fumecheng-7267	12	4	,	,	PUNCT
fumecheng-7267	12	5	eq	eq	NOUN
fumecheng-7267	12	6	.	.	PUNCT
fumecheng-7267	13	1	(	(	PUNCT
fumecheng-7267	13	2	1	1	NUM
fumecheng-7267	13	3	)	)	PUNCT
fumecheng-7267	13	4	,	,	PUNCT
fumecheng-7267	13	5	is	be	AUX
fumecheng-7267	13	6	an	an	DET
fumecheng-7267	13	7	informal	informal	ADJ
fumecheng-7267	13	8	standard	standard	NOUN
fumecheng-7267	13	9	widely	widely	ADV
fumecheng-7267	13	10	accepted	accept	VERB
fumecheng-7267	13	11	in	in	ADP
fumecheng-7267	13	12	engineering	engineering	NOUN
fumecheng-7267	13	13	practice	practice	NOUN
fumecheng-7267	13	14	for	for	ADP
fumecheng-7267	13	15	calculation	calculation	NOUN
fumecheng-7267	13	16	of	of	ADP
fumecheng-7267	13	17	turbulent	turbulent	ADJ
fumecheng-7267	13	18	darcy	darcy	PROPN
fumecheng-7267	13	19	’s	’s	PART
fumecheng-7267	13	20	fluid	fluid	ADJ
fumecheng-7267	13	21	flow	flow	NOUN
fumecheng-7267	13	22	friction	friction	NOUN
fumecheng-7267	13	23	factor	factor	NOUN
fumecheng-7267	13	24	.	.	PUNCT
fumecheng-7267	14	1	it	it	PRON
fumecheng-7267	14	2	is	be	AUX
fumecheng-7267	14	3	an	an	DET
fumecheng-7267	14	4	empirical	empirical	ADJ
fumecheng-7267	14	5	equation	equation	NOUN
fumecheng-7267	14	6	based	base	VERB
fumecheng-7267	14	7	on	on	ADP
fumecheng-7267	14	8	an	an	DET
fumecheng-7267	14	9	experiment	experiment	NOUN
fumecheng-7267	14	10	with	with	ADP
fumecheng-7267	14	11	air	air	NOUN
fumecheng-7267	14	12	flow	flow	NOUN
fumecheng-7267	14	13	through	through	ADP
fumecheng-7267	14	14	a	a	DET
fumecheng-7267	14	15	set	set	NOUN
fumecheng-7267	14	16	of	of	ADP
fumecheng-7267	14	17	smooth	smooth	NOUN
fumecheng-7267	14	18	to	to	ADP
fumecheng-7267	14	19	fully	fully	ADV
fumecheng-7267	14	20	rough	rough	ADJ
fumecheng-7267	14	21	pipes	pipe	NOUN
fumecheng-7267	14	22	performed	perform	VERB
fumecheng-7267	14	23	by	by	ADP
fumecheng-7267	14	24	colebrook	colebrook	PROPN
fumecheng-7267	14	25	and	and	CCONJ
fumecheng-7267	14	26	white	white	ADJ
fumecheng-7267	14	27	in	in	ADP
fumecheng-7267	14	28	1937	1937	NUM
fumecheng-7267	14	29	[	[	X
fumecheng-7267	14	30	2	2	NUM
fumecheng-7267	14	31	]	]	PUNCT
fumecheng-7267	14	32	.	.	PUNCT
fumecheng-7267	15	1	the	the	DET
fumecheng-7267	15	2	moody	moody	ADJ
fumecheng-7267	15	3	diagram	diagram	NOUN
fumecheng-7267	15	4	[	[	X
fumecheng-7267	15	5	3	3	X
fumecheng-7267	15	6	]	]	PUNCT
fumecheng-7267	15	7	in	in	ADP
fumecheng-7267	15	8	its	its	PRON
fumecheng-7267	15	9	turbulent	turbulent	ADJ
fumecheng-7267	15	10	part	part	NOUN
fumecheng-7267	15	11	represents	represent	VERB
fumecheng-7267	15	12	a	a	DET
fumecheng-7267	15	13	graphical	graphical	ADJ
fumecheng-7267	15	14	interpretation	interpretation	NOUN
fumecheng-7267	15	15	of	of	ADP
fumecheng-7267	15	16	the	the	DET
fumecheng-7267	15	17	colebrook	colebrook	PROPN
fumecheng-7267	15	18	equation	equation	NOUN
fumecheng-7267	15	19	.	.	PUNCT
fumecheng-7267	16	1	received	receive	VERB
fumecheng-7267	16	2	january	january	PROPN
fumecheng-7267	16	3	11	11	NUM
fumecheng-7267	16	4	,	,	PUNCT
fumecheng-7267	16	5	2021	2021	NUM
fumecheng-7267	16	6	/	/	SYM
fumecheng-7267	16	7	accepted	accept	VERB
fumecheng-7267	16	8	april	april	PROPN
fumecheng-7267	16	9	08	08	NUM
fumecheng-7267	16	10	,	,	PUNCT
fumecheng-7267	16	11	2021	2021	NUM
fumecheng-7267	16	12	corresponding	correspond	VERB
fumecheng-7267	16	13	author	author	NOUN
fumecheng-7267	16	14	:	:	PUNCT
fumecheng-7267	16	15	dejan	dejan	PROPN
fumecheng-7267	16	16	brkić	brkić	PROPN
fumecheng-7267	16	17	it4innovations	it4innovations	PROPN
fumecheng-7267	16	18	,	,	PUNCT
fumecheng-7267	16	19	vsb	vsb	PROPN
fumecheng-7267	16	20	–	–	PUNCT
fumecheng-7267	16	21	technical	technical	ADJ
fumecheng-7267	16	22	university	university	PROPN
fumecheng-7267	16	23	of	of	ADP
fumecheng-7267	16	24	ostrava	ostrava	PROPN
fumecheng-7267	16	25	,	,	PUNCT
fumecheng-7267	16	26	17	17	NUM
fumecheng-7267	16	27	.	.	PUNCT
fumecheng-7267	17	1	listopadu	listopadu	ADJ
fumecheng-7267	17	2	2172/15	2172/15	NUM
fumecheng-7267	17	3	,	,	PUNCT
fumecheng-7267	17	4	ostrava	ostrava	PROPN
fumecheng-7267	17	5	,	,	PUNCT
fumecheng-7267	17	6	czechia	czechia	PROPN
fumecheng-7267	17	7	e	e	NOUN
fumecheng-7267	17	8	-	-	NOUN
fumecheng-7267	17	9	mails	mail	NOUN
fumecheng-7267	17	10	:	:	PUNCT
fumecheng-7267	17	11	dejan.brkic@vsb.cz	dejan.brkic@vsb.cz	PROPN
fumecheng-7267	17	12	,	,	PUNCT
fumecheng-7267	17	13	dejanbrkic0611@gmail.com	dejanbrkic0611@gmail.com	NOUN
fumecheng-7267	17	14	254	254	NUM
fumecheng-7267	17	15	d.	d.	PROPN
fumecheng-7267	17	16	brkić	brkić	PROPN
fumecheng-7267	17	17	,	,	PUNCT
fumecheng-7267	17	18	z.	z.	PROPN
fumecheng-7267	17	19	stajić	stajić	PROPN
fumecheng-7267	18	1	1	1	NUM
fumecheng-7267	18	2	√f	√f	PRON
fumecheng-7267	18	3	=	=	SYM
fumecheng-7267	18	4	−	−	PROPN
fumecheng-7267	18	5	2	2	NUM
fumecheng-7267	18	6	·	·	PUNCT
fumecheng-7267	18	7	log	log	NOUN
fumecheng-7267	18	8	10	10	NUM
fumecheng-7267	18	9	(	(	PUNCT
fumecheng-7267	18	10	2.51	2.51	NUM
fumecheng-7267	18	11	re	re	ADP
fumecheng-7267	18	12	·	·	SYM
fumecheng-7267	18	13	1	1	NUM
fumecheng-7267	18	14	√f	√f	PRON
fumecheng-7267	18	15	+	+	CCONJ
fumecheng-7267	18	16	ε	ε	PROPN
fumecheng-7267	18	17	3.71	3.71	NUM
fumecheng-7267	18	18	)	)	PUNCT
fumecheng-7267	19	1	≈	≈	PROPN
fumecheng-7267	19	2	−	−	NUM
fumecheng-7267	19	3	0.8686	0.8686	NUM
fumecheng-7267	19	4	·	·	PUNCT
fumecheng-7267	19	5	ln	ln	X
fumecheng-7267	19	6	(	(	PUNCT
fumecheng-7267	19	7	2.51	2.51	NUM
fumecheng-7267	19	8	re	re	ADP
fumecheng-7267	19	9	·	·	SYM
fumecheng-7267	19	10	1	1	NUM
fumecheng-7267	19	11	√f	√f	PRON
fumecheng-7267	19	12	+	+	CCONJ
fumecheng-7267	19	13	ε	ε	PROPN
fumecheng-7267	19	14	3.71	3.71	NUM
fumecheng-7267	19	15	)	)	PUNCT
fumecheng-7267	19	16	(	(	PUNCT
fumecheng-7267	19	17	1	1	X
fumecheng-7267	19	18	)	)	PUNCT
fumecheng-7267	19	19	in	in	ADP
fumecheng-7267	19	20	eq	eq	ADP
fumecheng-7267	19	21	.	.	PUNCT
fumecheng-7267	20	1	(	(	PUNCT
fumecheng-7267	20	2	1	1	NUM
fumecheng-7267	20	3	)	)	PUNCT
fumecheng-7267	20	4	,	,	PUNCT
fumecheng-7267	20	5	dimensionless	dimensionless	ADJ
fumecheng-7267	20	6	turbulent	turbulent	ADJ
fumecheng-7267	20	7	darcy	darcy	PROPN
fumecheng-7267	20	8	flow	flow	NOUN
fumecheng-7267	20	9	friction	friction	NOUN
fumecheng-7267	20	10	factor	factor	NOUN
fumecheng-7267	20	11	is	be	AUX
fumecheng-7267	20	12	given	give	VERB
fumecheng-7267	20	13	as	as	ADP
fumecheng-7267	20	14	f	f	PROPN
fumecheng-7267	20	15	,	,	PUNCT
fumecheng-7267	20	16	the	the	DET
fumecheng-7267	20	17	dimensionless	dimensionless	NOUN
fumecheng-7267	20	18	reynolds	reynold	NOUN
fumecheng-7267	20	19	number	number	NOUN
fumecheng-7267	20	20	as	as	ADP
fumecheng-7267	20	21	re	re	PROPN
fumecheng-7267	20	22	,	,	PUNCT
fumecheng-7267	20	23	the	the	DET
fumecheng-7267	20	24	dimensionless	dimensionless	NOUN
fumecheng-7267	20	25	relative	relative	ADJ
fumecheng-7267	20	26	roughness	roughness	NOUN
fumecheng-7267	20	27	of	of	ADP
fumecheng-7267	20	28	inner	inner	ADJ
fumecheng-7267	20	29	pipe	pipe	NOUN
fumecheng-7267	20	30	surface	surface	NOUN
fumecheng-7267	20	31	as	as	ADP
fumecheng-7267	20	32	ε	ε	PROPN
fumecheng-7267	20	33	,	,	PUNCT
fumecheng-7267	20	34	while	while	SCONJ
fumecheng-7267	20	35	briggsian	briggsian	ADJ
fumecheng-7267	20	36	decimal	decimal	ADJ
fumecheng-7267	20	37	logarithm	logarithm	NOUN
fumecheng-7267	20	38	(	(	PUNCT
fumecheng-7267	20	39	to	to	PART
fumecheng-7267	20	40	base	base	VERB
fumecheng-7267	20	41	10	10	NUM
fumecheng-7267	20	42	)	)	PUNCT
fumecheng-7267	20	43	is	be	AUX
fumecheng-7267	20	44	given	give	VERB
fumecheng-7267	20	45	as	as	ADP
fumecheng-7267	20	46	log10	log10	PROPN
fumecheng-7267	20	47	and	and	CCONJ
fumecheng-7267	20	48	napierian	napierian	ADJ
fumecheng-7267	20	49	natural	natural	ADJ
fumecheng-7267	20	50	logarithm	logarithm	NOUN
fumecheng-7267	20	51	(	(	PUNCT
fumecheng-7267	20	52	to	to	PART
fumecheng-7267	20	53	base	base	VERB
fumecheng-7267	20	54	e	e	NOUN
fumecheng-7267	20	55	,	,	PUNCT
fumecheng-7267	20	56	where	where	SCONJ
fumecheng-7267	20	57	e≈2.718	e≈2.718	PROPN
fumecheng-7267	20	58	)	)	PUNCT
fumecheng-7267	20	59	as	as	ADP
fumecheng-7267	20	60	ln	ln	ADJ
fumecheng-7267	20	61	.	.	PROPN
fumecheng-7267	21	1	as	as	SCONJ
fumecheng-7267	21	2	shown	show	VERB
fumecheng-7267	21	3	in	in	ADP
fumecheng-7267	21	4	eq	eq	ADP
fumecheng-7267	21	5	.	.	PUNCT
fumecheng-7267	22	1	(	(	PUNCT
fumecheng-7267	22	2	1	1	NUM
fumecheng-7267	22	3	)	)	PUNCT
fumecheng-7267	22	4	,	,	PUNCT
fumecheng-7267	22	5	the	the	DET
fumecheng-7267	22	6	colebrook	colebrook	PROPN
fumecheng-7267	22	7	equation	equation	NOUN
fumecheng-7267	22	8	is	be	AUX
fumecheng-7267	22	9	given	give	VERB
fumecheng-7267	22	10	in	in	ADP
fumecheng-7267	22	11	an	an	DET
fumecheng-7267	22	12	implicitly	implicitly	ADV
fumecheng-7267	22	13	entangled	entangle	VERB
fumecheng-7267	22	14	logarithmic	logarithmic	ADJ
fumecheng-7267	22	15	form	form	NOUN
fumecheng-7267	22	16	which	which	PRON
fumecheng-7267	22	17	can	can	AUX
fumecheng-7267	22	18	not	not	PART
fumecheng-7267	22	19	be	be	AUX
fumecheng-7267	22	20	solved	solve	VERB
fumecheng-7267	22	21	in	in	ADP
fumecheng-7267	22	22	terms	term	NOUN
fumecheng-7267	22	23	of	of	ADP
fumecheng-7267	22	24	elementary	elementary	ADJ
fumecheng-7267	22	25	functions	function	NOUN
fumecheng-7267	22	26	.	.	PUNCT
fumecheng-7267	23	1	it	it	PRON
fumecheng-7267	23	2	can	can	AUX
fumecheng-7267	23	3	be	be	AUX
fumecheng-7267	23	4	solved	solve	VERB
fumecheng-7267	23	5	;	;	PUNCT
fumecheng-7267	23	6	1	1	X
fumecheng-7267	23	7	)	)	PUNCT
fumecheng-7267	23	8	iteratively	iteratively	ADV
fumecheng-7267	23	9	(	(	PUNCT
fumecheng-7267	23	10	such	such	ADJ
fumecheng-7267	23	11	solution	solution	NOUN
fumecheng-7267	23	12	can	can	AUX
fumecheng-7267	23	13	be	be	AUX
fumecheng-7267	23	14	treated	treat	VERB
fumecheng-7267	23	15	as	as	ADP
fumecheng-7267	23	16	accurate	accurate	ADJ
fumecheng-7267	23	17	after	after	ADP
fumecheng-7267	23	18	sufficient	sufficient	ADJ
fumecheng-7267	23	19	number	number	NOUN
fumecheng-7267	23	20	of	of	ADP
fumecheng-7267	23	21	iterations	iteration	NOUN
fumecheng-7267	23	22	)	)	PUNCT
fumecheng-7267	24	1	[	[	X
fumecheng-7267	24	2	4,5	4,5	NUM
fumecheng-7267	24	3	]	]	PUNCT
fumecheng-7267	24	4	,	,	PUNCT
fumecheng-7267	24	5	or	or	CCONJ
fumecheng-7267	24	6	2	2	X
fumecheng-7267	24	7	)	)	PUNCT
fumecheng-7267	24	8	using	use	VERB
fumecheng-7267	24	9	one	one	NUM
fumecheng-7267	24	10	-	-	PUNCT
fumecheng-7267	24	11	step	step	NOUN
fumecheng-7267	24	12	approximate	approximate	ADJ
fumecheng-7267	24	13	formulas	formula	NOUN
fumecheng-7267	24	14	specially	specially	ADV
fumecheng-7267	24	15	developed	develop	VERB
fumecheng-7267	24	16	for	for	ADP
fumecheng-7267	24	17	such	such	ADJ
fumecheng-7267	24	18	purpose	purpose	NOUN
fumecheng-7267	24	19	(	(	PUNCT
fumecheng-7267	24	20	maximal	maximal	ADJ
fumecheng-7267	24	21	error	error	NOUN
fumecheng-7267	24	22	of	of	ADP
fumecheng-7267	24	23	such	such	ADJ
fumecheng-7267	24	24	formulas	formula	NOUN
fumecheng-7267	24	25	can	can	AUX
fumecheng-7267	24	26	be	be	AUX
fumecheng-7267	24	27	estimated	estimate	VERB
fumecheng-7267	24	28	in	in	ADP
fumecheng-7267	24	29	advance	advance	NOUN
fumecheng-7267	24	30	)	)	PUNCT
fumecheng-7267	24	31	.	.	PUNCT
fumecheng-7267	25	1	therefore	therefore	ADV
fumecheng-7267	25	2	,	,	PUNCT
fumecheng-7267	25	3	for	for	ADP
fumecheng-7267	25	4	solving	solve	VERB
fumecheng-7267	25	5	the	the	DET
fumecheng-7267	25	6	colebrook	colebrook	PROPN
fumecheng-7267	25	7	equation	equation	NOUN
fumecheng-7267	25	8	,	,	PUNCT
fumecheng-7267	25	9	various	various	ADJ
fumecheng-7267	25	10	explicit	explicit	ADJ
fumecheng-7267	25	11	approximations	approximation	NOUN
fumecheng-7267	25	12	[	[	X
fumecheng-7267	25	13	6	6	NUM
fumecheng-7267	25	14	-	-	SYM
fumecheng-7267	25	15	11	11	NUM
fumecheng-7267	25	16	]	]	PUNCT
fumecheng-7267	25	17	can	can	AUX
fumecheng-7267	25	18	be	be	AUX
fumecheng-7267	25	19	used	use	VERB
fumecheng-7267	25	20	to	to	PART
fumecheng-7267	25	21	avoid	avoid	VERB
fumecheng-7267	25	22	long	long	ADJ
fumecheng-7267	25	23	computing	computing	NOUN
fumecheng-7267	25	24	times	time	NOUN
fumecheng-7267	25	25	caused	cause	VERB
fumecheng-7267	25	26	by	by	ADP
fumecheng-7267	25	27	iterative	iterative	NOUN
fumecheng-7267	25	28	schemes	scheme	NOUN
fumecheng-7267	25	29	during	during	ADP
fumecheng-7267	25	30	the	the	DET
fumecheng-7267	25	31	numerical	numerical	ADJ
fumecheng-7267	25	32	simulations	simulation	NOUN
fumecheng-7267	25	33	of	of	ADP
fumecheng-7267	25	34	pipelines	pipeline	NOUN
fumecheng-7267	25	35	for	for	ADP
fumecheng-7267	25	36	transport	transport	NOUN
fumecheng-7267	25	37	of	of	ADP
fumecheng-7267	25	38	various	various	ADJ
fumecheng-7267	25	39	fluids	fluid	NOUN
fumecheng-7267	25	40	[	[	X
fumecheng-7267	25	41	12,13	12,13	NUM
fumecheng-7267	25	42	]	]	PUNCT
fumecheng-7267	25	43	.	.	PUNCT
fumecheng-7267	26	1	also	also	ADV
fumecheng-7267	26	2	,	,	PUNCT
fumecheng-7267	26	3	the	the	DET
fumecheng-7267	26	4	colebrook	colebrook	PROPN
fumecheng-7267	26	5	equation	equation	NOUN
fumecheng-7267	26	6	can	can	AUX
fumecheng-7267	26	7	be	be	AUX
fumecheng-7267	26	8	analytically	analytically	ADV
fumecheng-7267	26	9	expressed	express	VERB
fumecheng-7267	26	10	through	through	ADP
fumecheng-7267	26	11	the	the	DET
fumecheng-7267	26	12	lambert	lambert	PROPN
fumecheng-7267	26	13	w	w	PROPN
fumecheng-7267	26	14	-	-	PUNCT
fumecheng-7267	26	15	function	function	NOUN
fumecheng-7267	26	16	[	[	X
fumecheng-7267	26	17	14	14	NUM
fumecheng-7267	26	18	-	-	SYM
fumecheng-7267	26	19	18	18	NUM
fumecheng-7267	26	20	]	]	PUNCT
fumecheng-7267	26	21	,	,	PUNCT
fumecheng-7267	26	22	but	but	CCONJ
fumecheng-7267	26	23	anyway	anyway	ADV
fumecheng-7267	26	24	the	the	DET
fumecheng-7267	26	25	lambert	lambert	PROPN
fumecheng-7267	26	26	w	w	PROPN
fumecheng-7267	26	27	-	-	PUNCT
fumecheng-7267	26	28	function	function	NOUN
fumecheng-7267	26	29	itself	itself	PRON
fumecheng-7267	26	30	is	be	AUX
fumecheng-7267	26	31	an	an	DET
fumecheng-7267	26	32	implicit	implicit	ADJ
fumecheng-7267	26	33	function	function	NOUN
fumecheng-7267	26	34	which	which	PRON
fumecheng-7267	26	35	can	can	AUX
fumecheng-7267	26	36	only	only	ADV
fumecheng-7267	26	37	be	be	AUX
fumecheng-7267	26	38	solved	solve	VERB
fumecheng-7267	26	39	either	either	CCONJ
fumecheng-7267	26	40	iteratively	iteratively	ADV
fumecheng-7267	26	41	or	or	CCONJ
fumecheng-7267	26	42	approximately	approximately	ADV
fumecheng-7267	26	43	using	use	VERB
fumecheng-7267	26	44	specially	specially	ADV
fumecheng-7267	26	45	developed	develop	VERB
fumecheng-7267	26	46	one	one	NUM
fumecheng-7267	26	47	-	-	PUNCT
fumecheng-7267	26	48	step	step	NOUN
fumecheng-7267	26	49	formulas	formula	NOUN
fumecheng-7267	26	50	[	[	X
fumecheng-7267	26	51	19,20	19,20	NUM
fumecheng-7267	26	52	]	]	PUNCT
fumecheng-7267	26	53	.	.	PUNCT
fumecheng-7267	27	1	fast	fast	ADJ
fumecheng-7267	27	2	and	and	CCONJ
fumecheng-7267	27	3	accurate	accurate	ADJ
fumecheng-7267	27	4	execution	execution	NOUN
fumecheng-7267	27	5	of	of	ADP
fumecheng-7267	27	6	codes	code	NOUN
fumecheng-7267	27	7	during	during	ADP
fumecheng-7267	27	8	calculation	calculation	NOUN
fumecheng-7267	27	9	of	of	ADP
fumecheng-7267	27	10	pipe	pipe	NOUN
fumecheng-7267	27	11	flow	flow	NOUN
fumecheng-7267	27	12	friction	friction	NOUN
fumecheng-7267	27	13	is	be	AUX
fumecheng-7267	27	14	essential	essential	ADJ
fumecheng-7267	27	15	for	for	ADP
fumecheng-7267	27	16	calculation	calculation	NOUN
fumecheng-7267	27	17	of	of	ADP
fumecheng-7267	27	18	pressure	pressure	NOUN
fumecheng-7267	27	19	drop	drop	NOUN
fumecheng-7267	27	20	and	and	CCONJ
fumecheng-7267	27	21	flow	flow	NOUN
fumecheng-7267	27	22	rate	rate	NOUN
fumecheng-7267	27	23	in	in	ADP
fumecheng-7267	27	24	oil	oil	NOUN
fumecheng-7267	27	25	and	and	CCONJ
fumecheng-7267	27	26	gas	gas	NOUN
fumecheng-7267	27	27	industry	industry	NOUN
fumecheng-7267	27	28	,	,	PUNCT
fumecheng-7267	27	29	water	water	NOUN
fumecheng-7267	27	30	distribution	distribution	NOUN
fumecheng-7267	27	31	,	,	PUNCT
fumecheng-7267	27	32	in	in	ADP
fumecheng-7267	27	33	chemical	chemical	ADJ
fumecheng-7267	27	34	engineering	engineering	NOUN
fumecheng-7267	27	35	,	,	PUNCT
fumecheng-7267	27	36	etc	etc	X
fumecheng-7267	27	37	.	.	X
fumecheng-7267	27	38	to	to	PART
fumecheng-7267	27	39	facilitate	facilitate	VERB
fumecheng-7267	27	40	use	use	NOUN
fumecheng-7267	27	41	of	of	ADP
fumecheng-7267	27	42	the	the	DET
fumecheng-7267	27	43	colebrook	colebrook	PROPN
fumecheng-7267	27	44	equation	equation	NOUN
fumecheng-7267	27	45	in	in	ADP
fumecheng-7267	27	46	spreadsheet	spreadsheet	PROPN
fumecheng-7267	27	47	solver	solver	PROPN
fumecheng-7267	27	48	ms	ms	PROPN
fumecheng-7267	27	49	excel	excel	VERB
fumecheng-7267	28	1	[	[	X
fumecheng-7267	28	2	21,22	21,22	NOUN
fumecheng-7267	28	3	]	]	X
fumecheng-7267	28	4	,	,	PUNCT
fumecheng-7267	28	5	codes	code	NOUN
fumecheng-7267	28	6	written	write	VERB
fumecheng-7267	28	7	in	in	ADP
fumecheng-7267	28	8	visual	visual	ADJ
fumecheng-7267	28	9	basic	basic	NOUN
fumecheng-7267	28	10	for	for	ADP
fumecheng-7267	28	11	applications	application	NOUN
fumecheng-7267	28	12	(	(	PUNCT
fumecheng-7267	28	13	vba	vba	NOUN
fumecheng-7267	28	14	)	)	PUNCT
fumecheng-7267	28	15	based	base	VERB
fumecheng-7267	28	16	on	on	ADP
fumecheng-7267	28	17	the	the	DET
fumecheng-7267	28	18	available	available	ADJ
fumecheng-7267	28	19	highly	highly	ADV
fumecheng-7267	28	20	precise	precise	ADJ
fumecheng-7267	28	21	explicit	explicit	ADJ
fumecheng-7267	28	22	approximations	approximation	NOUN
fumecheng-7267	28	23	[	[	X
fumecheng-7267	28	24	23	23	NUM
fumecheng-7267	28	25	-	-	SYM
fumecheng-7267	28	26	30	30	NUM
fumecheng-7267	28	27	]	]	PUNCT
fumecheng-7267	28	28	are	be	AUX
fumecheng-7267	28	29	given	give	VERB
fumecheng-7267	28	30	as	as	ADP
fumecheng-7267	28	31	user	user	NOUN
fumecheng-7267	28	32	defined	define	VERB
fumecheng-7267	28	33	functions	function	NOUN
fumecheng-7267	28	34	(	(	PUNCT
fumecheng-7267	28	35	udfs	udfs	ADJ
fumecheng-7267	28	36	)	)	PUNCT
fumecheng-7267	28	37	and	and	CCONJ
fumecheng-7267	28	38	compared	compare	VERB
fumecheng-7267	28	39	in	in	ADP
fumecheng-7267	28	40	this	this	DET
fumecheng-7267	28	41	review	review	NOUN
fumecheng-7267	28	42	paper	paper	NOUN
fumecheng-7267	28	43	.	.	PUNCT
fumecheng-7267	29	1	such	such	ADJ
fumecheng-7267	29	2	approach	approach	NOUN
fumecheng-7267	29	3	automates	automate	VERB
fumecheng-7267	29	4	computational	computational	ADJ
fumecheng-7267	29	5	processes	process	NOUN
fumecheng-7267	29	6	and	and	CCONJ
fumecheng-7267	29	7	speeds	speed	VERB
fumecheng-7267	29	8	up	up	ADP
fumecheng-7267	29	9	manual	manual	ADJ
fumecheng-7267	29	10	tasks	task	NOUN
fumecheng-7267	29	11	.	.	PUNCT
fumecheng-7267	30	1	2	2	X
fumecheng-7267	30	2	.	.	X
fumecheng-7267	30	3	visual	visual	ADJ
fumecheng-7267	30	4	basic	basic	NOUN
fumecheng-7267	30	5	for	for	ADP
fumecheng-7267	30	6	applications	application	NOUN
fumecheng-7267	30	7	excel	excel	VERB
fumecheng-7267	30	8	user	user	NOUN
fumecheng-7267	30	9	defined	define	VERB
fumecheng-7267	30	10	functions	function	VERB
fumecheng-7267	30	11	the	the	DET
fumecheng-7267	30	12	codes	code	NOUN
fumecheng-7267	30	13	for	for	ADP
fumecheng-7267	30	14	solving	solve	VERB
fumecheng-7267	30	15	the	the	DET
fumecheng-7267	30	16	colebrook	colebrook	PROPN
fumecheng-7267	30	17	equation	equation	NOUN
fumecheng-7267	30	18	used	use	VERB
fumecheng-7267	30	19	in	in	ADP
fumecheng-7267	30	20	this	this	DET
fumecheng-7267	30	21	review	review	NOUN
fumecheng-7267	30	22	paper	paper	NOUN
fumecheng-7267	30	23	are	be	AUX
fumecheng-7267	30	24	shown	show	VERB
fumecheng-7267	30	25	through	through	ADP
fumecheng-7267	30	26	macros	macro	NOUN
fumecheng-7267	30	27	for	for	ADP
fumecheng-7267	30	28	ms	ms	PROPN
fumecheng-7267	30	29	excel	excel	PROPN
fumecheng-7267	30	30	written	write	VERB
fumecheng-7267	30	31	in	in	ADP
fumecheng-7267	30	32	visual	visual	ADJ
fumecheng-7267	30	33	basic	basic	NOUN
fumecheng-7267	30	34	for	for	ADP
fumecheng-7267	30	35	applications	application	NOUN
fumecheng-7267	30	36	(	(	PUNCT
fumecheng-7267	30	37	vba	vba	PROPN
fumecheng-7267	30	38	)	)	PUNCT
fumecheng-7267	30	39	.	.	PUNCT
fumecheng-7267	31	1	in	in	ADP
fumecheng-7267	31	2	essence	essence	NOUN
fumecheng-7267	31	3	,	,	PUNCT
fumecheng-7267	31	4	a	a	DET
fumecheng-7267	31	5	macro	macro	NOUN
fumecheng-7267	31	6	is	be	AUX
fumecheng-7267	31	7	a	a	DET
fumecheng-7267	31	8	term	term	NOUN
fumecheng-7267	31	9	that	that	PRON
fumecheng-7267	31	10	refers	refer	VERB
fumecheng-7267	31	11	to	to	ADP
fumecheng-7267	31	12	a	a	DET
fumecheng-7267	31	13	set	set	NOUN
fumecheng-7267	31	14	of	of	ADP
fumecheng-7267	31	15	programming	programming	NOUN
fumecheng-7267	31	16	instructions	instruction	NOUN
fumecheng-7267	31	17	that	that	PRON
fumecheng-7267	31	18	automates	automate	VERB
fumecheng-7267	31	19	tasks	task	NOUN
fumecheng-7267	31	20	by	by	ADP
fumecheng-7267	31	21	creating	create	VERB
fumecheng-7267	31	22	custom	custom	NOUN
fumecheng-7267	31	23	calculations	calculation	NOUN
fumecheng-7267	31	24	that	that	PRON
fumecheng-7267	31	25	can	can	AUX
fumecheng-7267	31	26	be	be	AUX
fumecheng-7267	31	27	used	use	VERB
fumecheng-7267	31	28	repeatedly	repeatedly	ADV
fumecheng-7267	31	29	throughout	throughout	ADP
fumecheng-7267	31	30	workbooks	workbook	NOUN
fumecheng-7267	31	31	and	and	CCONJ
fumecheng-7267	31	32	which	which	PRON
fumecheng-7267	31	33	can	can	AUX
fumecheng-7267	31	34	be	be	AUX
fumecheng-7267	31	35	called	call	VERB
fumecheng-7267	31	36	by	by	ADP
fumecheng-7267	31	37	the	the	DET
fumecheng-7267	31	38	host	host	NOUN
fumecheng-7267	31	39	application	application	NOUN
fumecheng-7267	31	40	as	as	ADP
fumecheng-7267	31	41	user	user	NOUN
fumecheng-7267	31	42	defined	define	VERB
fumecheng-7267	31	43	function	function	NOUN
fumecheng-7267	31	44	(	(	PUNCT
fumecheng-7267	31	45	udf	udf	PROPN
fumecheng-7267	31	46	)	)	PUNCT
fumecheng-7267	31	47	.	.	PUNCT
fumecheng-7267	32	1	the	the	DET
fumecheng-7267	32	2	vba	vba	PROPN
fumecheng-7267	32	3	is	be	AUX
fumecheng-7267	32	4	closely	closely	ADV
fumecheng-7267	32	5	related	relate	VERB
fumecheng-7267	32	6	to	to	ADP
fumecheng-7267	32	7	visual	visual	ADJ
fumecheng-7267	32	8	basic	basic	ADJ
fumecheng-7267	32	9	programming	programming	NOUN
fumecheng-7267	32	10	language	language	NOUN
fumecheng-7267	32	11	,	,	PUNCT
fumecheng-7267	32	12	but	but	CCONJ
fumecheng-7267	32	13	on	on	ADP
fumecheng-7267	32	14	the	the	DET
fumecheng-7267	32	15	contrary	contrary	NOUN
fumecheng-7267	32	16	,	,	PUNCT
fumecheng-7267	32	17	vba	vba	PROPN
fumecheng-7267	32	18	codes	code	NOUN
fumecheng-7267	32	19	can	can	AUX
fumecheng-7267	32	20	only	only	ADV
fumecheng-7267	32	21	run	run	VERB
fumecheng-7267	32	22	within	within	ADP
fumecheng-7267	32	23	a	a	DET
fumecheng-7267	32	24	host	host	NOUN
fumecheng-7267	32	25	application	application	NOUN
fumecheng-7267	32	26	,	,	PUNCT
fumecheng-7267	32	27	and	and	CCONJ
fumecheng-7267	32	28	not	not	PART
fumecheng-7267	32	29	as	as	ADP
fumecheng-7267	32	30	a	a	DET
fumecheng-7267	32	31	standalone	standalone	NOUN
fumecheng-7267	32	32	program	program	NOUN
fumecheng-7267	32	33	.	.	PUNCT
fumecheng-7267	33	1	the	the	DET
fumecheng-7267	33	2	here	here	ADV
fumecheng-7267	33	3	presented	present	VERB
fumecheng-7267	33	4	codes	code	NOUN
fumecheng-7267	33	5	are	be	AUX
fumecheng-7267	33	6	compiled	compile	VERB
fumecheng-7267	33	7	to	to	ADP
fumecheng-7267	33	8	a	a	DET
fumecheng-7267	33	9	proprietary	proprietary	ADJ
fumecheng-7267	33	10	intermediate	intermediate	ADJ
fumecheng-7267	33	11	language	language	NOUN
fumecheng-7267	33	12	that	that	PRON
fumecheng-7267	33	13	can	can	AUX
fumecheng-7267	33	14	be	be	AUX
fumecheng-7267	33	15	executed	execute	VERB
fumecheng-7267	33	16	by	by	ADP
fumecheng-7267	33	17	ms	ms	PROPN
fumecheng-7267	33	18	excel	excel	PROPN
fumecheng-7267	33	19	,	,	PUNCT
fumecheng-7267	33	20	which	which	PRON
fumecheng-7267	33	21	is	be	AUX
fumecheng-7267	33	22	the	the	DET
fumecheng-7267	33	23	host	host	NOUN
fumecheng-7267	33	24	application	application	NOUN
fumecheng-7267	33	25	in	in	ADP
fumecheng-7267	33	26	this	this	DET
fumecheng-7267	33	27	case	case	NOUN
fumecheng-7267	33	28	.	.	PUNCT
fumecheng-7267	34	1	an	an	DET
fumecheng-7267	34	2	udf	udf	NOUN
fumecheng-7267	34	3	should	should	AUX
fumecheng-7267	34	4	be	be	AUX
fumecheng-7267	34	5	placed	place	VERB
fumecheng-7267	34	6	in	in	ADP
fumecheng-7267	34	7	module	module	NOUN
fumecheng-7267	34	8	following	follow	VERB
fumecheng-7267	34	9	the	the	DET
fumecheng-7267	34	10	appropriate	appropriate	ADJ
fumecheng-7267	34	11	syntax	syntax	NOUN
fumecheng-7267	34	12	of	of	ADP
fumecheng-7267	34	13	the	the	DET
fumecheng-7267	34	14	vba	vba	PROPN
fumecheng-7267	34	15	programming	programming	NOUN
fumecheng-7267	34	16	language	language	NOUN
fumecheng-7267	34	17	as	as	SCONJ
fumecheng-7267	34	18	shown	show	VERB
fumecheng-7267	34	19	in	in	ADP
fumecheng-7267	34	20	fig	fig	NOUN
fumecheng-7267	34	21	.	.	PUNCT
fumecheng-7267	35	1	1	1	X
fumecheng-7267	35	2	.	.	PUNCT
fumecheng-7267	35	3	to	to	PART
fumecheng-7267	35	4	prepare	prepare	VERB
fumecheng-7267	35	5	the	the	DET
fumecheng-7267	35	6	udfs	udfs	NOUN
fumecheng-7267	35	7	for	for	ADP
fumecheng-7267	35	8	the	the	DET
fumecheng-7267	35	9	explicit	explicit	ADJ
fumecheng-7267	35	10	approximations	approximation	NOUN
fumecheng-7267	35	11	of	of	ADP
fumecheng-7267	35	12	the	the	DET
fumecheng-7267	35	13	colebrook	colebrook	PROPN
fumecheng-7267	35	14	equation	equation	NOUN
fumecheng-7267	35	15	,	,	PUNCT
fumecheng-7267	35	16	the	the	DET
fumecheng-7267	35	17	following	follow	VERB
fumecheng-7267	35	18	steps	step	NOUN
fumecheng-7267	35	19	in	in	ADP
fumecheng-7267	35	20	ms	ms	PROPN
fumecheng-7267	35	21	excel	excel	NOUN
fumecheng-7267	35	22	need	need	NOUN
fumecheng-7267	35	23	to	to	PART
fumecheng-7267	35	24	be	be	AUX
fumecheng-7267	35	25	followed	follow	VERB
fumecheng-7267	35	26	:	:	PUNCT
fumecheng-7267	35	27	1	1	X
fumecheng-7267	35	28	)	)	PUNCT
fumecheng-7267	35	29	keyboard	keyboard	NOUN
fumecheng-7267	35	30	shortcut	shortcut	NOUN
fumecheng-7267	35	31	“	"	PUNCT
fumecheng-7267	35	32	alt	alt	VERB
fumecheng-7267	35	33	+	+	SYM
fumecheng-7267	35	34	f11	f11	X
fumecheng-7267	35	35	”	"	PUNCT
fumecheng-7267	35	36	should	should	AUX
fumecheng-7267	35	37	be	be	AUX
fumecheng-7267	35	38	pressed	press	VERB
fumecheng-7267	35	39	to	to	PART
fumecheng-7267	35	40	open	open	VERB
fumecheng-7267	35	41	the	the	DET
fumecheng-7267	35	42	visual	visual	ADJ
fumecheng-7267	35	43	basic	basic	ADJ
fumecheng-7267	35	44	editor	editor	NOUN
fumecheng-7267	35	45	(	(	PUNCT
fumecheng-7267	35	46	a	a	DET
fumecheng-7267	35	47	screen	screen	NOUN
fumecheng-7267	35	48	similar	similar	ADJ
fumecheng-7267	35	49	as	as	ADP
fumecheng-7267	35	50	in	in	ADP
fumecheng-7267	35	51	fig	fig	NOUN
fumecheng-7267	35	52	.	.	PUNCT
fumecheng-7267	36	1	1	1	NUM
fumecheng-7267	36	2	should	should	AUX
fumecheng-7267	36	3	appear	appear	VERB
fumecheng-7267	36	4	)	)	PUNCT
fumecheng-7267	36	5	,	,	PUNCT
fumecheng-7267	36	6	2	2	X
fumecheng-7267	36	7	)	)	PUNCT
fumecheng-7267	36	8	in	in	ADP
fumecheng-7267	36	9	the	the	DET
fumecheng-7267	36	10	visual	visual	ADJ
fumecheng-7267	36	11	basic	basic	ADJ
fumecheng-7267	36	12	editor	editor	NOUN
fumecheng-7267	36	13	,	,	PUNCT
fumecheng-7267	36	14	a	a	DET
fumecheng-7267	36	15	module	module	NOUN
fumecheng-7267	36	16	for	for	ADP
fumecheng-7267	36	17	udfs	udfs	NOUN
fumecheng-7267	36	18	,	,	PUNCT
fumecheng-7267	36	19	should	should	AUX
fumecheng-7267	36	20	be	be	AUX
fumecheng-7267	36	21	opened	open	VERB
fumecheng-7267	36	22	using	use	VERB
fumecheng-7267	36	23	“	"	PUNCT
fumecheng-7267	36	24	insert	insert	ADJ
fumecheng-7267	36	25	”	"	PUNCT
fumecheng-7267	36	26	button	button	NOUN
fumecheng-7267	36	27	from	from	ADP
fumecheng-7267	36	28	the	the	DET
fumecheng-7267	36	29	ribbon	ribbon	NOUN
fumecheng-7267	36	30	,	,	PUNCT
fumecheng-7267	36	31	and	and	CCONJ
fumecheng-7267	36	32	by	by	ADP
fumecheng-7267	36	33	choosing	choose	VERB
fumecheng-7267	36	34	“	"	PUNCT
fumecheng-7267	36	35	module	module	NOUN
fumecheng-7267	36	36	”	"	PUNCT
fumecheng-7267	36	37	from	from	ADP
fumecheng-7267	36	38	the	the	DET
fumecheng-7267	36	39	drop	drop	NOUN
fumecheng-7267	36	40	menu	menu	NOUN
fumecheng-7267	36	41	,	,	PUNCT
fumecheng-7267	36	42	3	3	X
fumecheng-7267	36	43	)	)	PUNCT
fumecheng-7267	36	44	in	in	ADP
fumecheng-7267	36	45	the	the	DET
fumecheng-7267	36	46	opened	open	VERB
fumecheng-7267	36	47	module	module	NOUN
fumecheng-7267	36	48	,	,	PUNCT
fumecheng-7267	36	49	the	the	DET
fumecheng-7267	36	50	udf	udf	NOUN
fumecheng-7267	36	51	should	should	AUX
fumecheng-7267	36	52	be	be	AUX
fumecheng-7267	36	53	written	write	VERB
fumecheng-7267	36	54	using	use	VERB
fumecheng-7267	36	55	appropriate	appropriate	ADJ
fumecheng-7267	36	56	syntax	syntax	NOUN
fumecheng-7267	36	57	of	of	ADP
fumecheng-7267	36	58	the	the	DET
fumecheng-7267	36	59	vba	vba	PROPN
fumecheng-7267	36	60	programming	programming	NOUN
fumecheng-7267	36	61	language	language	NOUN
fumecheng-7267	36	62	,	,	PUNCT
fumecheng-7267	36	63	excel	excel	VERB
fumecheng-7267	36	64	vba	vba	PROPN
fumecheng-7267	36	65	-	-	PUNCT
fumecheng-7267	36	66	based	base	VERB
fumecheng-7267	36	67	user	user	NOUN
fumecheng-7267	36	68	defined	define	VERB
fumecheng-7267	36	69	functions	function	NOUN
fumecheng-7267	36	70	for	for	ADP
fumecheng-7267	36	71	highly	highly	ADV
fumecheng-7267	36	72	precise	precise	ADJ
fumecheng-7267	36	73	colebrook	colebrook	PROPN
fumecheng-7267	36	74	’s	’s	PART
fumecheng-7267	36	75	pipe	pipe	NOUN
fumecheng-7267	36	76	flow	flow	NOUN
fumecheng-7267	36	77	friction	friction	NOUN
fumecheng-7267	36	78	...	...	PUNCT
fumecheng-7267	37	1	255	255	NUM
fumecheng-7267	37	2	4	4	NUM
fumecheng-7267	37	3	)	)	PUNCT
fumecheng-7267	37	4	using	use	VERB
fumecheng-7267	37	5	“	"	PUNCT
fumecheng-7267	37	6	debug	debug	NOUN
fumecheng-7267	37	7	”	"	PUNCT
fumecheng-7267	37	8	button	button	NOUN
fumecheng-7267	37	9	from	from	ADP
fumecheng-7267	37	10	the	the	DET
fumecheng-7267	37	11	ribbon	ribbon	NOUN
fumecheng-7267	37	12	,	,	PUNCT
fumecheng-7267	37	13	the	the	DET
fumecheng-7267	37	14	current	current	ADJ
fumecheng-7267	37	15	project	project	NOUN
fumecheng-7267	37	16	should	should	AUX
fumecheng-7267	37	17	be	be	AUX
fumecheng-7267	37	18	compiled	compile	VERB
fumecheng-7267	37	19	by	by	ADP
fumecheng-7267	37	20	choosing	choose	VERB
fumecheng-7267	37	21	“	"	PUNCT
fumecheng-7267	37	22	compile	compile	NOUN
fumecheng-7267	37	23	vbaproject	vbaproject	NOUN
fumecheng-7267	37	24	”	"	PUNCT
fumecheng-7267	37	25	from	from	ADP
fumecheng-7267	37	26	the	the	DET
fumecheng-7267	37	27	drop	drop	NOUN
fumecheng-7267	37	28	menu	menu	NOUN
fumecheng-7267	37	29	,	,	PUNCT
fumecheng-7267	37	30	and	and	CCONJ
fumecheng-7267	37	31	5	5	NUM
fumecheng-7267	37	32	)	)	PUNCT
fumecheng-7267	37	33	finally	finally	ADV
fumecheng-7267	37	34	,	,	PUNCT
fumecheng-7267	37	35	the	the	DET
fumecheng-7267	37	36	current	current	ADJ
fumecheng-7267	37	37	udf	udf	NOUN
fumecheng-7267	37	38	should	should	AUX
fumecheng-7267	37	39	be	be	AUX
fumecheng-7267	37	40	saved	save	VERB
fumecheng-7267	37	41	with	with	ADP
fumecheng-7267	37	42	extension	extension	NOUN
fumecheng-7267	37	43	“	"	PUNCT
fumecheng-7267	37	44	xlam	xlam	PROPN
fumecheng-7267	37	45	”	"	PUNCT
fumecheng-7267	37	46	,	,	PUNCT
fumecheng-7267	37	47	using	use	VERB
fumecheng-7267	37	48	“	"	PUNCT
fumecheng-7267	37	49	file	file	NOUN
fumecheng-7267	37	50	”	"	PUNCT
fumecheng-7267	37	51	button	button	NOUN
fumecheng-7267	37	52	and	and	CCONJ
fumecheng-7267	37	53	then	then	ADV
fumecheng-7267	37	54	“	"	PUNCT
fumecheng-7267	37	55	save	save	VERB
fumecheng-7267	37	56	as	as	ADP
fumecheng-7267	37	57	”	"	PUNCT
fumecheng-7267	37	58	from	from	ADP
fumecheng-7267	37	59	drop	drop	NOUN
fumecheng-7267	37	60	menu	menu	NOUN
fumecheng-7267	37	61	(	(	PUNCT
fumecheng-7267	37	62	it	it	PRON
fumecheng-7267	37	63	will	will	AUX
fumecheng-7267	37	64	be	be	AUX
fumecheng-7267	37	65	saved	save	VERB
fumecheng-7267	37	66	by	by	ADP
fumecheng-7267	37	67	default	default	NOUN
fumecheng-7267	37	68	in	in	ADP
fumecheng-7267	37	69	:	:	PUNCT
fumecheng-7267	37	70	'	'	PUNCT
fumecheng-7267	37	71	c:\users\[user	c:\users\[user	X
fumecheng-7267	37	72	name]\appdata\roaming\microsoft\addins\[name	name]\appdata\roaming\microsoft\addins\[name	NOUN
fumecheng-7267	37	73	of	of	ADP
fumecheng-7267	37	74	the	the	DET
fumecheng-7267	37	75	document].xlam	document].xlam	PROPN
fumecheng-7267	37	76	'	'	PUNCT
fumecheng-7267	37	77	)	)	PUNCT
fumecheng-7267	37	78	.	.	PUNCT
fumecheng-7267	38	1	fig	fig	NOUN
fumecheng-7267	38	2	.	.	PUNCT
fumecheng-7267	39	1	1	1	NUM
fumecheng-7267	39	2	visual	visual	ADJ
fumecheng-7267	39	3	basic	basic	ADJ
fumecheng-7267	39	4	editor	editor	NOUN
fumecheng-7267	39	5	the	the	DET
fumecheng-7267	39	6	syntax	syntax	NOUN
fumecheng-7267	39	7	of	of	ADP
fumecheng-7267	39	8	any	any	DET
fumecheng-7267	39	9	udf	udf	NOUN
fumecheng-7267	39	10	for	for	ADP
fumecheng-7267	39	11	ms	ms	PROPN
fumecheng-7267	39	12	excel	excel	PROPN
fumecheng-7267	39	13	written	write	VERB
fumecheng-7267	39	14	in	in	ADP
fumecheng-7267	39	15	vba	vba	PROPN
fumecheng-7267	39	16	programming	programming	NOUN
fumecheng-7267	39	17	language	language	NOUN
fumecheng-7267	39	18	has	have	VERB
fumecheng-7267	39	19	few	few	ADJ
fumecheng-7267	39	20	main	main	ADJ
fumecheng-7267	39	21	parts	part	NOUN
fumecheng-7267	39	22	,	,	PUNCT
fumecheng-7267	39	23	such	such	ADJ
fumecheng-7267	39	24	as	as	ADP
fumecheng-7267	39	25	:	:	PUNCT
fumecheng-7267	39	26	▪	▪	NOUN
fumecheng-7267	39	27	every	every	DET
fumecheng-7267	39	28	function	function	NOUN
fumecheng-7267	39	29	starts	start	VERB
fumecheng-7267	39	30	with	with	ADP
fumecheng-7267	39	31	“	"	PUNCT
fumecheng-7267	39	32	function	function	NOUN
fumecheng-7267	39	33	”	"	PUNCT
fumecheng-7267	39	34	and	and	CCONJ
fumecheng-7267	39	35	finishes	finish	VERB
fumecheng-7267	39	36	with	with	ADP
fumecheng-7267	39	37	“	"	PUNCT
fumecheng-7267	39	38	end	end	NOUN
fumecheng-7267	39	39	function	function	NOUN
fumecheng-7267	39	40	”	"	PUNCT
fumecheng-7267	39	41	,	,	PUNCT
fumecheng-7267	39	42	▪	▪	X
fumecheng-7267	39	43	specific	specific	ADJ
fumecheng-7267	39	44	name	name	NOUN
fumecheng-7267	39	45	of	of	ADP
fumecheng-7267	39	46	the	the	DET
fumecheng-7267	39	47	function	function	NOUN
fumecheng-7267	39	48	should	should	AUX
fumecheng-7267	39	49	be	be	AUX
fumecheng-7267	39	50	defined	define	VERB
fumecheng-7267	39	51	(	(	PUNCT
fumecheng-7267	39	52	designated	designate	VERB
fumecheng-7267	39	53	by	by	ADP
fumecheng-7267	39	54	user	user	NOUN
fumecheng-7267	39	55	and	and	CCONJ
fumecheng-7267	39	56	avoiding	avoid	VERB
fumecheng-7267	39	57	reserved	reserved	ADJ
fumecheng-7267	39	58	names	name	NOUN
fumecheng-7267	39	59	)	)	PUNCT
fumecheng-7267	39	60	,	,	PUNCT
fumecheng-7267	39	61	▪	▪	NOUN
fumecheng-7267	39	62	after	after	ADP
fumecheng-7267	39	63	the	the	DET
fumecheng-7267	39	64	designated	designate	VERB
fumecheng-7267	39	65	name	name	NOUN
fumecheng-7267	39	66	of	of	ADP
fumecheng-7267	39	67	the	the	DET
fumecheng-7267	39	68	function	function	NOUN
fumecheng-7267	39	69	,	,	PUNCT
fumecheng-7267	39	70	inputs	input	NOUN
fumecheng-7267	39	71	should	should	AUX
fumecheng-7267	39	72	be	be	AUX
fumecheng-7267	39	73	specified	specify	VERB
fumecheng-7267	39	74	in	in	ADP
fumecheng-7267	39	75	parentheses	parenthesis	NOUN
fumecheng-7267	39	76	,	,	PUNCT
fumecheng-7267	39	77	▪	▪	ADJ
fumecheng-7267	39	78	data	datum	NOUN
fumecheng-7267	39	79	type	type	NOUN
fumecheng-7267	39	80	of	of	ADP
fumecheng-7267	39	81	inputs	input	NOUN
fumecheng-7267	39	82	and	and	CCONJ
fumecheng-7267	39	83	output	output	NOUN
fumecheng-7267	39	84	should	should	AUX
fumecheng-7267	39	85	be	be	AUX
fumecheng-7267	39	86	defined	define	VERB
fumecheng-7267	39	87	using	use	VERB
fumecheng-7267	39	88	“	"	PUNCT
fumecheng-7267	39	89	as	as	ADP
fumecheng-7267	39	90	”	"	PUNCT
fumecheng-7267	39	91	(	(	PUNCT
fumecheng-7267	39	92	the	the	DET
fumecheng-7267	39	93	data	data	NOUN
fumecheng-7267	39	94	type	type	NOUN
fumecheng-7267	39	95	of	of	ADP
fumecheng-7267	39	96	other	other	ADJ
fumecheng-7267	39	97	used	use	VERB
fumecheng-7267	39	98	parameters	parameter	NOUN
fumecheng-7267	39	99	with	with	ADP
fumecheng-7267	39	100	“	"	PUNCT
fumecheng-7267	39	101	dim	dim	NOUN
fumecheng-7267	39	102	”	"	PUNCT
fumecheng-7267	39	103	and	and	CCONJ
fumecheng-7267	39	104	“	"	PUNCT
fumecheng-7267	39	105	as	as	ADP
fumecheng-7267	39	106	”	"	PUNCT
fumecheng-7267	39	107	)	)	PUNCT
fumecheng-7267	39	108	,	,	PUNCT
fumecheng-7267	39	109	▪	▪	NOUN
fumecheng-7267	39	110	in	in	ADP
fumecheng-7267	39	111	the	the	DET
fumecheng-7267	39	112	body	body	NOUN
fumecheng-7267	39	113	of	of	ADP
fumecheng-7267	39	114	the	the	DET
fumecheng-7267	39	115	function	function	NOUN
fumecheng-7267	39	116	,	,	PUNCT
fumecheng-7267	39	117	after	after	ADP
fumecheng-7267	39	118	the	the	DET
fumecheng-7267	39	119	part	part	NOUN
fumecheng-7267	39	120	with	with	ADP
fumecheng-7267	39	121	calculation	calculation	NOUN
fumecheng-7267	39	122	but	but	CCONJ
fumecheng-7267	39	123	before	before	ADP
fumecheng-7267	39	124	“	"	PUNCT
fumecheng-7267	39	125	end	end	NOUN
fumecheng-7267	39	126	function	function	NOUN
fumecheng-7267	39	127	”	"	PUNCT
fumecheng-7267	39	128	,	,	PUNCT
fumecheng-7267	39	129	a	a	DET
fumecheng-7267	39	130	return	return	NOUN
fumecheng-7267	39	131	value	value	NOUN
fumecheng-7267	39	132	should	should	AUX
fumecheng-7267	39	133	be	be	AUX
fumecheng-7267	39	134	assigned	assign	VERB
fumecheng-7267	39	135	to	to	ADP
fumecheng-7267	39	136	the	the	DET
fumecheng-7267	39	137	name	name	NOUN
fumecheng-7267	39	138	of	of	ADP
fumecheng-7267	39	139	the	the	DET
fumecheng-7267	39	140	function	function	NOUN
fumecheng-7267	39	141	.	.	PUNCT
fumecheng-7267	40	1	▪	▪	NOUN
fumecheng-7267	40	2	like	like	ADP
fumecheng-7267	40	3	any	any	DET
fumecheng-7267	40	4	other	other	ADJ
fumecheng-7267	40	5	excel	excel	NOUN
fumecheng-7267	40	6	function	function	NOUN
fumecheng-7267	40	7	,	,	PUNCT
fumecheng-7267	40	8	an	an	DET
fumecheng-7267	40	9	udf	udf	NOUN
fumecheng-7267	40	10	can	can	AUX
fumecheng-7267	40	11	be	be	AUX
fumecheng-7267	40	12	called	call	VERB
fumecheng-7267	40	13	from	from	ADP
fumecheng-7267	40	14	any	any	DET
fumecheng-7267	40	15	excel	excel	NOUN
fumecheng-7267	40	16	cell	cell	NOUN
fumecheng-7267	40	17	(	(	PUNCT
fumecheng-7267	40	18	if	if	SCONJ
fumecheng-7267	40	19	it	it	PRON
fumecheng-7267	40	20	is	be	AUX
fumecheng-7267	40	21	properly	properly	ADV
fumecheng-7267	40	22	loaded	load	VERB
fumecheng-7267	40	23	)	)	PUNCT
fumecheng-7267	40	24	.	.	PUNCT
fumecheng-7267	41	1	the	the	DET
fumecheng-7267	41	2	syntax	syntax	NOUN
fumecheng-7267	41	3	of	of	ADP
fumecheng-7267	41	4	the	the	DET
fumecheng-7267	41	5	ms	ms	PROPN
fumecheng-7267	41	6	excel	excel	PROPN
fumecheng-7267	41	7	and	and	CCONJ
fumecheng-7267	41	8	of	of	ADP
fumecheng-7267	41	9	the	the	DET
fumecheng-7267	41	10	vba	vba	PROPN
fumecheng-7267	41	11	programming	programming	NOUN
fumecheng-7267	41	12	language	language	NOUN
fumecheng-7267	41	13	are	be	AUX
fumecheng-7267	41	14	different	different	ADJ
fumecheng-7267	41	15	.	.	PUNCT
fumecheng-7267	42	1	for	for	ADP
fumecheng-7267	42	2	example	example	NOUN
fumecheng-7267	42	3	,	,	PUNCT
fumecheng-7267	42	4	in	in	ADP
fumecheng-7267	42	5	-	-	PUNCT
fumecheng-7267	42	6	built	build	VERB
fumecheng-7267	42	7	function	function	NOUN
fumecheng-7267	42	8	which	which	PRON
fumecheng-7267	42	9	returns	return	VERB
fumecheng-7267	42	10	value	value	VERB
fumecheng-7267	42	11	for	for	ADP
fumecheng-7267	42	12	the	the	DET
fumecheng-7267	42	13	napierian	napierian	ADJ
fumecheng-7267	42	14	natural	natural	ADJ
fumecheng-7267	42	15	logarithm	logarithm	NOUN
fumecheng-7267	42	16	,	,	PUNCT
fumecheng-7267	42	17	in	in	ADP
fumecheng-7267	42	18	the	the	DET
fumecheng-7267	42	19	vba	vba	PROPN
fumecheng-7267	42	20	programming	programming	NOUN
fumecheng-7267	42	21	language	language	NOUN
fumecheng-7267	42	22	is	be	AUX
fumecheng-7267	42	23	“	"	PUNCT
fumecheng-7267	42	24	log	log	NOUN
fumecheng-7267	42	25	”	"	PUNCT
fumecheng-7267	42	26	while	while	SCONJ
fumecheng-7267	42	27	in	in	ADP
fumecheng-7267	42	28	ms	ms	PROPN
fumecheng-7267	42	29	excel	excel	NOUN
fumecheng-7267	42	30	is	be	AUX
fumecheng-7267	42	31	“	"	PUNCT
fumecheng-7267	42	32	ln	ln	ADJ
fumecheng-7267	42	33	”	"	PUNCT
fumecheng-7267	42	34	(	(	PUNCT
fumecheng-7267	42	35	“	"	PUNCT
fumecheng-7267	42	36	ln	ln	X
fumecheng-7267	42	37	”	"	PUNCT
fumecheng-7267	42	38	is	be	AUX
fumecheng-7267	42	39	not	not	PART
fumecheng-7267	42	40	reserved	reserve	VERB
fumecheng-7267	42	41	name	name	NOUN
fumecheng-7267	42	42	in	in	ADP
fumecheng-7267	42	43	the	the	DET
fumecheng-7267	42	44	vba	vba	NOUN
fumecheng-7267	42	45	)	)	PUNCT
fumecheng-7267	42	46	.	.	PUNCT
fumecheng-7267	43	1	however	however	ADV
fumecheng-7267	43	2	,	,	PUNCT
fumecheng-7267	43	3	until	until	SCONJ
fumecheng-7267	43	4	recently	recently	ADV
fumecheng-7267	43	5	,	,	PUNCT
fumecheng-7267	43	6	reusable	reusable	ADJ
fumecheng-7267	43	7	udfs	udfs	NOUN
fumecheng-7267	43	8	could	could	AUX
fumecheng-7267	43	9	be	be	AUX
fumecheng-7267	43	10	implemented	implement	VERB
fumecheng-7267	43	11	only	only	ADV
fumecheng-7267	43	12	through	through	ADP
fumecheng-7267	43	13	scripts	script	NOUN
fumecheng-7267	43	14	written	write	VERB
fumecheng-7267	43	15	using	use	VERB
fumecheng-7267	43	16	different	different	ADJ
fumecheng-7267	43	17	syntax	syntax	NOUN
fumecheng-7267	43	18	than	than	ADP
fumecheng-7267	43	19	for	for	ADP
fumecheng-7267	43	20	excel	excel	NOUN
fumecheng-7267	43	21	formulas	formula	NOUN
fumecheng-7267	43	22	,	,	PUNCT
fumecheng-7267	43	23	using	use	VERB
fumecheng-7267	43	24	vba	vba	PROPN
fumecheng-7267	43	25	or	or	CCONJ
fumecheng-7267	43	26	using	use	VERB
fumecheng-7267	43	27	javascript	javascript	NOUN
fumecheng-7267	43	28	.	.	PUNCT
fumecheng-7267	44	1	now	now	ADV
fumecheng-7267	44	2	,	,	PUNCT
fumecheng-7267	44	3	excel	excel	VERB
fumecheng-7267	44	4	users	user	NOUN
fumecheng-7267	44	5	can	can	AUX
fumecheng-7267	44	6	use	use	VERB
fumecheng-7267	44	7	a	a	DET
fumecheng-7267	44	8	new	new	ADJ
fumecheng-7267	44	9	feature	feature	NOUN
fumecheng-7267	44	10	called	call	VERB
fumecheng-7267	44	11	“	"	PUNCT
fumecheng-7267	44	12	lambda	lambda	NOUN
fumecheng-7267	44	13	”	"	PUNCT
fumecheng-7267	44	14	which	which	PRON
fumecheng-7267	44	15	introduce	introduce	VERB
fumecheng-7267	44	16	the	the	DET
fumecheng-7267	44	17	ability	ability	NOUN
fumecheng-7267	44	18	to	to	PART
fumecheng-7267	44	19	create	create	VERB
fumecheng-7267	44	20	custom	custom	NOUN
fumecheng-7267	44	21	functions	function	NOUN
fumecheng-7267	44	22	using	use	VERB
fumecheng-7267	44	23	excel	excel	NOUN
fumecheng-7267	44	24	's	's	PART
fumecheng-7267	44	25	formula	formula	NOUN
fumecheng-7267	44	26	language	language	NOUN
fumecheng-7267	44	27	[	[	X
fumecheng-7267	44	28	31	31	NUM
fumecheng-7267	44	29	]	]	PUNCT
fumecheng-7267	44	30	.	.	PUNCT
fumecheng-7267	45	1	256	256	NUM
fumecheng-7267	45	2	d.	d.	PROPN
fumecheng-7267	45	3	brkić	brkić	PROPN
fumecheng-7267	45	4	,	,	PUNCT
fumecheng-7267	45	5	z.	z.	PROPN
fumecheng-7267	45	6	stajić	stajić	PROPN
fumecheng-7267	46	1	3	3	NUM
fumecheng-7267	46	2	.	.	PUNCT
fumecheng-7267	46	3	solutions	solution	NOUN
fumecheng-7267	46	4	to	to	ADP
fumecheng-7267	46	5	the	the	DET
fumecheng-7267	46	6	colebrook	colebrook	PROPN
fumecheng-7267	46	7	equation	equation	NOUN
fumecheng-7267	46	8	with	with	ADP
fumecheng-7267	46	9	their	their	PRON
fumecheng-7267	46	10	software	software	NOUN
fumecheng-7267	46	11	codes	code	NOUN
fumecheng-7267	46	12	using	use	VERB
fumecheng-7267	46	13	iterative	iterative	ADJ
fumecheng-7267	46	14	schemes	scheme	NOUN
fumecheng-7267	46	15	[	[	X
fumecheng-7267	46	16	4,5,22	4,5,22	NOUN
fumecheng-7267	46	17	]	]	X
fumecheng-7267	46	18	,	,	PUNCT
fumecheng-7267	46	19	the	the	DET
fumecheng-7267	46	20	colebrook	colebrook	PROPN
fumecheng-7267	46	21	equation	equation	NOUN
fumecheng-7267	46	22	in	in	ADP
fumecheng-7267	46	23	its	its	PRON
fumecheng-7267	46	24	native	native	ADJ
fumecheng-7267	46	25	implicit	implicit	ADJ
fumecheng-7267	46	26	form	form	NOUN
fumecheng-7267	46	27	can	can	AUX
fumecheng-7267	46	28	be	be	AUX
fumecheng-7267	46	29	solved	solve	VERB
fumecheng-7267	46	30	with	with	ADP
fumecheng-7267	46	31	high	high	ADJ
fumecheng-7267	46	32	accuracy	accuracy	NOUN
fumecheng-7267	46	33	after	after	ADP
fumecheng-7267	46	34	sufficient	sufficient	ADJ
fumecheng-7267	46	35	number	number	NOUN
fumecheng-7267	46	36	of	of	ADP
fumecheng-7267	46	37	iterations	iteration	NOUN
fumecheng-7267	46	38	.	.	PUNCT
fumecheng-7267	47	1	on	on	ADP
fumecheng-7267	47	2	the	the	DET
fumecheng-7267	47	3	other	other	ADJ
fumecheng-7267	47	4	hand	hand	NOUN
fumecheng-7267	47	5	,	,	PUNCT
fumecheng-7267	47	6	very	very	ADV
fumecheng-7267	47	7	accurate	accurate	ADJ
fumecheng-7267	47	8	explicit	explicit	ADJ
fumecheng-7267	47	9	approximations	approximation	NOUN
fumecheng-7267	47	10	of	of	ADP
fumecheng-7267	47	11	the	the	DET
fumecheng-7267	47	12	colebrook	colebrook	PROPN
fumecheng-7267	47	13	equation	equation	NOUN
fumecheng-7267	47	14	introduce	introduce	VERB
fumecheng-7267	47	15	certain	certain	ADJ
fumecheng-7267	47	16	small	small	ADJ
fumecheng-7267	47	17	error	error	NOUN
fumecheng-7267	47	18	which	which	PRON
fumecheng-7267	47	19	can	can	AUX
fumecheng-7267	47	20	be	be	AUX
fumecheng-7267	47	21	predicted	predict	VERB
fumecheng-7267	47	22	in	in	ADP
fumecheng-7267	47	23	advance	advance	NOUN
fumecheng-7267	47	24	[	[	X
fumecheng-7267	47	25	6	6	NUM
fumecheng-7267	47	26	-	-	SYM
fumecheng-7267	47	27	11	11	NUM
fumecheng-7267	47	28	]	]	PUNCT
fumecheng-7267	47	29	and	and	CCONJ
fumecheng-7267	47	30	which	which	PRON
fumecheng-7267	47	31	is	be	AUX
fumecheng-7267	47	32	analyzed	analyze	VERB
fumecheng-7267	47	33	in	in	ADP
fumecheng-7267	47	34	further	further	ADJ
fumecheng-7267	47	35	text	text	NOUN
fumecheng-7267	47	36	.	.	PUNCT
fumecheng-7267	48	1	alternatively	alternatively	ADV
fumecheng-7267	48	2	,	,	PUNCT
fumecheng-7267	48	3	the	the	DET
fumecheng-7267	48	4	colebrook	colebrook	PROPN
fumecheng-7267	48	5	equation	equation	NOUN
fumecheng-7267	48	6	can	can	AUX
fumecheng-7267	48	7	be	be	AUX
fumecheng-7267	48	8	transformed	transform	VERB
fumecheng-7267	48	9	analytically	analytically	ADV
fumecheng-7267	48	10	in	in	ADP
fumecheng-7267	48	11	an	an	DET
fumecheng-7267	48	12	explicit	explicit	ADJ
fumecheng-7267	48	13	form	form	NOUN
fumecheng-7267	48	14	through	through	ADP
fumecheng-7267	48	15	the	the	DET
fumecheng-7267	48	16	lambert	lambert	PROPN
fumecheng-7267	48	17	w	w	PROPN
fumecheng-7267	48	18	-	-	PUNCT
fumecheng-7267	48	19	function	function	NOUN
fumecheng-7267	48	20	[	[	X
fumecheng-7267	48	21	14	14	NUM
fumecheng-7267	48	22	-	-	SYM
fumecheng-7267	48	23	18	18	NUM
fumecheng-7267	48	24	]	]	PUNCT
fumecheng-7267	48	25	.	.	PUNCT
fumecheng-7267	49	1	this	this	DET
fumecheng-7267	49	2	approach	approach	NOUN
fumecheng-7267	49	3	provides	provide	VERB
fumecheng-7267	49	4	the	the	DET
fumecheng-7267	49	5	same	same	ADJ
fumecheng-7267	49	6	accuracy	accuracy	NOUN
fumecheng-7267	49	7	as	as	SCONJ
fumecheng-7267	49	8	obtained	obtain	VERB
fumecheng-7267	49	9	through	through	ADP
fumecheng-7267	49	10	an	an	DET
fumecheng-7267	49	11	iterative	iterative	NOUN
fumecheng-7267	49	12	solution	solution	NOUN
fumecheng-7267	49	13	,	,	PUNCT
fumecheng-7267	49	14	but	but	CCONJ
fumecheng-7267	49	15	with	with	ADP
fumecheng-7267	49	16	a	a	DET
fumecheng-7267	49	17	constraint	constraint	NOUN
fumecheng-7267	49	18	that	that	PRON
fumecheng-7267	49	19	an	an	DET
fumecheng-7267	49	20	overflow	overflow	NOUN
fumecheng-7267	49	21	error	error	NOUN
fumecheng-7267	49	22	can	can	AUX
fumecheng-7267	49	23	occur	occur	VERB
fumecheng-7267	49	24	in	in	ADP
fumecheng-7267	49	25	certain	certain	ADJ
fumecheng-7267	49	26	computational	computational	ADJ
fumecheng-7267	49	27	approaches	approach	NOUN
fumecheng-7267	49	28	for	for	ADP
fumecheng-7267	49	29	the	the	DET
fumecheng-7267	49	30	high	high	ADJ
fumecheng-7267	49	31	values	value	NOUN
fumecheng-7267	49	32	of	of	ADP
fumecheng-7267	49	33	the	the	DET
fumecheng-7267	49	34	argument	argument	NOUN
fumecheng-7267	49	35	of	of	ADP
fumecheng-7267	49	36	the	the	DET
fumecheng-7267	49	37	lamber	lamber	PROPN
fumecheng-7267	49	38	w	w	NOUN
fumecheng-7267	49	39	-	-	PUNCT
fumecheng-7267	49	40	function	function	NOUN
fumecheng-7267	49	41	if	if	SCONJ
fumecheng-7267	49	42	the	the	DET
fumecheng-7267	49	43	calculation	calculation	NOUN
fumecheng-7267	49	44	is	be	AUX
fumecheng-7267	49	45	performed	perform	VERB
fumecheng-7267	49	46	as	as	ADP
fumecheng-7267	49	47	usually	usually	ADV
fumecheng-7267	49	48	in	in	ADP
fumecheng-7267	49	49	a	a	DET
fumecheng-7267	49	50	computer	computer	NOUN
fumecheng-7267	49	51	with	with	ADP
fumecheng-7267	49	52	standard	standard	ADJ
fumecheng-7267	49	53	registers	register	NOUN
fumecheng-7267	49	54	[	[	X
fumecheng-7267	49	55	32,33	32,33	NUM
fumecheng-7267	49	56	]	]	PUNCT
fumecheng-7267	49	57	.	.	PUNCT
fumecheng-7267	50	1	the	the	DET
fumecheng-7267	50	2	lambert	lambert	PROPN
fumecheng-7267	50	3	w	w	PROPN
fumecheng-7267	50	4	-	-	PUNCT
fumecheng-7267	50	5	function	function	NOUN
fumecheng-7267	50	6	is	be	AUX
fumecheng-7267	50	7	itself	itself	PRON
fumecheng-7267	50	8	an	an	DET
fumecheng-7267	50	9	implicitly	implicitly	ADV
fumecheng-7267	50	10	given	give	VERB
fumecheng-7267	50	11	function	function	NOUN
fumecheng-7267	50	12	that	that	PRON
fumecheng-7267	50	13	needs	need	VERB
fumecheng-7267	50	14	to	to	PART
fumecheng-7267	50	15	be	be	AUX
fumecheng-7267	50	16	further	far	ADV
fumecheng-7267	50	17	evaluated	evaluate	VERB
fumecheng-7267	50	18	iteratively	iteratively	ADV
fumecheng-7267	50	19	or	or	CCONJ
fumecheng-7267	50	20	using	use	VERB
fumecheng-7267	50	21	specially	specially	ADV
fumecheng-7267	50	22	developed	develop	VERB
fumecheng-7267	50	23	approximate	approximate	ADJ
fumecheng-7267	50	24	formulas	formula	NOUN
fumecheng-7267	50	25	[	[	X
fumecheng-7267	50	26	34	34	NUM
fumecheng-7267	50	27	]	]	X
fumecheng-7267	50	28	(	(	PUNCT
fumecheng-7267	50	29	such	such	ADJ
fumecheng-7267	50	30	solutions	solution	NOUN
fumecheng-7267	50	31	of	of	ADP
fumecheng-7267	50	32	the	the	DET
fumecheng-7267	50	33	lambert	lambert	PROPN
fumecheng-7267	50	34	w	w	PROPN
fumecheng-7267	50	35	-	-	PUNCT
fumecheng-7267	50	36	function	function	NOUN
fumecheng-7267	50	37	have	have	VERB
fumecheng-7267	50	38	wide	wide	ADJ
fumecheng-7267	50	39	application	application	NOUN
fumecheng-7267	50	40	in	in	ADP
fumecheng-7267	50	41	engineering	engineering	NOUN
fumecheng-7267	50	42	and	and	CCONJ
fumecheng-7267	50	43	physics	physics	NOUN
fumecheng-7267	51	1	[	[	X
fumecheng-7267	51	2	19	19	NUM
fumecheng-7267	51	3	]	]	PUNCT
fumecheng-7267	51	4	)	)	PUNCT
fumecheng-7267	51	5	.	.	PUNCT
fumecheng-7267	52	1	after	after	ADP
fumecheng-7267	52	2	thorough	thorough	ADJ
fumecheng-7267	52	3	examination	examination	NOUN
fumecheng-7267	52	4	of	of	ADP
fumecheng-7267	52	5	the	the	DET
fumecheng-7267	52	6	approximations	approximation	NOUN
fumecheng-7267	52	7	of	of	ADP
fumecheng-7267	52	8	the	the	DET
fumecheng-7267	52	9	colebrook	colebrook	PROPN
fumecheng-7267	52	10	equation	equation	NOUN
fumecheng-7267	52	11	from	from	ADP
fumecheng-7267	52	12	available	available	ADJ
fumecheng-7267	52	13	literature	literature	NOUN
fumecheng-7267	52	14	[	[	X
fumecheng-7267	52	15	6	6	NUM
fumecheng-7267	52	16	-	-	SYM
fumecheng-7267	52	17	11	11	NUM
fumecheng-7267	52	18	]	]	PUNCT
fumecheng-7267	52	19	,	,	PUNCT
fumecheng-7267	52	20	nine	nine	NUM
fumecheng-7267	52	21	most	most	ADV
fumecheng-7267	52	22	accurate	accurate	ADJ
fumecheng-7267	52	23	explicit	explicit	ADJ
fumecheng-7267	52	24	approximations	approximation	NOUN
fumecheng-7267	52	25	[	[	X
fumecheng-7267	52	26	23	23	NUM
fumecheng-7267	52	27	-	-	SYM
fumecheng-7267	52	28	30	30	NUM
fumecheng-7267	52	29	]	]	PUNCT
fumecheng-7267	52	30	were	be	AUX
fumecheng-7267	52	31	selected	select	VERB
fumecheng-7267	52	32	for	for	ADP
fumecheng-7267	52	33	analysis	analysis	NOUN
fumecheng-7267	52	34	and	and	CCONJ
fumecheng-7267	52	35	for	for	ADP
fumecheng-7267	52	36	comparisons	comparison	NOUN
fumecheng-7267	52	37	performed	perform	VERB
fumecheng-7267	52	38	in	in	ADP
fumecheng-7267	52	39	this	this	DET
fumecheng-7267	52	40	review	review	NOUN
fumecheng-7267	52	41	paper	paper	NOUN
fumecheng-7267	52	42	.	.	PUNCT
fumecheng-7267	53	1	the	the	DET
fumecheng-7267	53	2	examined	examine	VERB
fumecheng-7267	53	3	approximations	approximation	NOUN
fumecheng-7267	53	4	are	be	AUX
fumecheng-7267	53	5	ranked	rank	VERB
fumecheng-7267	53	6	in	in	ADP
fumecheng-7267	53	7	table	table	NOUN
fumecheng-7267	53	8	1	1	NUM
fumecheng-7267	53	9	in	in	ADP
fumecheng-7267	53	10	terms	term	NOUN
fumecheng-7267	53	11	of	of	ADP
fumecheng-7267	53	12	1	1	NUM
fumecheng-7267	53	13	)	)	PUNCT
fumecheng-7267	53	14	accuracy	accuracy	NOUN
fumecheng-7267	53	15	,	,	PUNCT
fumecheng-7267	53	16	and	and	CCONJ
fumecheng-7267	53	17	2	2	X
fumecheng-7267	53	18	)	)	PUNCT
fumecheng-7267	53	19	time	time	NOUN
fumecheng-7267	53	20	taken	take	VERB
fumecheng-7267	53	21	for	for	ADP
fumecheng-7267	53	22	execution	execution	NOUN
fumecheng-7267	53	23	:	:	PUNCT
fumecheng-7267	53	24	1	1	X
fumecheng-7267	53	25	)	)	PUNCT
fumecheng-7267	53	26	the	the	DET
fumecheng-7267	53	27	relative	relative	ADJ
fumecheng-7267	53	28	error	error	NOUN
fumecheng-7267	53	29	is	be	AUX
fumecheng-7267	53	30	calculated	calculate	VERB
fumecheng-7267	53	31	as	as	ADP
fumecheng-7267	53	32	│	│	VERB
fumecheng-7267	53	33	(	(	PUNCT
fumecheng-7267	53	34	f	f	NOUN
fumecheng-7267	53	35	-	-	PUNCT
fumecheng-7267	53	36	fi)/fi	fi)/fi	ADJ
fumecheng-7267	53	37	│	│	NUM
fumecheng-7267	53	38	·100	·100	NOUN
fumecheng-7267	53	39	%	%	NOUN
fumecheng-7267	53	40	,	,	PUNCT
fumecheng-7267	53	41	where	where	SCONJ
fumecheng-7267	53	42	fi	fi	NOUN
fumecheng-7267	53	43	is	be	AUX
fumecheng-7267	53	44	the	the	DET
fumecheng-7267	53	45	friction	friction	NOUN
fumecheng-7267	53	46	factor	factor	NOUN
fumecheng-7267	53	47	from	from	ADP
fumecheng-7267	53	48	an	an	DET
fumecheng-7267	53	49	iterative	iterative	NOUN
fumecheng-7267	53	50	scheme	scheme	NOUN
fumecheng-7267	53	51	,	,	PUNCT
fumecheng-7267	53	52	while	while	SCONJ
fumecheng-7267	53	53	f	f	PROPN
fumecheng-7267	53	54	is	be	AUX
fumecheng-7267	53	55	calculated	calculate	VERB
fumecheng-7267	53	56	using	use	VERB
fumecheng-7267	53	57	the	the	DET
fumecheng-7267	53	58	observed	observed	ADJ
fumecheng-7267	53	59	approximation	approximation	NOUN
fumecheng-7267	53	60	.	.	PUNCT
fumecheng-7267	54	1	2	2	NUM
fumecheng-7267	54	2	)	)	PUNCT
fumecheng-7267	54	3	approximations	approximation	NOUN
fumecheng-7267	54	4	require	require	VERB
fumecheng-7267	54	5	computational	computational	ADJ
fumecheng-7267	54	6	resources	resource	NOUN
fumecheng-7267	54	7	in	in	ADP
fumecheng-7267	54	8	terms	term	NOUN
fumecheng-7267	54	9	of	of	ADP
fumecheng-7267	54	10	the	the	DET
fumecheng-7267	54	11	number	number	NOUN
fumecheng-7267	54	12	of	of	ADP
fumecheng-7267	54	13	floating	float	VERB
fumecheng-7267	54	14	points	point	NOUN
fumecheng-7267	54	15	for	for	ADP
fumecheng-7267	54	16	execution	execution	NOUN
fumecheng-7267	54	17	and	and	CCONJ
fumecheng-7267	54	18	therefore	therefore	ADV
fumecheng-7267	54	19	simpler	simple	ADJ
fumecheng-7267	54	20	approximations	approximation	NOUN
fumecheng-7267	54	21	are	be	AUX
fumecheng-7267	54	22	faster	fast	ADJ
fumecheng-7267	54	23	in	in	ADP
fumecheng-7267	54	24	computer	computer	NOUN
fumecheng-7267	54	25	simulations	simulation	NOUN
fumecheng-7267	54	26	[	[	X
fumecheng-7267	54	27	37	37	NUM
fumecheng-7267	54	28	-	-	SYM
fumecheng-7267	54	29	41	41	NUM
fumecheng-7267	54	30	]	]	PUNCT
fumecheng-7267	54	31	(	(	PUNCT
fumecheng-7267	54	32	speed	speed	NOUN
fumecheng-7267	54	33	of	of	ADP
fumecheng-7267	54	34	nine	nine	NUM
fumecheng-7267	54	35	selected	select	VERB
fumecheng-7267	54	36	approximations	approximation	NOUN
fumecheng-7267	54	37	are	be	AUX
fumecheng-7267	54	38	evaluated	evaluate	VERB
fumecheng-7267	54	39	using	use	VERB
fumecheng-7267	54	40	methodology	methodology	NOUN
fumecheng-7267	54	41	from	from	ADP
fumecheng-7267	54	42	[	[	X
fumecheng-7267	54	43	42,43	42,43	NOUN
fumecheng-7267	54	44	]	]	PUNCT
fumecheng-7267	54	45	)	)	PUNCT
fumecheng-7267	54	46	.	.	PUNCT
fumecheng-7267	55	1	computational	computational	ADJ
fumecheng-7267	55	2	effort	effort	NOUN
fumecheng-7267	55	3	for	for	ADP
fumecheng-7267	55	4	the	the	DET
fumecheng-7267	55	5	mathematical	mathematical	ADJ
fumecheng-7267	55	6	operations	operation	NOUN
fumecheng-7267	55	7	was	be	AUX
fumecheng-7267	55	8	determined	determine	VERB
fumecheng-7267	55	9	by	by	ADP
fumecheng-7267	55	10	performing	perform	VERB
fumecheng-7267	55	11	100	100	NUM
fumecheng-7267	55	12	million	million	NUM
fumecheng-7267	55	13	calculations	calculation	NOUN
fumecheng-7267	55	14	for	for	ADP
fumecheng-7267	55	15	each	each	DET
fumecheng-7267	55	16	mathematical	mathematical	ADJ
fumecheng-7267	55	17	operation	operation	NOUN
fumecheng-7267	55	18	using	use	VERB
fumecheng-7267	55	19	random	random	ADJ
fumecheng-7267	55	20	input	input	NOUN
fumecheng-7267	55	21	each	each	PRON
fumecheng-7267	55	22	repeated	repeat	VERB
fumecheng-7267	55	23	five	five	NUM
fumecheng-7267	55	24	times	time	NOUN
fumecheng-7267	55	25	,	,	PUNCT
fumecheng-7267	55	26	with	with	SCONJ
fumecheng-7267	55	27	the	the	DET
fumecheng-7267	55	28	average	average	ADJ
fumecheng-7267	55	29	computational	computational	ADJ
fumecheng-7267	55	30	time	time	NOUN
fumecheng-7267	55	31	recorded	record	VERB
fumecheng-7267	55	32	.	.	PUNCT
fumecheng-7267	56	1	the	the	DET
fumecheng-7267	56	2	results	result	NOUN
fumecheng-7267	56	3	are	be	AUX
fumecheng-7267	56	4	[	[	X
fumecheng-7267	56	5	44	44	NUM
fumecheng-7267	56	6	]	]	SYM
fumecheng-7267	56	7	:	:	PUNCT
fumecheng-7267	56	8	addition-23.40sec	addition-23.40sec	PROPN
fumecheng-7267	56	9	,	,	PUNCT
fumecheng-7267	56	10	subtraction27.50sec	subtraction27.50sec	PROPN
fumecheng-7267	56	11	,	,	PUNCT
fumecheng-7267	56	12	multiplication-36.20sec	multiplication-36.20sec	NOUN
fumecheng-7267	56	13	,	,	PUNCT
fumecheng-7267	56	14	division-31.70sec	division-31.70sec	PROPN
fumecheng-7267	56	15	,	,	PUNCT
fumecheng-7267	56	16	squared-51.10sec	squared-51.10sec	PROPN
fumecheng-7267	56	17	,	,	PUNCT
fumecheng-7267	56	18	square	square	NOUN
fumecheng-7267	56	19	root-53.70sec	root-53.70sec	PROPN
fumecheng-7267	56	20	,	,	PUNCT
fumecheng-7267	56	21	fractional	fractional	PROPN
fumecheng-7267	56	22	exponential-77.60sec	exponential-77.60sec	PROPN
fumecheng-7267	56	23	,	,	PUNCT
fumecheng-7267	56	24	napierian	napierian	ADJ
fumecheng-7267	56	25	natural	natural	ADJ
fumecheng-7267	56	26	logarithm-63.00sec	logarithm-63.00sec	PROPN
fumecheng-7267	56	27	,	,	PUNCT
fumecheng-7267	56	28	and	and	CCONJ
fumecheng-7267	56	29	briggsian	briggsian	ADJ
fumecheng-7267	56	30	decimal	decimal	ADJ
fumecheng-7267	56	31	logarithm	logarithm	NOUN
fumecheng-7267	56	32	to	to	PART
fumecheng-7267	56	33	base	base	VERB
fumecheng-7267	56	34	10	10	NUM
fumecheng-7267	56	35	-	-	SYM
fumecheng-7267	56	36	78.80sec	78.80sec	PROPN
fumecheng-7267	56	37	.	.	PUNCT
fumecheng-7267	57	1	accuracy	accuracy	NOUN
fumecheng-7267	57	2	is	be	AUX
fumecheng-7267	57	3	checked	check	VERB
fumecheng-7267	57	4	using	use	VERB
fumecheng-7267	57	5	2	2	NUM
fumecheng-7267	57	6	million	million	NUM
fumecheng-7267	57	7	quasi	quasi	ADJ
fumecheng-7267	57	8	-	-	ADJ
fumecheng-7267	57	9	random	random	ADJ
fumecheng-7267	57	10	and	and	CCONJ
fumecheng-7267	57	11	as	as	ADV
fumecheng-7267	57	12	well	well	ADV
fumecheng-7267	57	13	90	90	NUM
fumecheng-7267	57	14	thousand	thousand	NUM
fumecheng-7267	57	15	and	and	CCONJ
fumecheng-7267	57	16	740	740	NUM
fumecheng-7267	57	17	uniformly	uniformly	ADV
fumecheng-7267	57	18	distributed	distribute	VERB
fumecheng-7267	57	19	samples	sample	NOUN
fumecheng-7267	57	20	,	,	PUNCT
fumecheng-7267	57	21	as	as	ADP
fumecheng-7267	57	22	in	in	ADP
fumecheng-7267	57	23	[	[	NOUN
fumecheng-7267	57	24	9,23,35,36	9,23,35,36	NUM
fumecheng-7267	57	25	]	]	PUNCT
fumecheng-7267	57	26	,	,	PUNCT
fumecheng-7267	57	27	which	which	PRON
fumecheng-7267	57	28	covers	cover	VERB
fumecheng-7267	57	29	the	the	DET
fumecheng-7267	57	30	whole	whole	ADJ
fumecheng-7267	57	31	domain	domain	NOUN
fumecheng-7267	57	32	of	of	ADP
fumecheng-7267	57	33	the	the	DET
fumecheng-7267	57	34	reynolds	reynolds	PROPN
fumecheng-7267	57	35	number	number	PROPN
fumecheng-7267	57	36	,	,	PUNCT
fumecheng-7267	57	37	re	re	ADP
fumecheng-7267	57	38	and	and	CCONJ
fumecheng-7267	57	39	of	of	ADP
fumecheng-7267	57	40	the	the	DET
fumecheng-7267	57	41	relative	relative	ADJ
fumecheng-7267	57	42	roughness	roughness	NOUN
fumecheng-7267	57	43	of	of	ADP
fumecheng-7267	57	44	inner	inner	ADJ
fumecheng-7267	57	45	pipe	pipe	NOUN
fumecheng-7267	57	46	surface	surface	NOUN
fumecheng-7267	57	47	,	,	PUNCT
fumecheng-7267	57	48	ε	ε	PROPN
fumecheng-7267	57	49	,	,	PUNCT
fumecheng-7267	57	50	which	which	PRON
fumecheng-7267	57	51	are	be	AUX
fumecheng-7267	57	52	commonly	commonly	ADV
fumecheng-7267	57	53	used	use	VERB
fumecheng-7267	57	54	in	in	ADP
fumecheng-7267	57	55	engineering	engineering	NOUN
fumecheng-7267	57	56	practice	practice	NOUN
fumecheng-7267	57	57	;	;	PUNCT
fumecheng-7267	57	58	2320	2320	NUM
fumecheng-7267	57	59	<	<	NOUN
fumecheng-7267	57	60	re<108	re<108	NOUN
fumecheng-7267	57	61	and	and	CCONJ
fumecheng-7267	57	62	0	0	NUM
fumecheng-7267	57	63	<	<	NOUN
fumecheng-7267	57	64	ε<0.05	ε<0.05	PROPN
fumecheng-7267	57	65	.	.	PUNCT
fumecheng-7267	58	1	explicit	explicit	ADJ
fumecheng-7267	58	2	approximations	approximation	NOUN
fumecheng-7267	58	3	of	of	ADP
fumecheng-7267	58	4	the	the	DET
fumecheng-7267	58	5	colebrook	colebrook	PROPN
fumecheng-7267	58	6	equation	equation	NOUN
fumecheng-7267	58	7	should	should	AUX
fumecheng-7267	58	8	be	be	AUX
fumecheng-7267	58	9	not	not	PART
fumecheng-7267	58	10	only	only	ADV
fumecheng-7267	58	11	accurate	accurate	ADJ
fumecheng-7267	58	12	but	but	CCONJ
fumecheng-7267	58	13	also	also	ADV
fumecheng-7267	58	14	simple	simple	ADJ
fumecheng-7267	58	15	for	for	ADP
fumecheng-7267	58	16	computation	computation	NOUN
fumecheng-7267	58	17	(	(	PUNCT
fumecheng-7267	58	18	fig	fig	NOUN
fumecheng-7267	58	19	.	.	PUNCT
fumecheng-7267	59	1	2	2	NUM
fumecheng-7267	59	2	shows	show	VERB
fumecheng-7267	59	3	error	error	NOUN
fumecheng-7267	59	4	distribution	distribution	NOUN
fumecheng-7267	59	5	for	for	ADP
fumecheng-7267	59	6	the	the	DET
fumecheng-7267	59	7	four	four	NUM
fumecheng-7267	59	8	most	most	ADV
fumecheng-7267	59	9	accurate	accurate	ADJ
fumecheng-7267	59	10	approximations	approximation	NOUN
fumecheng-7267	59	11	)	)	PUNCT
fumecheng-7267	59	12	.	.	PUNCT
fumecheng-7267	60	1	the	the	DET
fumecheng-7267	60	2	approximations	approximation	NOUN
fumecheng-7267	60	3	of	of	ADP
fumecheng-7267	60	4	the	the	DET
fumecheng-7267	60	5	colebrook	colebrook	PROPN
fumecheng-7267	60	6	equation	equation	NOUN
fumecheng-7267	60	7	from	from	ADP
fumecheng-7267	60	8	table	table	NOUN
fumecheng-7267	60	9	1	1	NUM
fumecheng-7267	60	10	are	be	AUX
fumecheng-7267	60	11	shown	show	VERB
fumecheng-7267	60	12	in	in	ADP
fumecheng-7267	60	13	further	further	ADJ
fumecheng-7267	60	14	text	text	NOUN
fumecheng-7267	60	15	,	,	PUNCT
fumecheng-7267	60	16	while	while	SCONJ
fumecheng-7267	60	17	the	the	DET
fumecheng-7267	60	18	related	related	ADJ
fumecheng-7267	60	19	algorithms	algorithm	NOUN
fumecheng-7267	60	20	and	and	CCONJ
fumecheng-7267	60	21	codes	code	NOUN
fumecheng-7267	60	22	are	be	AUX
fumecheng-7267	60	23	given	give	VERB
fumecheng-7267	60	24	for	for	ADP
fumecheng-7267	60	25	the	the	DET
fumecheng-7267	60	26	four	four	NUM
fumecheng-7267	60	27	most	most	ADV
fumecheng-7267	60	28	accurate	accurate	ADJ
fumecheng-7267	60	29	approximations	approximation	NOUN
fumecheng-7267	60	30	.	.	PUNCT
fumecheng-7267	61	1	the	the	DET
fumecheng-7267	61	2	distribution	distribution	NOUN
fumecheng-7267	61	3	of	of	ADP
fumecheng-7267	61	4	the	the	DET
fumecheng-7267	61	5	maximal	maximal	ADJ
fumecheng-7267	61	6	relative	relative	ADJ
fumecheng-7267	61	7	error	error	NOUN
fumecheng-7267	61	8	is	be	AUX
fumecheng-7267	61	9	irregular	irregular	ADJ
fumecheng-7267	61	10	for	for	ADP
fumecheng-7267	61	11	all	all	DET
fumecheng-7267	61	12	available	available	ADJ
fumecheng-7267	61	13	approximations	approximation	NOUN
fumecheng-7267	61	14	of	of	ADP
fumecheng-7267	61	15	the	the	DET
fumecheng-7267	61	16	colebrook	colebrook	PROPN
fumecheng-7267	61	17	equation	equation	NOUN
fumecheng-7267	61	18	.	.	PUNCT
fumecheng-7267	62	1	excel	excel	VERB
fumecheng-7267	62	2	vba	vba	PROPN
fumecheng-7267	62	3	-	-	PUNCT
fumecheng-7267	62	4	based	base	VERB
fumecheng-7267	62	5	user	user	NOUN
fumecheng-7267	62	6	defined	define	VERB
fumecheng-7267	62	7	functions	function	NOUN
fumecheng-7267	62	8	for	for	ADP
fumecheng-7267	62	9	highly	highly	ADV
fumecheng-7267	62	10	precise	precise	ADJ
fumecheng-7267	62	11	colebrook	colebrook	PROPN
fumecheng-7267	62	12	’s	’s	PART
fumecheng-7267	62	13	pipe	pipe	NOUN
fumecheng-7267	62	14	flow	flow	NOUN
fumecheng-7267	62	15	friction	friction	NOUN
fumecheng-7267	62	16	...	...	PUNCT
fumecheng-7267	62	17	257	257	NUM
fumecheng-7267	62	18	fig	fig	NOUN
fumecheng-7267	62	19	.	.	PUNCT
fumecheng-7267	63	1	2	2	NUM
fumecheng-7267	63	2	distribution	distribution	NOUN
fumecheng-7267	63	3	of	of	ADP
fumecheng-7267	63	4	the	the	DET
fumecheng-7267	63	5	maximal	maximal	ADJ
fumecheng-7267	63	6	relative	relative	ADJ
fumecheng-7267	63	7	error	error	NOUN
fumecheng-7267	63	8	of	of	ADP
fumecheng-7267	63	9	the	the	DET
fumecheng-7267	63	10	extremely	extremely	ADV
fumecheng-7267	63	11	accurate	accurate	ADJ
fumecheng-7267	63	12	explicit	explicit	ADJ
fumecheng-7267	63	13	approximations	approximation	NOUN
fumecheng-7267	63	14	(	(	PUNCT
fumecheng-7267	63	15	the	the	DET
fumecheng-7267	63	16	error	error	NOUN
fumecheng-7267	63	17	less	less	ADJ
fumecheng-7267	63	18	than	than	ADP
fumecheng-7267	63	19	0.01	0.01	NUM
fumecheng-7267	63	20	%	%	NOUN
fumecheng-7267	63	21	)	)	PUNCT
fumecheng-7267	63	22	258	258	NUM
fumecheng-7267	63	23	d.	d.	PROPN
fumecheng-7267	63	24	brkić	brkić	PROPN
fumecheng-7267	63	25	,	,	PUNCT
fumecheng-7267	63	26	z.	z.	PROPN
fumecheng-7267	63	27	stajić	stajić	PROPN
fumecheng-7267	63	28	table	table	NOUN
fumecheng-7267	63	29	1	1	NUM
fumecheng-7267	63	30	results	result	NOUN
fumecheng-7267	63	31	of	of	ADP
fumecheng-7267	63	32	accuracy	accuracy	NOUN
fumecheng-7267	63	33	and	and	CCONJ
fumecheng-7267	63	34	efficiency	efficiency	NOUN
fumecheng-7267	63	35	of	of	ADP
fumecheng-7267	63	36	the	the	DET
fumecheng-7267	63	37	examined	examine	VERB
fumecheng-7267	63	38	approximations	approximation	NOUN
fumecheng-7267	63	39	with	with	ADP
fumecheng-7267	63	40	the	the	DET
fumecheng-7267	63	41	relative	relative	ADJ
fumecheng-7267	63	42	error	error	NOUN
fumecheng-7267	63	43	lower	low	ADJ
fumecheng-7267	63	44	than	than	ADP
fumecheng-7267	63	45	0.1	0.1	NUM
fumecheng-7267	63	46	%	%	NOUN
fumecheng-7267	63	47	.	.	PUNCT
fumecheng-7267	64	1	approximation	approximation	NOUN
fumecheng-7267	64	2	maximum	maximum	ADJ
fumecheng-7267	64	3	relative	relative	ADJ
fumecheng-7267	64	4	error	error	NOUN
fumecheng-7267	64	5	(	(	PUNCT
fumecheng-7267	64	6	%	%	INTJ
fumecheng-7267	64	7	)	)	PUNCT
fumecheng-7267	64	8	execution	execution	NOUN
fumecheng-7267	64	9	time	time	NOUN
fumecheng-7267	64	10	(	(	PUNCT
fumecheng-7267	64	11	sec	sec	PROPN
fumecheng-7267	64	12	)	)	PUNCT
fumecheng-7267	64	13	ratio	ratio	NOUN
fumecheng-7267	64	14	of	of	ADP
fumecheng-7267	64	15	maximum	maximum	ADJ
fumecheng-7267	64	16	relative	relative	ADJ
fumecheng-7267	64	17	error	error	NOUN
fumecheng-7267	64	18	ratio	ratio	NOUN
fumecheng-7267	64	19	of	of	ADP
fumecheng-7267	64	20	execution	execution	NOUN
fumecheng-7267	64	21	time	time	NOUN
fumecheng-7267	64	22	praks	prak	NOUN
fumecheng-7267	64	23	and	and	CCONJ
fumecheng-7267	64	24	brkić	brkić	VERB
fumecheng-7267	64	25	-sr1	-sr1	PROPN
fumecheng-7267	65	1	[	[	X
fumecheng-7267	65	2	23	23	NUM
fumecheng-7267	65	3	]	]	PUNCT
fumecheng-7267	65	4	–	–	PUNCT
fumecheng-7267	65	5	eq	eq	NOUN
fumecheng-7267	65	6	.	.	PUNCT
fumecheng-7267	66	1	(	(	PUNCT
fumecheng-7267	66	2	4	4	X
fumecheng-7267	66	3	)	)	PUNCT
fumecheng-7267	66	4	0.001204	0.001204	NUM
fumecheng-7267	66	5	450.7	450.7	NUM
fumecheng-7267	66	6	1	1	NUM
fumecheng-7267	66	7	1.02	1.02	NUM
fumecheng-7267	66	8	serghides	serghide	NOUN
fumecheng-7267	66	9	[	[	X
fumecheng-7267	66	10	29	29	NUM
fumecheng-7267	66	11	]	]	PUNCT
fumecheng-7267	66	12	–	–	PUNCT
fumecheng-7267	66	13	eq	eq	NOUN
fumecheng-7267	66	14	.	.	PUNCT
fumecheng-7267	67	1	(	(	PUNCT
fumecheng-7267	67	2	5	5	X
fumecheng-7267	67	3	)	)	PUNCT
fumecheng-7267	67	4	0.002560	0.002560	NOUN
fumecheng-7267	67	5	906.4	906.4	NUM
fumecheng-7267	67	6	2.13	2.13	NUM
fumecheng-7267	67	7	2.06	2.06	NUM
fumecheng-7267	67	8	vatankhah	vatankhah	NOUN
fumecheng-7267	68	1	[	[	X
fumecheng-7267	68	2	25	25	NUM
fumecheng-7267	68	3	]	]	PUNCT
fumecheng-7267	68	4	–	–	PUNCT
fumecheng-7267	68	5	eq	eq	NOUN
fumecheng-7267	68	6	.	.	PUNCT
fumecheng-7267	68	7	(	(	PUNCT
fumecheng-7267	68	8	6	6	NUM
fumecheng-7267	68	9	)	)	SYM
fumecheng-7267	68	10	0.005952	0.005952	NUM
fumecheng-7267	68	11	760	760	NUM
fumecheng-7267	68	12	4.94	4.94	NUM
fumecheng-7267	68	13	1.73	1.73	NUM
fumecheng-7267	68	14	romeo	romeo	PROPN
fumecheng-7267	68	15	et	et	PROPN
fumecheng-7267	68	16	al	al	PROPN
fumecheng-7267	68	17	.	.	PUNCT
fumecheng-7267	69	1	[	[	X
fumecheng-7267	69	2	28	28	NUM
fumecheng-7267	69	3	]	]	PUNCT
fumecheng-7267	69	4	–	–	PUNCT
fumecheng-7267	69	5	eq	eq	NOUN
fumecheng-7267	69	6	.	.	PUNCT
fumecheng-7267	70	1	(	(	PUNCT
fumecheng-7267	70	2	7	7	X
fumecheng-7267	70	3	)	)	PUNCT
fumecheng-7267	70	4	0.007468	0.007468	NUM
fumecheng-7267	70	5	817.2	817.2	NUM
fumecheng-7267	70	6	6.20	6.20	NUM
fumecheng-7267	70	7	1.86	1.86	NUM
fumecheng-7267	70	8	buzzelli	buzzelli	NOUN
fumecheng-7267	71	1	[	[	X
fumecheng-7267	71	2	27	27	NUM
fumecheng-7267	71	3	]	]	PUNCT
fumecheng-7267	71	4	–	–	PUNCT
fumecheng-7267	71	5	eq	eq	NOUN
fumecheng-7267	71	6	.	.	PUNCT
fumecheng-7267	72	1	(	(	PUNCT
fumecheng-7267	72	2	8)	8)	NUM
fumecheng-7267	72	3	0.019944	0.019944	NUM
fumecheng-7267	72	4	667.8	667.8	NUM
fumecheng-7267	72	5	16.56	16.56	NUM
fumecheng-7267	72	6	1.52	1.52	NUM
fumecheng-7267	72	7	praks	prak	NOUN
fumecheng-7267	72	8	and	and	CCONJ
fumecheng-7267	72	9	brkić	brkić	ADJ
fumecheng-7267	72	10	-se2	-se2	PUNCT
fumecheng-7267	73	1	[	[	X
fumecheng-7267	73	2	23	23	NUM
fumecheng-7267	73	3	]	]	PUNCT
fumecheng-7267	73	4	–	–	PUNCT
fumecheng-7267	73	5	eq	eq	NOUN
fumecheng-7267	73	6	.	.	PUNCT
fumecheng-7267	74	1	(	(	PUNCT
fumecheng-7267	74	2	9	9	X
fumecheng-7267	74	3	)	)	PUNCT
fumecheng-7267	74	4	0.058517	0.058517	NUM
fumecheng-7267	74	5	573.9	573.9	NUM
fumecheng-7267	74	6	48.60	48.60	NUM
fumecheng-7267	74	7	1.30	1.30	NUM
fumecheng-7267	74	8	offor	offor	ADP
fumecheng-7267	74	9	and	and	CCONJ
fumecheng-7267	74	10	alabi	alabi	NOUN
fumecheng-7267	74	11	[	[	X
fumecheng-7267	74	12	26	26	NUM
fumecheng-7267	74	13	]	]	PUNCT
fumecheng-7267	74	14	–	–	PUNCT
fumecheng-7267	74	15	eq	eq	NOUN
fumecheng-7267	74	16	.	.	PUNCT
fumecheng-7267	75	1	(	(	PUNCT
fumecheng-7267	75	2	10	10	NUM
fumecheng-7267	75	3	)	)	PUNCT
fumecheng-7267	75	4	0.062704	0.062704	NUM
fumecheng-7267	76	1	477.1	477.1	NUM
fumecheng-7267	76	2	52.08	52.08	NUM
fumecheng-7267	76	3	1.08	1.08	NUM
fumecheng-7267	76	4	shacham	shacham	NOUN
fumecheng-7267	76	5	[	[	X
fumecheng-7267	76	6	30	30	NUM
fumecheng-7267	76	7	]	]	PUNCT
fumecheng-7267	76	8	–	–	PUNCT
fumecheng-7267	76	9	eq	eq	NOUN
fumecheng-7267	76	10	.	.	PUNCT
fumecheng-7267	77	1	(	(	PUNCT
fumecheng-7267	77	2	11	11	NUM
fumecheng-7267	77	3	)	)	PUNCT
fumecheng-7267	77	4	0.083068	0.083068	NUM
fumecheng-7267	77	5	567	567	NUM
fumecheng-7267	77	6	68.99	68.99	NUM
fumecheng-7267	77	7	1.29	1.29	NUM
fumecheng-7267	77	8	lamri	lamri	NOUN
fumecheng-7267	77	9	[	[	X
fumecheng-7267	77	10	24	24	NUM
fumecheng-7267	77	11	]	]	PUNCT
fumecheng-7267	77	12	–	–	PUNCT
fumecheng-7267	77	13	eq	eq	NOUN
fumecheng-7267	77	14	.	.	PUNCT
fumecheng-7267	78	1	(	(	PUNCT
fumecheng-7267	78	2	12	12	NUM
fumecheng-7267	78	3	)	)	PUNCT
fumecheng-7267	78	4	0.097438	0.097438	NUM
fumecheng-7267	78	5	440.2	440.2	NUM
fumecheng-7267	78	6	80.93	80.93	NUM
fumecheng-7267	78	7	1	1	NUM
fumecheng-7267	78	8	1sr	1sr	ADJ
fumecheng-7267	78	9	symbolic	symbolic	ADJ
fumecheng-7267	78	10	regression	regression	NOUN
fumecheng-7267	78	11	of	of	ADP
fumecheng-7267	78	12	the	the	DET
fumecheng-7267	78	13	wright	wright	PROPN
fumecheng-7267	78	14	ω	ω	PROPN
fumecheng-7267	78	15	-	-	PUNCT
fumecheng-7267	78	16	function	function	NOUN
fumecheng-7267	78	17	,	,	PUNCT
fumecheng-7267	78	18	2se	2se	ADJ
fumecheng-7267	78	19	series	series	NOUN
fumecheng-7267	78	20	expansion	expansion	NOUN
fumecheng-7267	78	21	of	of	ADP
fumecheng-7267	78	22	the	the	DET
fumecheng-7267	78	23	wright	wright	PROPN
fumecheng-7267	78	24	ωfunction	ωfunction	NOUN
fumecheng-7267	79	1	;	;	PUNCT
fumecheng-7267	79	2	ratios	ratio	NOUN
fumecheng-7267	79	3	are	be	AUX
fumecheng-7267	79	4	given	give	VERB
fumecheng-7267	79	5	in	in	ADP
fumecheng-7267	79	6	respect	respect	NOUN
fumecheng-7267	79	7	to	to	ADP
fumecheng-7267	79	8	the	the	DET
fumecheng-7267	79	9	most	most	ADV
fumecheng-7267	79	10	accurate	accurate	ADJ
fumecheng-7267	79	11	and	and	CCONJ
fumecheng-7267	79	12	fastest	fast	ADJ
fumecheng-7267	79	13	approximation	approximation	NOUN
fumecheng-7267	79	14	.	.	PUNCT
fumecheng-7267	80	1	3.1	3.1	NUM
fumecheng-7267	80	2	.	.	PUNCT
fumecheng-7267	80	3	iterative	iterative	NOUN
fumecheng-7267	80	4	solutions	solution	NOUN
fumecheng-7267	80	5	iterative	iterative	NOUN
fumecheng-7267	80	6	schemes	scheme	NOUN
fumecheng-7267	80	7	are	be	AUX
fumecheng-7267	80	8	most	most	ADV
fumecheng-7267	80	9	suitable	suitable	ADJ
fumecheng-7267	80	10	for	for	ADP
fumecheng-7267	80	11	the	the	DET
fumecheng-7267	80	12	implicitly	implicitly	ADV
fumecheng-7267	80	13	given	give	VERB
fumecheng-7267	80	14	types	type	NOUN
fumecheng-7267	80	15	of	of	ADP
fumecheng-7267	80	16	equations	equation	NOUN
fumecheng-7267	80	17	,	,	PUNCT
fumecheng-7267	80	18	such	such	ADJ
fumecheng-7267	80	19	as	as	ADP
fumecheng-7267	80	20	for	for	ADP
fumecheng-7267	80	21	the	the	DET
fumecheng-7267	80	22	colebrook	colebrook	PROPN
fumecheng-7267	80	23	equation	equation	NOUN
fumecheng-7267	80	24	[	[	X
fumecheng-7267	80	25	4,5	4,5	NUM
fumecheng-7267	80	26	]	]	PUNCT
fumecheng-7267	80	27	.	.	PUNCT
fumecheng-7267	81	1	the	the	DET
fumecheng-7267	81	2	lambert	lambert	PROPN
fumecheng-7267	81	3	w	w	PROPN
fumecheng-7267	81	4	-	-	PUNCT
fumecheng-7267	81	5	function	function	NOUN
fumecheng-7267	81	6	which	which	PRON
fumecheng-7267	81	7	is	be	AUX
fumecheng-7267	81	8	used	use	VERB
fumecheng-7267	81	9	to	to	PART
fumecheng-7267	81	10	express	express	VERB
fumecheng-7267	81	11	the	the	DET
fumecheng-7267	81	12	colebrook	colebrook	PROPN
fumecheng-7267	81	13	equation	equation	NOUN
fumecheng-7267	81	14	in	in	ADP
fumecheng-7267	81	15	explicit	explicit	ADJ
fumecheng-7267	81	16	form	form	NOUN
fumecheng-7267	81	17	,	,	PUNCT
fumecheng-7267	81	18	is	be	AUX
fumecheng-7267	81	19	also	also	ADV
fumecheng-7267	81	20	implicitly	implicitly	ADV
fumecheng-7267	81	21	given	give	VERB
fumecheng-7267	81	22	and	and	CCONJ
fumecheng-7267	81	23	therefore	therefore	ADV
fumecheng-7267	81	24	is	be	AUX
fumecheng-7267	81	25	also	also	ADV
fumecheng-7267	81	26	suitable	suitable	ADJ
fumecheng-7267	81	27	for	for	ADP
fumecheng-7267	81	28	evaluation	evaluation	NOUN
fumecheng-7267	81	29	using	use	VERB
fumecheng-7267	81	30	iterative	iterative	ADJ
fumecheng-7267	81	31	methods	method	NOUN
fumecheng-7267	81	32	[	[	X
fumecheng-7267	81	33	34	34	NUM
fumecheng-7267	81	34	]	]	PUNCT
fumecheng-7267	81	35	.	.	PUNCT
fumecheng-7267	82	1	3.1.1	3.1.1	X
fumecheng-7267	82	2	.	.	PUNCT
fumecheng-7267	82	3	simple	simple	ADJ
fumecheng-7267	82	4	fixed	fix	VERB
fumecheng-7267	82	5	-	-	PUNCT
fumecheng-7267	82	6	point	point	NOUN
fumecheng-7267	82	7	iterative	iterative	NOUN
fumecheng-7267	82	8	scheme	scheme	NOUN
fumecheng-7267	82	9	the	the	DET
fumecheng-7267	82	10	colebrook	colebrook	PROPN
fumecheng-7267	82	11	equation	equation	NOUN
fumecheng-7267	82	12	for	for	ADP
fumecheng-7267	82	13	flow	flow	NOUN
fumecheng-7267	82	14	friction	friction	NOUN
fumecheng-7267	82	15	is	be	AUX
fumecheng-7267	82	16	suitable	suitable	ADJ
fumecheng-7267	82	17	for	for	ADP
fumecheng-7267	82	18	calculation	calculation	NOUN
fumecheng-7267	82	19	in	in	ADP
fumecheng-7267	82	20	its	its	PRON
fumecheng-7267	82	21	native	native	ADJ
fumecheng-7267	82	22	form	form	NOUN
fumecheng-7267	82	23	through	through	ADP
fumecheng-7267	82	24	an	an	DET
fumecheng-7267	82	25	iterative	iterative	NOUN
fumecheng-7267	82	26	method	method	NOUN
fumecheng-7267	82	27	.	.	PUNCT
fumecheng-7267	83	1	a	a	DET
fumecheng-7267	83	2	chosen	choose	VERB
fumecheng-7267	83	3	simple	simple	ADJ
fumecheng-7267	83	4	starting	starting	NOUN
fumecheng-7267	83	5	point	point	NOUN
fumecheng-7267	83	6	x0=5	x0=5	PROPN
fumecheng-7267	83	7	for	for	ADP
fumecheng-7267	83	8	the	the	DET
fumecheng-7267	83	9	fixed	fix	VERB
fumecheng-7267	83	10	-	-	PUNCT
fumecheng-7267	83	11	point	point	NOUN
fumecheng-7267	83	12	iterative	iterative	NOUN
fumecheng-7267	83	13	scheme	scheme	NOUN
fumecheng-7267	83	14	as	as	ADP
fumecheng-7267	83	15	from	from	ADP
fumecheng-7267	83	16	the	the	DET
fumecheng-7267	83	17	algorithm	algorithm	NOUN
fumecheng-7267	83	18	in	in	ADP
fumecheng-7267	83	19	fig	fig	NOUN
fumecheng-7267	83	20	.	.	PUNCT
fumecheng-7267	84	1	3	3	NUM
fumecheng-7267	84	2	is	be	AUX
fumecheng-7267	84	3	in	in	ADP
fumecheng-7267	84	4	the	the	DET
fumecheng-7267	84	5	range	range	NOUN
fumecheng-7267	84	6	of	of	ADP
fumecheng-7267	84	7	applicability	applicability	NOUN
fumecheng-7267	84	8	of	of	ADP
fumecheng-7267	84	9	the	the	DET
fumecheng-7267	84	10	colebrook	colebrook	PROPN
fumecheng-7267	84	11	equation	equation	NOUN
fumecheng-7267	84	12	and	and	CCONJ
fumecheng-7267	84	13	can	can	AUX
fumecheng-7267	84	14	assure	assure	VERB
fumecheng-7267	84	15	fast	fast	ADJ
fumecheng-7267	84	16	convergence	convergence	NOUN
fumecheng-7267	84	17	,	,	PUNCT
fumecheng-7267	84	18	while	while	SCONJ
fumecheng-7267	84	19	the	the	DET
fumecheng-7267	84	20	final	final	ADJ
fumecheng-7267	84	21	solution	solution	NOUN
fumecheng-7267	84	22	can	can	AUX
fumecheng-7267	84	23	be	be	AUX
fumecheng-7267	84	24	reached	reach	VERB
fumecheng-7267	84	25	after	after	ADP
fumecheng-7267	84	26	2	2	NUM
fumecheng-7267	84	27	to	to	PART
fumecheng-7267	84	28	11	11	NUM
fumecheng-7267	84	29	iterations	iteration	NOUN
fumecheng-7267	84	30	using	use	VERB
fumecheng-7267	84	31	xi	xi	X
fumecheng-7267	84	32	=	=	PUNCT
fumecheng-7267	84	33	−0.8686	−0.8686	X
fumecheng-7267	84	34	·	·	PUNCT
fumecheng-7267	84	35	ln	ln	X
fumecheng-7267	84	36	(	(	PUNCT
fumecheng-7267	84	37	2.51·xi−1	2.51·xi−1	NUM
fumecheng-7267	84	38	re	re	NOUN
fumecheng-7267	84	39	+	+	CCONJ
fumecheng-7267	84	40	ε	ε	PROPN
fumecheng-7267	84	41	3.71	3.71	NUM
fumecheng-7267	84	42	)	)	PUNCT
fumecheng-7267	84	43	,	,	PUNCT
fumecheng-7267	84	44	where	where	SCONJ
fumecheng-7267	84	45	x	x	SYM
fumecheng-7267	84	46	=	=	SYM
fumecheng-7267	84	47	1	1	NUM
fumecheng-7267	84	48	√f	√f	PRON
fumecheng-7267	84	49	.	.	PUNCT
fumecheng-7267	85	1	yes	yes	INTJ
fumecheng-7267	85	2	no	no	DET
fumecheng-7267	85	3	error	error	NOUN
fumecheng-7267	86	1	yes	yes	INTJ
fumecheng-7267	86	2	no	no	DET
fumecheng-7267	86	3	simple	simple	ADJ
fumecheng-7267	86	4	fixed	fix	VERB
fumecheng-7267	86	5	-	-	PUNCT
fumecheng-7267	86	6	point	point	NOUN
fumecheng-7267	86	7	iterative	iterative	NOUN
fumecheng-7267	86	8	scheme	scheme	NOUN
fumecheng-7267	86	9	fig	fig	NOUN
fumecheng-7267	86	10	.	.	PUNCT
fumecheng-7267	87	1	3	3	NUM
fumecheng-7267	87	2	algorithm	algorithm	NOUN
fumecheng-7267	87	3	for	for	ADP
fumecheng-7267	87	4	simple	simple	ADJ
fumecheng-7267	87	5	fixed	fix	VERB
fumecheng-7267	87	6	-	-	PUNCT
fumecheng-7267	87	7	point	point	NOUN
fumecheng-7267	87	8	iterative	iterative	NOUN
fumecheng-7267	87	9	scheme	scheme	NOUN
fumecheng-7267	87	10	for	for	ADP
fumecheng-7267	87	11	solving	solve	VERB
fumecheng-7267	87	12	the	the	DET
fumecheng-7267	87	13	colebrook	colebrook	PROPN
fumecheng-7267	87	14	equation	equation	NOUN
fumecheng-7267	87	15	excel	excel	VERB
fumecheng-7267	87	16	vba	vba	PROPN
fumecheng-7267	87	17	-	-	PUNCT
fumecheng-7267	87	18	based	base	VERB
fumecheng-7267	87	19	user	user	NOUN
fumecheng-7267	87	20	defined	define	VERB
fumecheng-7267	87	21	functions	function	NOUN
fumecheng-7267	87	22	for	for	ADP
fumecheng-7267	87	23	highly	highly	ADV
fumecheng-7267	87	24	precise	precise	ADJ
fumecheng-7267	87	25	colebrook	colebrook	PROPN
fumecheng-7267	87	26	’s	’s	PART
fumecheng-7267	87	27	pipe	pipe	NOUN
fumecheng-7267	87	28	flow	flow	NOUN
fumecheng-7267	87	29	friction	friction	NOUN
fumecheng-7267	87	30	...	...	PUNCT
fumecheng-7267	88	1	259	259	NUM
fumecheng-7267	88	2	the	the	DET
fumecheng-7267	88	3	vba	vba	PROPN
fumecheng-7267	88	4	code	code	NOUN
fumecheng-7267	88	5	for	for	ADP
fumecheng-7267	88	6	solving	solve	VERB
fumecheng-7267	88	7	the	the	DET
fumecheng-7267	88	8	colebrook	colebrook	PROPN
fumecheng-7267	88	9	equation	equation	NOUN
fumecheng-7267	88	10	through	through	ADP
fumecheng-7267	88	11	simple	simple	ADJ
fumecheng-7267	88	12	fixed	fix	VERB
fumecheng-7267	88	13	-	-	PUNCT
fumecheng-7267	88	14	point	point	NOUN
fumecheng-7267	88	15	iterative	iterative	NOUN
fumecheng-7267	88	16	scheme	scheme	NOUN
fumecheng-7267	88	17	is	be	AUX
fumecheng-7267	88	18	given	give	VERB
fumecheng-7267	88	19	as	as	SCONJ
fumecheng-7267	88	20	follows	follow	VERB
fumecheng-7267	88	21	:	:	PUNCT
fumecheng-7267	88	22	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	PRON
fumecheng-7267	88	23	𝐶𝑂𝐿𝐸𝐵𝑅𝑂𝑂𝐾𝐼𝑇𝐸(𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝐶𝑂𝐿𝐸𝐵𝑅𝑂𝑂𝐾𝐼𝑇𝐸(𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	VERB
fumecheng-7267	88	24	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	88	25	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	88	26	,	,	PUNCT
fumecheng-7267	88	27	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	88	28	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	88	29	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	88	30	)	)	PUNCT
fumecheng-7267	89	1	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	89	2	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	89	3	𝐷𝑖𝑚	𝐷𝑖𝑚	PROPN
fumecheng-7267	89	4	𝑥	𝑥	NOUN
fumecheng-7267	89	5	,	,	PUNCT
fumecheng-7267	89	6	𝑥𝑐𝑜𝑛𝑡	𝑥𝑐𝑜𝑛𝑡	PROPN
fumecheng-7267	90	1	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	90	2	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	90	3	𝐼𝑓	𝐼𝑓	PROPN
fumecheng-7267	90	4	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	NOUN
fumecheng-7267	90	5	<	<	X
fumecheng-7267	90	6	2320	2320	NUM
fumecheng-7267	90	7	𝑂𝑟	𝑂𝑟	NOUN
fumecheng-7267	90	8	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	NOUN
fumecheng-7267	90	9	>	>	X
fumecheng-7267	90	10	100000000	100000000	NUM
fumecheng-7267	90	11	#	#	NOUN
fumecheng-7267	90	12	𝑂𝑟	𝑂𝑟	PROPN
fumecheng-7267	90	13	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	90	14	<	<	X
fumecheng-7267	90	15	0	0	PUNCT
fumecheng-7267	91	1	𝑂𝑟	𝑂𝑟	PROPN
fumecheng-7267	91	2	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	91	3	>	>	X
fumecheng-7267	91	4	0.05	0.05	NUM
fumecheng-7267	91	5	𝑇ℎ𝑒𝑛	𝑇ℎ𝑒𝑛	PROPN
fumecheng-7267	91	6	𝐶𝑂𝐿𝐸𝐵𝑅𝑂𝑂𝐾𝐼𝑇𝐸	𝐶𝑂𝐿𝐸𝐵𝑅𝑂𝑂𝐾𝐼𝑇𝐸	NOUN
fumecheng-7267	91	7	=	=	SYM
fumecheng-7267	91	8	𝐶𝑉𝐸𝑟𝑟(𝑥𝑙𝐸𝑟𝑟𝑉𝑎𝑙𝑢𝑒	𝐶𝑉𝐸𝑟𝑟(𝑥𝑙𝐸𝑟𝑟𝑉𝑎𝑙𝑢𝑒	PROPN
fumecheng-7267	91	9	)	)	PUNCT
fumecheng-7267	92	1	𝐸𝑥𝑖𝑡	𝐸𝑥𝑖𝑡	PROPN
fumecheng-7267	92	2	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	PROPN
fumecheng-7267	92	3	𝐸𝑛𝑑	𝐸𝑛𝑑	PROPN
fumecheng-7267	92	4	𝐼𝑓	𝐼𝑓	PROPN
fumecheng-7267	92	5	𝑥𝑐𝑜𝑛𝑡	𝑥𝑐𝑜𝑛𝑡	NOUN
fumecheng-7267	92	6	=	=	SYM
fumecheng-7267	92	7	0	0	PUNCT
fumecheng-7267	93	1	𝑥	𝑥	NOUN
fumecheng-7267	93	2	=	=	SYM
fumecheng-7267	93	3	5	5	NUM
fumecheng-7267	93	4	𝐷𝑜	𝐷𝑜	NOUN
fumecheng-7267	93	5	𝑈𝑛𝑡𝑖𝑙	𝑈𝑛𝑡𝑖𝑙	PROPN
fumecheng-7267	93	6	𝐴𝑏𝑠(𝑥	𝐴𝑏𝑠(𝑥	NOUN
fumecheng-7267	93	7	−	−	NOUN
fumecheng-7267	93	8	𝑥𝑐𝑜𝑛𝑡	𝑥𝑐𝑜𝑛𝑡	PROPN
fumecheng-7267	93	9	)	)	PUNCT
fumecheng-7267	93	10	<	<	X
fumecheng-7267	93	11	0.000000001	0.000000001	NUM
fumecheng-7267	93	12	𝑥𝑐𝑜𝑛𝑡	𝑥𝑐𝑜𝑛𝑡	NOUN
fumecheng-7267	93	13	=	=	PUNCT
fumecheng-7267	93	14	𝑥	𝑥	PRON
fumecheng-7267	93	15	𝑥	𝑥	NOUN
fumecheng-7267	93	16	=	=	PUNCT
fumecheng-7267	93	17	−2	−2	NOUN
fumecheng-7267	93	18	/	/	SYM
fumecheng-7267	93	19	𝐿𝑜𝑔(10	𝐿𝑜𝑔(10	NOUN
fumecheng-7267	93	20	)	)	PUNCT
fumecheng-7267	93	21	∗	∗	NOUN
fumecheng-7267	93	22	𝐿𝑜𝑔(2.51	𝐿𝑜𝑔(2.51	PROPN
fumecheng-7267	93	23	∗	∗	VERB
fumecheng-7267	93	24	𝑥	𝑥	X
fumecheng-7267	93	25	/	/	SYM
fumecheng-7267	93	26	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	NOUN
fumecheng-7267	93	27	+	+	CCONJ
fumecheng-7267	93	28	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	93	29	/	/	SYM
fumecheng-7267	93	30	3.71	3.71	NUM
fumecheng-7267	93	31	)	)	PUNCT
fumecheng-7267	94	1	𝐿𝑜𝑜𝑝	𝐿𝑜𝑜𝑝	NOUN
fumecheng-7267	94	2	𝑥	𝑥	NOUN
fumecheng-7267	94	3	=	=	SYM
fumecheng-7267	94	4	𝑥	𝑥	NOUN
fumecheng-7267	94	5	^	^	SYM
fumecheng-7267	94	6	−	−	PROPN
fumecheng-7267	94	7	2	2	NUM
fumecheng-7267	94	8	𝐶𝑂𝐿𝐸𝐵𝑅𝑂𝑂𝐾𝐼𝑇𝐸	𝐶𝑂𝐿𝐸𝐵𝑅𝑂𝑂𝐾𝐼𝑇𝐸	NOUN
fumecheng-7267	94	9	=	=	PUNCT
fumecheng-7267	94	10	𝑥	𝑥	PRON
fumecheng-7267	94	11	𝐸𝑛𝑑	𝐸𝑛𝑑	PROPN
fumecheng-7267	94	12	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	PROPN
fumecheng-7267	94	13	3.1.2	3.1.2	NUM
fumecheng-7267	94	14	.	.	PUNCT
fumecheng-7267	95	1	lambert	lambert	PROPN
fumecheng-7267	95	2	w	w	PROPN
fumecheng-7267	95	3	-	-	PUNCT
fumecheng-7267	95	4	function	function	NOUN
fumecheng-7267	95	5	to	to	ADP
fumecheng-7267	95	6	date	date	NOUN
fumecheng-7267	95	7	,	,	PUNCT
fumecheng-7267	95	8	the	the	DET
fumecheng-7267	95	9	only	only	ADJ
fumecheng-7267	95	10	way	way	NOUN
fumecheng-7267	95	11	to	to	PART
fumecheng-7267	95	12	transform	transform	VERB
fumecheng-7267	95	13	analytically	analytically	ADV
fumecheng-7267	95	14	the	the	DET
fumecheng-7267	95	15	colebrook	colebrook	PROPN
fumecheng-7267	95	16	equation	equation	NOUN
fumecheng-7267	95	17	from	from	ADP
fumecheng-7267	95	18	its	its	PRON
fumecheng-7267	95	19	native	native	ADJ
fumecheng-7267	95	20	implicit	implicit	ADJ
fumecheng-7267	95	21	form	form	NOUN
fumecheng-7267	95	22	into	into	ADP
fumecheng-7267	95	23	an	an	DET
fumecheng-7267	95	24	explicit	explicit	ADJ
fumecheng-7267	95	25	form	form	NOUN
fumecheng-7267	95	26	is	be	AUX
fumecheng-7267	95	27	through	through	ADP
fumecheng-7267	95	28	the	the	DET
fumecheng-7267	95	29	lambert	lambert	PROPN
fumecheng-7267	95	30	w	w	PROPN
fumecheng-7267	95	31	-	-	PUNCT
fumecheng-7267	95	32	function	function	NOUN
fumecheng-7267	95	33	[	[	X
fumecheng-7267	95	34	18	18	NUM
fumecheng-7267	95	35	]	]	PUNCT
fumecheng-7267	95	36	.	.	PUNCT
fumecheng-7267	96	1	a	a	DET
fumecheng-7267	96	2	version	version	NOUN
fumecheng-7267	96	3	from	from	ADP
fumecheng-7267	96	4	[	[	X
fumecheng-7267	96	5	23,36	23,36	X
fumecheng-7267	96	6	]	]	PUNCT
fumecheng-7267	96	7	is	be	AUX
fumecheng-7267	96	8	given	give	VERB
fumecheng-7267	96	9	in	in	ADP
fumecheng-7267	96	10	eq	eq	ADP
fumecheng-7267	96	11	.	.	PUNCT
fumecheng-7267	97	1	(	(	PUNCT
fumecheng-7267	97	2	2	2	NUM
fumecheng-7267	97	3	)	)	PUNCT
fumecheng-7267	97	4	,	,	PUNCT
fumecheng-7267	97	5	with	with	ADP
fumecheng-7267	97	6	the	the	DET
fumecheng-7267	97	7	related	related	ADJ
fumecheng-7267	97	8	algorithm	algorithm	NOUN
fumecheng-7267	97	9	in	in	ADP
fumecheng-7267	97	10	fig	fig	NOUN
fumecheng-7267	97	11	.	.	PUNCT
fumecheng-7267	98	1	4	4	NUM
fumecheng-7267	98	2	and	and	CCONJ
fumecheng-7267	98	3	the	the	DET
fumecheng-7267	98	4	code	code	NOUN
fumecheng-7267	98	5	as	as	SCONJ
fumecheng-7267	98	6	follows	follow	VERB
fumecheng-7267	98	7	(	(	PUNCT
fumecheng-7267	98	8	to	to	PART
fumecheng-7267	98	9	use	use	VERB
fumecheng-7267	98	10	this	this	DET
fumecheng-7267	98	11	code	code	NOUN
fumecheng-7267	98	12	,	,	PUNCT
fumecheng-7267	98	13	additional	additional	ADJ
fumecheng-7267	98	14	udf	udf	ADJ
fumecheng-7267	98	15	“	"	PUNCT
fumecheng-7267	98	16	lambert	lambert	PROPN
fumecheng-7267	98	17	”	"	PUNCT
fumecheng-7267	98	18	should	should	AUX
fumecheng-7267	98	19	be	be	AUX
fumecheng-7267	98	20	defined	define	VERB
fumecheng-7267	98	21	as	as	SCONJ
fumecheng-7267	98	22	explained	explain	VERB
fumecheng-7267	98	23	in	in	ADP
fumecheng-7267	98	24	further	further	ADJ
fumecheng-7267	98	25	text	text	NOUN
fumecheng-7267	98	26	)	)	PUNCT
fumecheng-7267	98	27	.	.	PUNCT
fumecheng-7267	99	1	1	1	NUM
fumecheng-7267	99	2	√f	√f	PRON
fumecheng-7267	99	3	=	=	PUNCT
fumecheng-7267	99	4	z	z	NOUN
fumecheng-7267	99	5	2.51	2.51	NUM
fumecheng-7267	99	6	·	·	PUNCT
fumecheng-7267	99	7	(	(	PUNCT
fumecheng-7267	99	8	b+y	b+y	NOUN
fumecheng-7267	99	9	)	)	PUNCT
fumecheng-7267	99	10	z	z	NOUN
fumecheng-7267	100	1	=	=	SYM
fumecheng-7267	100	2	2·2.51	2·2.51	PROPN
fumecheng-7267	100	3	ln(10	ln(10	ADJ
fumecheng-7267	100	4	)	)	PUNCT
fumecheng-7267	100	5	a	a	DET
fumecheng-7267	100	6	=	=	SYM
fumecheng-7267	100	7	re	re	NOUN
fumecheng-7267	100	8	z	z	PROPN
fumecheng-7267	100	9	·	·	PUNCT
fumecheng-7267	100	10	ε	ε	PROPN
fumecheng-7267	100	11	3.71	3.71	NUM
fumecheng-7267	100	12	b	b	X
fumecheng-7267	100	13	=	=	SYM
fumecheng-7267	100	14	ln(re	ln(re	PROPN
fumecheng-7267	100	15	)	)	PUNCT
fumecheng-7267	100	16	−	−	NOUN
fumecheng-7267	100	17	ln(z	ln(z	NOUN
fumecheng-7267	100	18	)	)	PUNCT
fumecheng-7267	100	19	x	x	X
fumecheng-7267	101	1	=	=	PUNCT
fumecheng-7267	101	2	a	a	PRON
fumecheng-7267	101	3	+	+	NOUN
fumecheng-7267	101	4	b	b	PROPN
fumecheng-7267	101	5	y	y	PROPN
fumecheng-7267	101	6	=	=	PUNCT
fumecheng-7267	101	7	w(ex	w(ex	NUM
fumecheng-7267	101	8	)	)	PUNCT
fumecheng-7267	101	9	−	−	NOUN
fumecheng-7267	101	10	x	x	SYM
fumecheng-7267	101	11	}	}	PUNCT
fumecheng-7267	101	12	(	(	PUNCT
fumecheng-7267	101	13	2	2	X
fumecheng-7267	101	14	)	)	PUNCT
fumecheng-7267	101	15	yes	yes	INTJ
fumecheng-7267	102	1	no	no	DET
fumecheng-7267	102	2	error	error	NOUN
fumecheng-7267	102	3	lambert	lambert	PROPN
fumecheng-7267	102	4	w	w	PROPN
fumecheng-7267	102	5	-	-	PUNCT
fumecheng-7267	102	6	based	base	VERB
fumecheng-7267	102	7	solution	solution	NOUN
fumecheng-7267	102	8	of	of	ADP
fumecheng-7267	102	9	the	the	DET
fumecheng-7267	102	10	colebrook	colebrook	PROPN
fumecheng-7267	102	11	equation	equation	PROPN
fumecheng-7267	102	12	fig	fig	NOUN
fumecheng-7267	102	13	.	.	PUNCT
fumecheng-7267	103	1	4	4	NUM
fumecheng-7267	103	2	algorithm	algorithm	NOUN
fumecheng-7267	103	3	for	for	ADP
fumecheng-7267	103	4	solving	solve	VERB
fumecheng-7267	103	5	the	the	DET
fumecheng-7267	103	6	colebrook	colebrook	PROPN
fumecheng-7267	103	7	equation	equation	NOUN
fumecheng-7267	103	8	expressed	express	VERB
fumecheng-7267	103	9	through	through	ADP
fumecheng-7267	103	10	the	the	DET
fumecheng-7267	103	11	lambert	lambert	PROPN
fumecheng-7267	103	12	w	w	PROPN
fumecheng-7267	103	13	-	-	PUNCT
fumecheng-7267	103	14	function	function	NOUN
fumecheng-7267	103	15	260	260	NUM
fumecheng-7267	103	16	d.	d.	PROPN
fumecheng-7267	103	17	brkić	brkić	PROPN
fumecheng-7267	103	18	,	,	PUNCT
fumecheng-7267	103	19	z.	z.	PROPN
fumecheng-7267	103	20	stajić	stajić	PROPN
fumecheng-7267	104	1	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	PROPN
fumecheng-7267	104	2	𝐶𝑂𝐿𝐸𝐵𝑅𝑂𝑂𝐾𝐿𝐴𝑀𝐵𝐸𝑅𝑇(𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝐶𝑂𝐿𝐸𝐵𝑅𝑂𝑂𝐾𝐿𝐴𝑀𝐵𝐸𝑅𝑇(𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	NOUN
fumecheng-7267	104	3	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	104	4	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	104	5	,	,	PUNCT
fumecheng-7267	104	6	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	104	7	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	104	8	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	104	9	)	)	PUNCT
fumecheng-7267	105	1	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	105	2	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	105	3	𝐷𝑖𝑚	𝐷𝑖𝑚	PROPN
fumecheng-7267	105	4	𝑧	𝑧	PROPN
fumecheng-7267	105	5	,	,	PUNCT
fumecheng-7267	105	6	𝐴	𝐴	PROPN
fumecheng-7267	105	7	,	,	PUNCT
fumecheng-7267	105	8	𝐵	𝐵	PROPN
fumecheng-7267	105	9	,	,	PUNCT
fumecheng-7267	105	10	𝑥	𝑥	PROPN
fumecheng-7267	105	11	,	,	PUNCT
fumecheng-7267	105	12	𝑦	𝑦	NOUN
fumecheng-7267	105	13	,	,	PUNCT
fumecheng-7267	105	14	𝑓	𝑓	DET
fumecheng-7267	105	15	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	105	16	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	105	17	𝐼𝑓	𝐼𝑓	PROPN
fumecheng-7267	105	18	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	NOUN
fumecheng-7267	105	19	<	<	X
fumecheng-7267	105	20	2320	2320	NUM
fumecheng-7267	105	21	𝑂𝑟	𝑂𝑟	NOUN
fumecheng-7267	105	22	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	NOUN
fumecheng-7267	105	23	>	>	X
fumecheng-7267	105	24	100000000	100000000	NUM
fumecheng-7267	105	25	#	#	NOUN
fumecheng-7267	105	26	𝑂𝑟	𝑂𝑟	PROPN
fumecheng-7267	105	27	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	105	28	<	<	X
fumecheng-7267	105	29	0	0	PUNCT
fumecheng-7267	106	1	𝑂𝑟	𝑂𝑟	PROPN
fumecheng-7267	106	2	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	106	3	>	>	X
fumecheng-7267	106	4	0.05	0.05	NUM
fumecheng-7267	106	5	𝑇ℎ𝑒𝑛	𝑇ℎ𝑒𝑛	PROPN
fumecheng-7267	106	6	𝐶𝑂𝐿𝐸𝐵𝑅𝑂𝑂𝐾𝐿𝐴𝑀𝐵𝐸𝑅𝑇	𝐶𝑂𝐿𝐸𝐵𝑅𝑂𝑂𝐾𝐿𝐴𝑀𝐵𝐸𝑅𝑇	NOUN
fumecheng-7267	106	7	=	=	SYM
fumecheng-7267	106	8	𝐶𝑉𝐸𝑟𝑟(𝑥𝑙𝐸𝑟𝑟𝑉𝑎𝑙𝑢𝑒	𝐶𝑉𝐸𝑟𝑟(𝑥𝑙𝐸𝑟𝑟𝑉𝑎𝑙𝑢𝑒	ADJ
fumecheng-7267	106	9	)	)	PUNCT
fumecheng-7267	107	1	𝐸𝑥𝑖𝑡	𝐸𝑥𝑖𝑡	PROPN
fumecheng-7267	107	2	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	PROPN
fumecheng-7267	107	3	𝐸𝑛𝑑	𝐸𝑛𝑑	PROPN
fumecheng-7267	107	4	𝐼𝑓	𝐼𝑓	PROPN
fumecheng-7267	107	5	𝑧	𝑧	NOUN
fumecheng-7267	107	6	=	=	SYM
fumecheng-7267	107	7	2	2	NUM
fumecheng-7267	107	8	∗	∗	NOUN
fumecheng-7267	107	9	2.51	2.51	NUM
fumecheng-7267	107	10	/	/	SYM
fumecheng-7267	107	11	𝐿𝑜𝑔(10	𝐿𝑜𝑔(10	PROPN
fumecheng-7267	107	12	)	)	PUNCT
fumecheng-7267	107	13	𝐴	𝐴	NOUN
fumecheng-7267	107	14	=	=	PUNCT
fumecheng-7267	107	15	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	PROPN
fumecheng-7267	107	16	∗	∗	X
fumecheng-7267	107	17	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	107	18	/	/	PUNCT
fumecheng-7267	107	19	(	(	PUNCT
fumecheng-7267	107	20	3.71	3.71	NUM
fumecheng-7267	107	21	∗	∗	NOUN
fumecheng-7267	107	22	𝑧	𝑧	NOUN
fumecheng-7267	107	23	)	)	PUNCT
fumecheng-7267	107	24	𝐵	𝐵	NOUN
fumecheng-7267	107	25	=	=	SYM
fumecheng-7267	107	26	𝐿𝑜𝑔(𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝐿𝑜𝑔(𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	PROPN
fumecheng-7267	107	27	)	)	PUNCT
fumecheng-7267	107	28	−	−	PROPN
fumecheng-7267	107	29	𝐿𝑜𝑔(𝑧	𝐿𝑜𝑔(𝑧	PROPN
fumecheng-7267	107	30	)	)	PUNCT
fumecheng-7267	107	31	𝑥	𝑥	NOUN
fumecheng-7267	107	32	=	=	SYM
fumecheng-7267	107	33	𝐴	𝐴	PROPN
fumecheng-7267	107	34	+	+	CCONJ
fumecheng-7267	107	35	𝐵	𝐵	PROPN
fumecheng-7267	107	36	𝑦	𝑦	NOUN
fumecheng-7267	107	37	=	=	SYM
fumecheng-7267	107	38	𝐿𝐴𝑀𝐵𝐸𝑅𝑇(𝐸𝑥𝑝(𝑥	𝐿𝐴𝑀𝐵𝐸𝑅𝑇(𝐸𝑥𝑝(𝑥	NOUN
fumecheng-7267	107	39	)	)	PUNCT
fumecheng-7267	107	40	)	)	PUNCT
fumecheng-7267	108	1	−	−	ADP
fumecheng-7267	109	1	𝑥	𝑥	PRON
fumecheng-7267	109	2	𝑓	𝑓	PROPN
fumecheng-7267	109	3	=	=	X
fumecheng-7267	109	4	(	(	PUNCT
fumecheng-7267	109	5	(	(	PUNCT
fumecheng-7267	109	6	𝑧	𝑧	PROPN
fumecheng-7267	109	7	/	/	SYM
fumecheng-7267	109	8	2.51	2.51	NUM
fumecheng-7267	109	9	)	)	PUNCT
fumecheng-7267	109	10	∗	∗	NOUN
fumecheng-7267	109	11	(	(	PUNCT
fumecheng-7267	109	12	𝐵	𝐵	NOUN
fumecheng-7267	109	13	+	+	NOUN
fumecheng-7267	109	14	𝑦	𝑦	NOUN
fumecheng-7267	109	15	)	)	PUNCT
fumecheng-7267	109	16	)	)	PUNCT
fumecheng-7267	109	17	^	^	PUNCT
fumecheng-7267	110	1	−	−	PROPN
fumecheng-7267	110	2	2	2	NUM
fumecheng-7267	110	3	𝐶𝑂𝐿𝐸𝐵𝑅𝑂𝑂𝐾𝐿𝐴𝑀𝐵𝐸𝑅𝑇	𝐶𝑂𝐿𝐸𝐵𝑅𝑂𝑂𝐾𝐿𝐴𝑀𝐵𝐸𝑅𝑇	PROPN
fumecheng-7267	110	4	=	=	SYM
fumecheng-7267	110	5	𝑓	𝑓	PROPN
fumecheng-7267	110	6	𝐸𝑛𝑑	𝐸𝑛𝑑	PROPN
fumecheng-7267	110	7	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	PROPN
fumecheng-7267	110	8	in	in	ADP
fumecheng-7267	110	9	some	some	PRON
fumecheng-7267	110	10	of	of	ADP
fumecheng-7267	110	11	the	the	DET
fumecheng-7267	110	12	cases	case	NOUN
fumecheng-7267	110	13	such	such	ADJ
fumecheng-7267	110	14	as	as	ADP
fumecheng-7267	110	15	in	in	ADP
fumecheng-7267	110	16	[	[	X
fumecheng-7267	110	17	18,32	18,32	NUM
fumecheng-7267	110	18	]	]	PUNCT
fumecheng-7267	110	19	,	,	PUNCT
fumecheng-7267	110	20	the	the	DET
fumecheng-7267	110	21	argument	argument	NOUN
fumecheng-7267	110	22	of	of	ADP
fumecheng-7267	110	23	the	the	DET
fumecheng-7267	110	24	lambert	lambert	PROPN
fumecheng-7267	110	25	w	w	PROPN
fumecheng-7267	110	26	-	-	PUNCT
fumecheng-7267	110	27	function	function	NOUN
fumecheng-7267	110	28	is	be	AUX
fumecheng-7267	110	29	fastgrowing	fastgrowe	VERB
fumecheng-7267	110	30	and	and	CCONJ
fumecheng-7267	110	31	for	for	ADP
fumecheng-7267	110	32	the	the	DET
fumecheng-7267	110	33	values	value	NOUN
fumecheng-7267	110	34	of	of	ADP
fumecheng-7267	110	35	x	x	X
fumecheng-7267	110	36	>	>	X
fumecheng-7267	110	37	e709.7827	e709.7827	PROPN
fumecheng-7267	110	38	,	,	PUNCT
fumecheng-7267	110	39	e≈2.718	e≈2.718	PROPN
fumecheng-7267	110	40	,	,	PUNCT
fumecheng-7267	110	41	an	an	DET
fumecheng-7267	110	42	overflow	overflow	NOUN
fumecheng-7267	110	43	error	error	NOUN
fumecheng-7267	110	44	can	can	AUX
fumecheng-7267	110	45	occur	occur	VERB
fumecheng-7267	110	46	[	[	X
fumecheng-7267	110	47	33	33	NUM
fumecheng-7267	110	48	]	]	PUNCT
fumecheng-7267	110	49	while	while	SCONJ
fumecheng-7267	110	50	the	the	DET
fumecheng-7267	110	51	colebrook	colebrook	PROPN
fumecheng-7267	110	52	equation	equation	NOUN
fumecheng-7267	110	53	expressed	express	VERB
fumecheng-7267	110	54	in	in	ADP
fumecheng-7267	110	55	that	that	DET
fumecheng-7267	110	56	way	way	NOUN
fumecheng-7267	110	57	can	can	AUX
fumecheng-7267	110	58	not	not	PART
fumecheng-7267	110	59	be	be	AUX
fumecheng-7267	110	60	solved	solve	VERB
fumecheng-7267	110	61	always	always	ADV
fumecheng-7267	110	62	in	in	ADP
fumecheng-7267	110	63	a	a	DET
fumecheng-7267	110	64	computer	computer	NOUN
fumecheng-7267	110	65	due	due	ADP
fumecheng-7267	110	66	to	to	ADP
fumecheng-7267	110	67	its	its	PRON
fumecheng-7267	110	68	limited	limited	ADJ
fumecheng-7267	110	69	capacity	capacity	NOUN
fumecheng-7267	110	70	of	of	ADP
fumecheng-7267	110	71	registers	register	NOUN
fumecheng-7267	110	72	(	(	PUNCT
fumecheng-7267	110	73	see	see	VERB
fumecheng-7267	110	74	fig	fig	NOUN
fumecheng-7267	110	75	.	.	PUNCT
fumecheng-7267	111	1	5	5	NUM
fumecheng-7267	111	2	)	)	PUNCT
fumecheng-7267	111	3	.	.	PUNCT
fumecheng-7267	112	1	however	however	ADV
fumecheng-7267	112	2	,	,	PUNCT
fumecheng-7267	112	3	a	a	DET
fumecheng-7267	112	4	version	version	NOUN
fumecheng-7267	112	5	from	from	ADP
fumecheng-7267	112	6	[	[	X
fumecheng-7267	112	7	23,36	23,36	X
fumecheng-7267	112	8	]	]	PUNCT
fumecheng-7267	112	9	as	as	SCONJ
fumecheng-7267	112	10	given	give	VERB
fumecheng-7267	112	11	in	in	ADP
fumecheng-7267	112	12	eq	eq	ADP
fumecheng-7267	112	13	.	.	PUNCT
fumecheng-7267	113	1	(	(	PUNCT
fumecheng-7267	113	2	2	2	X
fumecheng-7267	113	3	)	)	PUNCT
fumecheng-7267	113	4	uses	use	VERB
fumecheng-7267	113	5	the	the	DET
fumecheng-7267	113	6	lambert	lambert	PROPN
fumecheng-7267	113	7	w	w	NOUN
fumecheng-7267	113	8	-	-	PUNCT
fumecheng-7267	113	9	function	function	NOUN
fumecheng-7267	113	10	with	with	ADP
fumecheng-7267	113	11	a	a	DET
fumecheng-7267	113	12	shifted	shift	VERB
fumecheng-7267	113	13	argument	argument	NOUN
fumecheng-7267	113	14	which	which	PRON
fumecheng-7267	113	15	allows	allow	VERB
fumecheng-7267	113	16	computation	computation	NOUN
fumecheng-7267	113	17	avoiding	avoid	VERB
fumecheng-7267	113	18	the	the	DET
fumecheng-7267	113	19	explained	explain	VERB
fumecheng-7267	113	20	overflow	overflow	NOUN
fumecheng-7267	113	21	error	error	NOUN
fumecheng-7267	113	22	.	.	PUNCT
fumecheng-7267	114	1	fig	fig	NOUN
fumecheng-7267	114	2	.	.	PUNCT
fumecheng-7267	115	1	5	5	NUM
fumecheng-7267	115	2	constraints	constraint	NOUN
fumecheng-7267	115	3	for	for	ADP
fumecheng-7267	115	4	using	use	VERB
fumecheng-7267	115	5	the	the	DET
fumecheng-7267	115	6	lambert	lambert	PROPN
fumecheng-7267	115	7	w	w	NOUN
fumecheng-7267	115	8	-	-	PUNCT
fumecheng-7267	115	9	function	function	NOUN
fumecheng-7267	115	10	for	for	ADP
fumecheng-7267	115	11	solving	solve	VERB
fumecheng-7267	115	12	the	the	DET
fumecheng-7267	115	13	colebrook	colebrook	PROPN
fumecheng-7267	115	14	equation	equation	NOUN
fumecheng-7267	115	15	(	(	PUNCT
fumecheng-7267	115	16	based	base	VERB
fumecheng-7267	115	17	on	on	ADP
fumecheng-7267	115	18	[	[	X
fumecheng-7267	115	19	18,32	18,32	NUM
fumecheng-7267	115	20	]	]	PUNCT
fumecheng-7267	115	21	)	)	PUNCT
fumecheng-7267	115	22	the	the	DET
fumecheng-7267	115	23	halley	halley	PROPN
fumecheng-7267	115	24	iterative	iterative	PROPN
fumecheng-7267	115	25	scheme	scheme	NOUN
fumecheng-7267	115	26	,	,	PUNCT
fumecheng-7267	115	27	eq	eq	NOUN
fumecheng-7267	115	28	.	.	PUNCT
fumecheng-7267	115	29	(	(	PUNCT
fumecheng-7267	115	30	3	3	NUM
fumecheng-7267	115	31	)	)	PUNCT
fumecheng-7267	115	32	,	,	PUNCT
fumecheng-7267	115	33	is	be	AUX
fumecheng-7267	115	34	used	use	VERB
fumecheng-7267	115	35	here	here	ADV
fumecheng-7267	115	36	for	for	ADP
fumecheng-7267	115	37	evaluation	evaluation	NOUN
fumecheng-7267	115	38	of	of	ADP
fumecheng-7267	115	39	the	the	DET
fumecheng-7267	115	40	principal	principal	ADJ
fumecheng-7267	115	41	branch	branch	NOUN
fumecheng-7267	115	42	of	of	ADP
fumecheng-7267	115	43	the	the	DET
fumecheng-7267	115	44	lambert	lambert	PROPN
fumecheng-7267	115	45	w	w	PROPN
fumecheng-7267	115	46	-	-	PUNCT
fumecheng-7267	115	47	function	function	NOUN
fumecheng-7267	115	48	.	.	PUNCT
fumecheng-7267	116	1	the	the	DET
fumecheng-7267	116	2	lambert	lambert	PROPN
fumecheng-7267	116	3	w	w	PROPN
fumecheng-7267	116	4	-	-	PUNCT
fumecheng-7267	116	5	function	function	NOUN
fumecheng-7267	116	6	function	function	NOUN
fumecheng-7267	116	7	in	in	ADP
fumecheng-7267	116	8	suitable	suitable	ADJ
fumecheng-7267	116	9	form	form	NOUN
fumecheng-7267	116	10	is	be	AUX
fumecheng-7267	116	11	given	give	VERB
fumecheng-7267	116	12	as	as	ADP
fumecheng-7267	116	13	li-1	li-1	NOUN
fumecheng-7267	116	14	,	,	PUNCT
fumecheng-7267	116	15	with	with	ADP
fumecheng-7267	116	16	its	its	PRON
fumecheng-7267	116	17	first	first	ADJ
fumecheng-7267	116	18	and	and	CCONJ
fumecheng-7267	116	19	second	second	ADJ
fumecheng-7267	116	20	derivative	derivative	NOUN
fumecheng-7267	116	21	given	give	VERB
fumecheng-7267	116	22	as	as	ADP
fumecheng-7267	116	23	l’i-1	l’i-1	PROPN
fumecheng-7267	116	24	and	and	CCONJ
fumecheng-7267	116	25	l”i-1	l”i-1	NOUN
fumecheng-7267	116	26	.	.	PUNCT
fumecheng-7267	117	1	this	this	DET
fumecheng-7267	117	2	solution	solution	NOUN
fumecheng-7267	117	3	is	be	AUX
fumecheng-7267	117	4	valid	valid	ADJ
fumecheng-7267	117	5	for	for	ADP
fumecheng-7267	117	6	real	real	ADJ
fumecheng-7267	117	7	values	value	NOUN
fumecheng-7267	117	8	for	for	ADP
fumecheng-7267	117	9	x>-1	x>-1	PROPN
fumecheng-7267	117	10	/	/	SYM
fumecheng-7267	117	11	e	e	NOUN
fumecheng-7267	117	12	,	,	PUNCT
fumecheng-7267	117	13	where	where	SCONJ
fumecheng-7267	117	14	e≈2.718	e≈2.718	PROPN
fumecheng-7267	117	15	.	.	PUNCT
fumecheng-7267	118	1	to	to	PART
fumecheng-7267	118	2	start	start	VERB
fumecheng-7267	118	3	the	the	DET
fumecheng-7267	118	4	halley	halley	PROPN
fumecheng-7267	118	5	iterative	iterative	NOUN
fumecheng-7267	118	6	scheme	scheme	NOUN
fumecheng-7267	118	7	for	for	ADP
fumecheng-7267	118	8	solving	solve	VERB
fumecheng-7267	118	9	the	the	DET
fumecheng-7267	118	10	principal	principal	ADJ
fumecheng-7267	118	11	branch	branch	NOUN
fumecheng-7267	118	12	of	of	ADP
fumecheng-7267	118	13	the	the	DET
fumecheng-7267	118	14	lambert	lambert	PROPN
fumecheng-7267	118	15	wfunction	wfunction	NOUN
fumecheng-7267	118	16	,	,	PUNCT
fumecheng-7267	118	17	a	a	DET
fumecheng-7267	118	18	simple	simple	ADJ
fumecheng-7267	118	19	and	and	CCONJ
fumecheng-7267	118	20	sufficient	sufficient	ADJ
fumecheng-7267	118	21	starting	starting	NOUN
fumecheng-7267	118	22	point	point	NOUN
fumecheng-7267	118	23	x0=1	x0=1	PUNCT
fumecheng-7267	118	24	can	can	AUX
fumecheng-7267	118	25	be	be	AUX
fumecheng-7267	118	26	chosen	choose	VERB
fumecheng-7267	118	27	,	,	PUNCT
fumecheng-7267	118	28	which	which	PRON
fumecheng-7267	118	29	makes	make	VERB
fumecheng-7267	118	30	the	the	DET
fumecheng-7267	118	31	algorithm	algorithm	NOUN
fumecheng-7267	118	32	from	from	ADP
fumecheng-7267	118	33	fig	fig	NOUN
fumecheng-7267	118	34	.	.	PUNCT
fumecheng-7267	119	1	6	6	NUM
fumecheng-7267	119	2	fast	fast	ADV
fumecheng-7267	119	3	for	for	ADP
fumecheng-7267	119	4	execution	execution	NOUN
fumecheng-7267	119	5	.	.	PUNCT
fumecheng-7267	120	1	the	the	DET
fumecheng-7267	120	2	principal	principal	ADJ
fumecheng-7267	120	3	branch	branch	NOUN
fumecheng-7267	120	4	of	of	ADP
fumecheng-7267	120	5	the	the	DET
fumecheng-7267	120	6	lambert	lambert	PROPN
fumecheng-7267	120	7	w	w	PROPN
fumecheng-7267	120	8	-	-	PUNCT
fumecheng-7267	120	9	function	function	NOUN
fumecheng-7267	120	10	is	be	AUX
fumecheng-7267	120	11	used	use	VERB
fumecheng-7267	120	12	often	often	ADV
fumecheng-7267	120	13	in	in	ADP
fumecheng-7267	120	14	engineering	engineering	NOUN
fumecheng-7267	120	15	and	and	CCONJ
fumecheng-7267	120	16	physics	physics	NOUN
fumecheng-7267	121	1	[	[	X
fumecheng-7267	121	2	19	19	NUM
fumecheng-7267	121	3	]	]	SYM
fumecheng-7267	121	4	meaning	mean	VERB
fumecheng-7267	121	5	that	that	SCONJ
fumecheng-7267	121	6	the	the	DET
fumecheng-7267	121	7	algorithm	algorithm	NOUN
fumecheng-7267	121	8	from	from	ADP
fumecheng-7267	121	9	fig	fig	NOUN
fumecheng-7267	121	10	.	.	PUNCT
fumecheng-7267	121	11	6	6	NUM
fumecheng-7267	121	12	can	can	AUX
fumecheng-7267	121	13	have	have	VERB
fumecheng-7267	121	14	much	much	ADV
fumecheng-7267	121	15	wider	wide	ADJ
fumecheng-7267	121	16	application	application	NOUN
fumecheng-7267	121	17	aside	aside	ADV
fumecheng-7267	121	18	for	for	ADP
fumecheng-7267	121	19	the	the	DET
fumecheng-7267	121	20	colebrook	colebrook	PROPN
fumecheng-7267	121	21	equation	equation	NOUN
fumecheng-7267	121	22	.	.	PUNCT
fumecheng-7267	122	1	excel	excel	VERB
fumecheng-7267	122	2	vba	vba	PROPN
fumecheng-7267	122	3	-	-	PUNCT
fumecheng-7267	122	4	based	base	VERB
fumecheng-7267	122	5	user	user	NOUN
fumecheng-7267	122	6	defined	define	VERB
fumecheng-7267	122	7	functions	function	NOUN
fumecheng-7267	122	8	for	for	ADP
fumecheng-7267	122	9	highly	highly	ADV
fumecheng-7267	122	10	precise	precise	ADJ
fumecheng-7267	122	11	colebrook	colebrook	PROPN
fumecheng-7267	122	12	’s	’s	PART
fumecheng-7267	122	13	pipe	pipe	NOUN
fumecheng-7267	122	14	flow	flow	NOUN
fumecheng-7267	122	15	friction	friction	NOUN
fumecheng-7267	122	16	...	...	PUNCT
fumecheng-7267	122	17	261	261	NUM
fumecheng-7267	122	18	wi(x	wi(x	NOUN
fumecheng-7267	122	19	)	)	PUNCT
fumecheng-7267	122	20	=	=	SYM
fumecheng-7267	122	21	wi−1(x	wi−1(x	PROPN
fumecheng-7267	122	22	)	)	PUNCT
fumecheng-7267	122	23	−	−	PROPN
fumecheng-7267	122	24	li−1	li−1	PROPN
fumecheng-7267	122	25	l′i−1−	l′i−1−	PROPN
fumecheng-7267	122	26	li−1·l"i−1	li−1·l"i−1	PROPN
fumecheng-7267	122	27	2·l′i−1	2·l′i−1	NUM
fumecheng-7267	122	28	li−1	li−1	PROPN
fumecheng-7267	122	29	=	=	SYM
fumecheng-7267	122	30	wi−1(x	wi−1(x	PROPN
fumecheng-7267	122	31	)	)	PUNCT
fumecheng-7267	122	32	·	·	PUNCT
fumecheng-7267	123	1	e	e	X
fumecheng-7267	123	2	wi−1(x	wi−1(x	NOUN
fumecheng-7267	123	3	)	)	PUNCT
fumecheng-7267	123	4	−	−	NOUN
fumecheng-7267	123	5	x	x	SYM
fumecheng-7267	124	1	=	=	SYM
fumecheng-7267	124	2	0	0	NUM
fumecheng-7267	124	3	l′i−1	l′i−1	PROPN
fumecheng-7267	124	4	=	=	SYM
fumecheng-7267	124	5	ewi−1(x)(wi−1(x	ewi−1(x)(wi−1(x	PROPN
fumecheng-7267	124	6	)	)	PUNCT
fumecheng-7267	125	1	+	+	NOUN
fumecheng-7267	125	2	1	1	X
fumecheng-7267	125	3	)	)	PUNCT
fumecheng-7267	126	1	l"i−1	l"i−1	X
fumecheng-7267	126	2	=	=	SYM
fumecheng-7267	126	3	e	e	NOUN
fumecheng-7267	126	4	wi−1(x)(wi−1(x	wi−1(x)(wi−1(x	NOUN
fumecheng-7267	126	5	)	)	PUNCT
fumecheng-7267	127	1	+	+	CCONJ
fumecheng-7267	127	2	2	2	X
fumecheng-7267	127	3	)	)	PUNCT
fumecheng-7267	128	1	}	}	PUNCT
fumecheng-7267	128	2	(	(	PUNCT
fumecheng-7267	128	3	3	3	X
fumecheng-7267	128	4	)	)	PUNCT
fumecheng-7267	128	5	yes	yes	INTJ
fumecheng-7267	128	6	no	no	DET
fumecheng-7267	128	7	error	error	NOUN
fumecheng-7267	128	8	yes	yes	INTJ
fumecheng-7267	128	9	no	no	DET
fumecheng-7267	128	10	principal	principal	ADJ
fumecheng-7267	128	11	branch	branch	NOUN
fumecheng-7267	128	12	of	of	ADP
fumecheng-7267	128	13	the	the	DET
fumecheng-7267	128	14	lambert	lambert	PROPN
fumecheng-7267	128	15	w	w	PROPN
fumecheng-7267	128	16	-	-	PUNCT
fumecheng-7267	128	17	function	function	NOUN
fumecheng-7267	128	18	fig	fig	NOUN
fumecheng-7267	128	19	.	.	PUNCT
fumecheng-7267	129	1	6	6	NUM
fumecheng-7267	129	2	algorithm	algorithm	NOUN
fumecheng-7267	129	3	for	for	ADP
fumecheng-7267	129	4	the	the	DET
fumecheng-7267	129	5	principal	principal	ADJ
fumecheng-7267	129	6	branch	branch	NOUN
fumecheng-7267	129	7	of	of	ADP
fumecheng-7267	129	8	the	the	DET
fumecheng-7267	129	9	lambert	lambert	PROPN
fumecheng-7267	129	10	w	w	PROPN
fumecheng-7267	129	11	-	-	PUNCT
fumecheng-7267	129	12	function	function	VERB
fumecheng-7267	129	13	the	the	DET
fumecheng-7267	129	14	code	code	NOUN
fumecheng-7267	129	15	for	for	ADP
fumecheng-7267	129	16	solving	solve	VERB
fumecheng-7267	129	17	the	the	DET
fumecheng-7267	129	18	principal	principal	ADJ
fumecheng-7267	129	19	branch	branch	NOUN
fumecheng-7267	129	20	of	of	ADP
fumecheng-7267	129	21	the	the	DET
fumecheng-7267	129	22	lambert	lambert	PROPN
fumecheng-7267	129	23	w	w	PROPN
fumecheng-7267	129	24	-	-	PUNCT
fumecheng-7267	129	25	function	function	NOUN
fumecheng-7267	129	26	is	be	AUX
fumecheng-7267	129	27	given	give	VERB
fumecheng-7267	129	28	as	as	SCONJ
fumecheng-7267	129	29	follows	follow	VERB
fumecheng-7267	129	30	:	:	PUNCT
fumecheng-7267	129	31	function	function	NOUN
fumecheng-7267	129	32	lambert(x	lambert(x	NOUN
fumecheng-7267	129	33	as	as	ADV
fumecheng-7267	129	34	double	double	ADJ
fumecheng-7267	129	35	)	)	PUNCT
fumecheng-7267	129	36	as	as	ADV
fumecheng-7267	129	37	double	double	ADJ
fumecheng-7267	129	38	′	′	NUM
fumecheng-7267	129	39	computes	compute	VERB
fumecheng-7267	129	40	the	the	DET
fumecheng-7267	129	41	principal	principal	ADJ
fumecheng-7267	129	42	branch	branch	NOUN
fumecheng-7267	129	43	for	for	ADP
fumecheng-7267	129	44	x	x	X
fumecheng-7267	129	45	>	>	X
fumecheng-7267	129	46	−exp(−1	−exp(−1	PROPN
fumecheng-7267	129	47	)	)	PUNCT
fumecheng-7267	129	48	and	and	CCONJ
fumecheng-7267	129	49	for	for	ADP
fumecheng-7267	129	50	real	real	ADJ
fumecheng-7267	129	51	values	value	NOUN
fumecheng-7267	129	52	only	only	ADV
fumecheng-7267	129	53	dim	dim	ADJ
fumecheng-7267	129	54	wx	wx	PROPN
fumecheng-7267	129	55	,	,	PUNCT
fumecheng-7267	129	56	wxcont	wxcont	NOUN
fumecheng-7267	129	57	,	,	PUNCT
fumecheng-7267	129	58	l	l	NOUN
fumecheng-7267	129	59	,	,	PUNCT
fumecheng-7267	129	60	lprim	lprim	NOUN
fumecheng-7267	129	61	,	,	PUNCT
fumecheng-7267	129	62	lsec	lsec	VERB
fumecheng-7267	129	63	as	as	ADV
fumecheng-7267	129	64	double	double	ADJ
fumecheng-7267	129	65	dim	dim	ADJ
fumecheng-7267	129	66	iter	iter	NOUN
fumecheng-7267	129	67	as	as	ADP
fumecheng-7267	129	68	integer	integer	NOUN
fumecheng-7267	129	69	if	if	SCONJ
fumecheng-7267	129	70	x	x	X
fumecheng-7267	129	71	<	<	X
fumecheng-7267	129	72	−exp(−1	−exp(−1	PROPN
fumecheng-7267	129	73	)	)	PUNCT
fumecheng-7267	129	74	then	then	ADV
fumecheng-7267	129	75	lambert	lambert	PROPN
fumecheng-7267	129	76	=	=	PROPN
fumecheng-7267	129	77	cverr(xlerrvalue	cverr(xlerrvalue	PROPN
fumecheng-7267	129	78	)	)	PUNCT
fumecheng-7267	129	79	exit	exit	NOUN
fumecheng-7267	129	80	function	function	NOUN
fumecheng-7267	129	81	end	end	VERB
fumecheng-7267	129	82	if	if	SCONJ
fumecheng-7267	129	83	wx	wx	PROPN
fumecheng-7267	129	84	=	=	SYM
fumecheng-7267	129	85	1	1	NUM
fumecheng-7267	129	86	do	do	VERB
fumecheng-7267	129	87	until	until	ADP
fumecheng-7267	129	88	abs(wxcont	abs(wxcont	ADP
fumecheng-7267	129	89	−	−	NUM
fumecheng-7267	129	90	wx	wx	NOUN
fumecheng-7267	129	91	)	)	PUNCT
fumecheng-7267	129	92	<	<	X
fumecheng-7267	129	93	0.000000001	0.000000001	NUM
fumecheng-7267	129	94	wxcont	wxcont	NOUN
fumecheng-7267	129	95	=	=	SYM
fumecheng-7267	129	96	wx	wx	PROPN
fumecheng-7267	129	97	l	l	NOUN
fumecheng-7267	129	98	=	=	SYM
fumecheng-7267	129	99	wx	wx	PROPN
fumecheng-7267	129	100	∗	∗	NOUN
fumecheng-7267	129	101	exp(wx	exp(wx	NOUN
fumecheng-7267	129	102	)	)	PUNCT
fumecheng-7267	129	103	–	–	PUNCT
fumecheng-7267	130	1	x	x	X
fumecheng-7267	130	2	lprim	lprim	NOUN
fumecheng-7267	130	3	=	=	SYM
fumecheng-7267	130	4	exp(wx	exp(wx	NOUN
fumecheng-7267	130	5	)	)	PUNCT
fumecheng-7267	130	6	∗	∗	NOUN
fumecheng-7267	130	7	(	(	PUNCT
fumecheng-7267	130	8	wx	wx	PROPN
fumecheng-7267	130	9	+	+	CCONJ
fumecheng-7267	130	10	1	1	X
fumecheng-7267	130	11	)	)	PUNCT
fumecheng-7267	130	12	lsec	lsec	ADJ
fumecheng-7267	130	13	=	=	SYM
fumecheng-7267	130	14	exp(wx	exp(wx	NOUN
fumecheng-7267	130	15	)	)	PUNCT
fumecheng-7267	130	16	∗	∗	NOUN
fumecheng-7267	130	17	(	(	PUNCT
fumecheng-7267	130	18	wx	wx	PROPN
fumecheng-7267	130	19	+	+	CCONJ
fumecheng-7267	130	20	2	2	X
fumecheng-7267	130	21	)	)	PUNCT
fumecheng-7267	130	22	wx	wx	PROPN
fumecheng-7267	130	23	=	=	SYM
fumecheng-7267	130	24	wx	wx	PROPN
fumecheng-7267	130	25	−	−	PROPN
fumecheng-7267	130	26	l	l	NOUN
fumecheng-7267	130	27	/	/	SYM
fumecheng-7267	130	28	(	(	PUNCT
fumecheng-7267	130	29	lprim	lprim	NOUN
fumecheng-7267	130	30	−	−	X
fumecheng-7267	130	31	(	(	PUNCT
fumecheng-7267	130	32	l	l	NOUN
fumecheng-7267	130	33	∗	∗	X
fumecheng-7267	130	34	lsec	lsec	PROPN
fumecheng-7267	130	35	/	/	SYM
fumecheng-7267	130	36	(	(	PUNCT
fumecheng-7267	130	37	2	2	NUM
fumecheng-7267	130	38	∗	∗	NOUN
fumecheng-7267	130	39	lprim	lprim	NOUN
fumecheng-7267	130	40	)	)	PUNCT
fumecheng-7267	130	41	)	)	PUNCT
fumecheng-7267	130	42	)	)	PUNCT
fumecheng-7267	130	43	loop	loop	NOUN
fumecheng-7267	130	44	lambert	lambert	PROPN
fumecheng-7267	130	45	=	=	SYM
fumecheng-7267	130	46	wx	wx	PROPN
fumecheng-7267	130	47	end	end	NOUN
fumecheng-7267	130	48	function	function	NOUN
fumecheng-7267	130	49	3.2	3.2	NUM
fumecheng-7267	130	50	.	.	PUNCT
fumecheng-7267	131	1	explicit	explicit	ADJ
fumecheng-7267	131	2	approximations	approximation	NOUN
fumecheng-7267	131	3	of	of	ADP
fumecheng-7267	131	4	the	the	DET
fumecheng-7267	131	5	colebrook	colebrook	PROPN
fumecheng-7267	131	6	equation	equation	NOUN
fumecheng-7267	131	7	explicit	explicit	ADJ
fumecheng-7267	131	8	approximations	approximation	NOUN
fumecheng-7267	131	9	of	of	ADP
fumecheng-7267	131	10	the	the	DET
fumecheng-7267	131	11	colebrook	colebrook	PROPN
fumecheng-7267	131	12	equation	equation	NOUN
fumecheng-7267	131	13	which	which	PRON
fumecheng-7267	131	14	introduce	introduce	VERB
fumecheng-7267	131	15	a	a	DET
fumecheng-7267	131	16	maximal	maximal	ADJ
fumecheng-7267	131	17	relative	relative	ADJ
fumecheng-7267	131	18	error	error	NOUN
fumecheng-7267	131	19	less	less	ADJ
fumecheng-7267	131	20	than	than	ADP
fumecheng-7267	131	21	0.1	0.1	NUM
fumecheng-7267	131	22	%	%	NOUN
fumecheng-7267	131	23	are	be	AUX
fumecheng-7267	131	24	given	give	VERB
fumecheng-7267	131	25	in	in	ADP
fumecheng-7267	131	26	table	table	NOUN
fumecheng-7267	131	27	1	1	NUM
fumecheng-7267	131	28	.	.	X
fumecheng-7267	131	29	four	four	NUM
fumecheng-7267	131	30	of	of	ADP
fumecheng-7267	131	31	them	they	PRON
fumecheng-7267	131	32	,	,	PUNCT
fumecheng-7267	131	33	praks	prak	NOUN
fumecheng-7267	131	34	and	and	CCONJ
fumecheng-7267	131	35	brkić	brkić	ADV
fumecheng-7267	131	36	based	base	VERB
fumecheng-7267	131	37	on	on	ADP
fumecheng-7267	131	38	symbolic	symbolic	ADJ
fumecheng-7267	131	39	regression	regression	NOUN
fumecheng-7267	131	40	and	and	CCONJ
fumecheng-7267	131	41	on	on	ADP
fumecheng-7267	131	42	the	the	DET
fumecheng-7267	131	43	wright	wright	PROPN
fumecheng-7267	131	44	ω	ω	PROPN
fumecheng-7267	131	45	-	-	PUNCT
fumecheng-7267	131	46	function	function	NOUN
fumecheng-7267	131	47	[	[	X
fumecheng-7267	131	48	23	23	NUM
fumecheng-7267	131	49	]	]	PUNCT
fumecheng-7267	131	50	,	,	PUNCT
fumecheng-7267	131	51	serghides	serghide	VERB
fumecheng-7267	131	52	[	[	X
fumecheng-7267	131	53	29	29	NUM
fumecheng-7267	131	54	]	]	PUNCT
fumecheng-7267	131	55	,	,	PUNCT
fumecheng-7267	131	56	vatankhah	vatankhah	PROPN
fumecheng-7267	132	1	[	[	X
fumecheng-7267	132	2	25	25	NUM
fumecheng-7267	132	3	]	]	PUNCT
fumecheng-7267	132	4	and	and	CCONJ
fumecheng-7267	132	5	romeo	romeo	PROPN
fumecheng-7267	132	6	et	et	PROPN
fumecheng-7267	132	7	al	al	PROPN
fumecheng-7267	132	8	.	.	PUNCT
fumecheng-7267	133	1	[	[	X
fumecheng-7267	133	2	28	28	NUM
fumecheng-7267	133	3	]	]	PUNCT
fumecheng-7267	133	4	,	,	PUNCT
fumecheng-7267	133	5	introduce	introduce	VERB
fumecheng-7267	133	6	a	a	DET
fumecheng-7267	133	7	relative	relative	ADJ
fumecheng-7267	133	8	error	error	NOUN
fumecheng-7267	133	9	of	of	ADP
fumecheng-7267	133	10	less	less	ADJ
fumecheng-7267	133	11	than	than	ADP
fumecheng-7267	133	12	0.01	0.01	NUM
fumecheng-7267	133	13	%	%	NOUN
fumecheng-7267	133	14	and	and	CCONJ
fumecheng-7267	133	15	can	can	AUX
fumecheng-7267	133	16	be	be	AUX
fumecheng-7267	133	17	classified	classify	VERB
fumecheng-7267	133	18	as	as	ADP
fumecheng-7267	133	19	extremely	extremely	ADV
fumecheng-7267	133	20	accurate	accurate	ADJ
fumecheng-7267	133	21	,	,	PUNCT
fumecheng-7267	133	22	while	while	SCONJ
fumecheng-7267	133	23	those	those	DET
fumecheng-7267	133	24	five	five	NUM
fumecheng-7267	133	25	,	,	PUNCT
fumecheng-7267	133	26	buzzelli	buzzelli	PROPN
fumecheng-7267	134	1	[	[	X
fumecheng-7267	134	2	27	27	NUM
fumecheng-7267	134	3	]	]	PUNCT
fumecheng-7267	134	4	,	,	PUNCT
fumecheng-7267	134	5	praks	prak	NOUN
fumecheng-7267	134	6	and	and	CCONJ
fumecheng-7267	134	7	brkić	brkić	ADV
fumecheng-7267	134	8	based	base	VERB
fumecheng-7267	134	9	on	on	ADP
fumecheng-7267	134	10	series	series	NOUN
fumecheng-7267	134	11	expansion	expansion	NOUN
fumecheng-7267	134	12	of	of	ADP
fumecheng-7267	134	13	the	the	DET
fumecheng-7267	134	14	262	262	NUM
fumecheng-7267	134	15	d.	d.	PROPN
fumecheng-7267	134	16	brkić	brkić	PROPN
fumecheng-7267	134	17	,	,	PUNCT
fumecheng-7267	134	18	z.	z.	PROPN
fumecheng-7267	134	19	stajić	stajić	PROPN
fumecheng-7267	134	20	wright	wright	PROPN
fumecheng-7267	134	21	ω	ω	PROPN
fumecheng-7267	134	22	-	-	PUNCT
fumecheng-7267	134	23	function	function	NOUN
fumecheng-7267	134	24	[	[	X
fumecheng-7267	134	25	23	23	NUM
fumecheng-7267	134	26	]	]	PUNCT
fumecheng-7267	134	27	,	,	PUNCT
fumecheng-7267	134	28	offor	offor	ADV
fumecheng-7267	134	29	and	and	CCONJ
fumecheng-7267	134	30	alabi	alabi	NOUN
fumecheng-7267	135	1	[	[	X
fumecheng-7267	135	2	26	26	NUM
fumecheng-7267	135	3	]	]	PUNCT
fumecheng-7267	135	4	,	,	PUNCT
fumecheng-7267	135	5	shacham	shacham	PROPN
fumecheng-7267	136	1	[	[	X
fumecheng-7267	136	2	30	30	NUM
fumecheng-7267	136	3	]	]	PUNCT
fumecheng-7267	136	4	and	and	CCONJ
fumecheng-7267	136	5	lamri	lamri	NOUN
fumecheng-7267	137	1	[	[	X
fumecheng-7267	137	2	24	24	NUM
fumecheng-7267	137	3	]	]	PUNCT
fumecheng-7267	137	4	,	,	PUNCT
fumecheng-7267	137	5	with	with	ADP
fumecheng-7267	137	6	the	the	DET
fumecheng-7267	137	7	maximal	maximal	ADJ
fumecheng-7267	137	8	relative	relative	ADJ
fumecheng-7267	137	9	error	error	NOUN
fumecheng-7267	137	10	between	between	ADP
fumecheng-7267	137	11	0.01	0.01	NUM
fumecheng-7267	137	12	%	%	NOUN
fumecheng-7267	137	13	and	and	CCONJ
fumecheng-7267	137	14	0.1	0.1	NUM
fumecheng-7267	137	15	%	%	NOUN
fumecheng-7267	137	16	can	can	AUX
fumecheng-7267	137	17	be	be	AUX
fumecheng-7267	137	18	classified	classify	VERB
fumecheng-7267	137	19	as	as	ADP
fumecheng-7267	137	20	very	very	ADV
fumecheng-7267	137	21	accurate	accurate	ADJ
fumecheng-7267	137	22	approximations	approximation	NOUN
fumecheng-7267	137	23	.	.	PUNCT
fumecheng-7267	138	1	algorithms	algorithm	NOUN
fumecheng-7267	138	2	and	and	CCONJ
fumecheng-7267	138	3	vba	vba	NOUN
fumecheng-7267	138	4	codes	code	NOUN
fumecheng-7267	138	5	are	be	AUX
fumecheng-7267	138	6	given	give	VERB
fumecheng-7267	138	7	here	here	ADV
fumecheng-7267	138	8	only	only	ADV
fumecheng-7267	138	9	for	for	ADP
fumecheng-7267	138	10	extremely	extremely	ADV
fumecheng-7267	138	11	accurate	accurate	ADJ
fumecheng-7267	138	12	approximations	approximation	NOUN
fumecheng-7267	138	13	while	while	SCONJ
fumecheng-7267	138	14	coding	code	VERB
fumecheng-7267	138	15	of	of	ADP
fumecheng-7267	138	16	the	the	DET
fumecheng-7267	138	17	further	further	ADJ
fumecheng-7267	138	18	approximations	approximation	NOUN
fumecheng-7267	138	19	is	be	AUX
fumecheng-7267	138	20	not	not	PART
fumecheng-7267	138	21	shown	show	VERB
fumecheng-7267	138	22	[	[	PUNCT
fumecheng-7267	138	23	44	44	NUM
fumecheng-7267	138	24	]	]	PUNCT
fumecheng-7267	138	25	.	.	PUNCT
fumecheng-7267	139	1	3.2.1	3.2.1	NUM
fumecheng-7267	139	2	.	.	PUNCT
fumecheng-7267	140	1	praks	prak	NOUN
fumecheng-7267	140	2	and	and	CCONJ
fumecheng-7267	140	3	brkić	brkić	ADJ
fumecheng-7267	140	4	approximation	approximation	NOUN
fumecheng-7267	140	5	based	base	VERB
fumecheng-7267	140	6	on	on	ADP
fumecheng-7267	140	7	the	the	DET
fumecheng-7267	140	8	wright	wright	PROPN
fumecheng-7267	140	9	ω	ω	PROPN
fumecheng-7267	140	10	-	-	PUNCT
fumecheng-7267	140	11	function	function	PROPN
fumecheng-7267	140	12	and	and	CCONJ
fumecheng-7267	140	13	symbolic	symbolic	ADJ
fumecheng-7267	140	14	regression	regression	NOUN
fumecheng-7267	140	15	praks	prak	NOUN
fumecheng-7267	140	16	and	and	CCONJ
fumecheng-7267	140	17	brkić	brkić	ADJ
fumecheng-7267	140	18	approximation	approximation	NOUN
fumecheng-7267	140	19	[	[	X
fumecheng-7267	140	20	23	23	NUM
fumecheng-7267	140	21	]	]	PUNCT
fumecheng-7267	140	22	,	,	PUNCT
fumecheng-7267	140	23	given	give	VERB
fumecheng-7267	140	24	in	in	ADP
fumecheng-7267	140	25	eq	eq	ADP
fumecheng-7267	140	26	.	.	PUNCT
fumecheng-7267	141	1	(	(	PUNCT
fumecheng-7267	141	2	4	4	NUM
fumecheng-7267	141	3	)	)	PUNCT
fumecheng-7267	141	4	with	with	ADP
fumecheng-7267	141	5	the	the	DET
fumecheng-7267	141	6	algorithm	algorithm	NOUN
fumecheng-7267	141	7	in	in	ADP
fumecheng-7267	141	8	fig	fig	NOUN
fumecheng-7267	141	9	.	.	PUNCT
fumecheng-7267	142	1	7	7	NUM
fumecheng-7267	142	2	,	,	PUNCT
fumecheng-7267	142	3	is	be	AUX
fumecheng-7267	142	4	based	base	VERB
fumecheng-7267	142	5	on	on	ADP
fumecheng-7267	142	6	the	the	DET
fumecheng-7267	142	7	wright	wright	PROPN
fumecheng-7267	142	8	ω	ω	PROPN
fumecheng-7267	142	9	-	-	PUNCT
fumecheng-7267	142	10	function	function	NOUN
fumecheng-7267	142	11	and	and	CCONJ
fumecheng-7267	142	12	on	on	ADP
fumecheng-7267	142	13	symbolic	symbolic	ADJ
fumecheng-7267	142	14	regression	regression	NOUN
fumecheng-7267	142	15	.	.	PUNCT
fumecheng-7267	143	1	the	the	DET
fumecheng-7267	143	2	wright	wright	PROPN
fumecheng-7267	143	3	ω	ω	PROPN
fumecheng-7267	143	4	-	-	PUNCT
fumecheng-7267	143	5	function	function	NOUN
fumecheng-7267	143	6	is	be	AUX
fumecheng-7267	143	7	a	a	DET
fumecheng-7267	143	8	cognate	cognate	NOUN
fumecheng-7267	143	9	of	of	ADP
fumecheng-7267	143	10	the	the	DET
fumecheng-7267	143	11	lambert	lambert	PROPN
fumecheng-7267	143	12	w	w	PROPN
fumecheng-7267	143	13	-	-	PUNCT
fumecheng-7267	143	14	function	function	NOUN
fumecheng-7267	143	15	where	where	SCONJ
fumecheng-7267	143	16	w(ex)-x	w(ex)-x	NOUN
fumecheng-7267	143	17	=	=	SYM
fumecheng-7267	143	18	ω(x)-x	ω(x)-x	NUM
fumecheng-7267	143	19	,	,	PUNCT
fumecheng-7267	143	20	which	which	PRON
fumecheng-7267	143	21	is	be	AUX
fumecheng-7267	143	22	used	use	VERB
fumecheng-7267	143	23	to	to	PART
fumecheng-7267	143	24	eliminate	eliminate	VERB
fumecheng-7267	143	25	fastgrowing	fastgrowe	VERB
fumecheng-7267	143	26	term	term	NOUN
fumecheng-7267	143	27	ex	ex	NOUN
fumecheng-7267	143	28	from	from	ADP
fumecheng-7267	143	29	calculation	calculation	NOUN
fumecheng-7267	143	30	.	.	PUNCT
fumecheng-7267	144	1	the	the	DET
fumecheng-7267	144	2	shown	show	VERB
fumecheng-7267	144	3	approximation	approximation	NOUN
fumecheng-7267	144	4	y	y	PROPN
fumecheng-7267	144	5	of	of	ADP
fumecheng-7267	144	6	ω(x)-x	ω(x)-x	NOUN
fumecheng-7267	144	7	is	be	AUX
fumecheng-7267	144	8	very	very	ADV
fumecheng-7267	144	9	accurate	accurate	ADJ
fumecheng-7267	144	10	within	within	ADP
fumecheng-7267	144	11	the	the	DET
fumecheng-7267	144	12	domain	domain	NOUN
fumecheng-7267	144	13	valid	valid	NOUN
fumecheng-7267	144	14	for	for	ADP
fumecheng-7267	144	15	the	the	DET
fumecheng-7267	144	16	colebrook	colebrook	PROPN
fumecheng-7267	144	17	equation	equation	NOUN
fumecheng-7267	144	18	,	,	PUNCT
fumecheng-7267	144	19	i.e.	i.e.	X
fumecheng-7267	144	20	,	,	PUNCT
fumecheng-7267	144	21	between	between	ADP
fumecheng-7267	144	22	7.51	7.51	NUM
fumecheng-7267	144	23	<	<	NOUN
fumecheng-7267	144	24	x<619	x<619	PROPN
fumecheng-7267	145	1	(	(	PUNCT
fumecheng-7267	145	2	symbolic	symbolic	ADJ
fumecheng-7267	145	3	regression	regression	NOUN
fumecheng-7267	145	4	is	be	AUX
fumecheng-7267	145	5	used	use	VERB
fumecheng-7267	145	6	to	to	PART
fumecheng-7267	145	7	approximate	approximate	VERB
fumecheng-7267	145	8	ω(x)-x	ω(x)-x	NOUN
fumecheng-7267	145	9	in	in	ADP
fumecheng-7267	145	10	this	this	DET
fumecheng-7267	145	11	domain	domain	NOUN
fumecheng-7267	145	12	)	)	PUNCT
fumecheng-7267	145	13	.	.	PUNCT
fumecheng-7267	146	1	1	1	NUM
fumecheng-7267	146	2	√f	√f	PRON
fumecheng-7267	146	3	≈	≈	PROPN
fumecheng-7267	146	4	0.8685972	0.8685972	NUM
fumecheng-7267	146	5	·	·	PUNCT
fumecheng-7267	146	6	(	(	PUNCT
fumecheng-7267	146	7	b	b	X
fumecheng-7267	146	8	+	+	CCONJ
fumecheng-7267	146	9	y	y	NOUN
fumecheng-7267	146	10	)	)	PUNCT
fumecheng-7267	147	1	a	a	PRON
fumecheng-7267	147	2	≈	≈	PROPN
fumecheng-7267	147	3	re·ε	re·ε	PROPN
fumecheng-7267	147	4	8.0897	8.0897	NUM
fumecheng-7267	147	5	b	b	PROPN
fumecheng-7267	147	6	≈	≈	PROPN
fumecheng-7267	147	7	ln(re	ln(re	PROPN
fumecheng-7267	147	8	)	)	PUNCT
fumecheng-7267	147	9	−0.779626	−0.779626	X
fumecheng-7267	148	1	x	x	X
fumecheng-7267	149	1	≈	≈	NOUN
fumecheng-7267	149	2	a	a	DET
fumecheng-7267	149	3	+	+	X
fumecheng-7267	149	4	b	b	PROPN
fumecheng-7267	149	5	c	c	X
fumecheng-7267	149	6	≈	≈	PROPN
fumecheng-7267	149	7	ln(x	ln(x	X
fumecheng-7267	149	8	)	)	PUNCT
fumecheng-7267	150	1	y	y	PROPN
fumecheng-7267	151	1	≈	≈	PROPN
fumecheng-7267	151	2	c	c	PROPN
fumecheng-7267	151	3	x−0.5588·c+1.2079	x−0.5588·c+1.2079	PROPN
fumecheng-7267	152	1	−	−	PROPN
fumecheng-7267	152	2	c	c	NOUN
fumecheng-7267	152	3	}	}	PUNCT
fumecheng-7267	152	4	(	(	PUNCT
fumecheng-7267	152	5	4	4	X
fumecheng-7267	152	6	)	)	PUNCT
fumecheng-7267	152	7	yes	yes	INTJ
fumecheng-7267	153	1	no	no	DET
fumecheng-7267	153	2	error	error	NOUN
fumecheng-7267	153	3	praks	prak	NOUN
fumecheng-7267	153	4	and	and	CCONJ
fumecheng-7267	153	5	brkić	brkić	ADJ
fumecheng-7267	153	6	(	(	PUNCT
fumecheng-7267	153	7	symbolic	symbolic	ADJ
fumecheng-7267	153	8	regression	regression	NOUN
fumecheng-7267	153	9	)	)	PUNCT
fumecheng-7267	154	1	eq	eq	ADP
fumecheng-7267	154	2	.	.	PUNCT
fumecheng-7267	155	1	(	(	PUNCT
fumecheng-7267	155	2	4	4	X
fumecheng-7267	155	3	)	)	PUNCT
fumecheng-7267	155	4	fig	fig	NOUN
fumecheng-7267	155	5	.	.	PUNCT
fumecheng-7267	156	1	7	7	NUM
fumecheng-7267	156	2	algorithm	algorithm	NOUN
fumecheng-7267	156	3	for	for	ADP
fumecheng-7267	156	4	the	the	DET
fumecheng-7267	156	5	praks	praks	NOUN
fumecheng-7267	156	6	-	-	PUNCT
fumecheng-7267	156	7	brkić	brkić	NOUN
fumecheng-7267	156	8	(	(	PUNCT
fumecheng-7267	156	9	symbolic	symbolic	ADJ
fumecheng-7267	156	10	regression	regression	NOUN
fumecheng-7267	156	11	)	)	PUNCT
fumecheng-7267	156	12	approximation	approximation	NOUN
fumecheng-7267	156	13	excel	excel	VERB
fumecheng-7267	156	14	vba	vba	PROPN
fumecheng-7267	156	15	-	-	PUNCT
fumecheng-7267	156	16	based	base	VERB
fumecheng-7267	156	17	user	user	NOUN
fumecheng-7267	156	18	defined	define	VERB
fumecheng-7267	156	19	functions	function	NOUN
fumecheng-7267	156	20	for	for	ADP
fumecheng-7267	156	21	highly	highly	ADV
fumecheng-7267	156	22	precise	precise	ADJ
fumecheng-7267	156	23	colebrook	colebrook	PROPN
fumecheng-7267	156	24	’s	’s	PART
fumecheng-7267	156	25	pipe	pipe	NOUN
fumecheng-7267	156	26	flow	flow	NOUN
fumecheng-7267	156	27	friction	friction	NOUN
fumecheng-7267	156	28	...	...	PUNCT
fumecheng-7267	157	1	263	263	NUM
fumecheng-7267	157	2	the	the	DET
fumecheng-7267	157	3	vba	vba	PROPN
fumecheng-7267	157	4	code	code	NOUN
fumecheng-7267	157	5	based	base	VERB
fumecheng-7267	157	6	on	on	ADP
fumecheng-7267	157	7	algorithm	algorithm	NOUN
fumecheng-7267	157	8	from	from	ADP
fumecheng-7267	157	9	fig	fig	NOUN
fumecheng-7267	157	10	.	.	PUNCT
fumecheng-7267	158	1	7	7	NUM
fumecheng-7267	158	2	is	be	AUX
fumecheng-7267	158	3	given	give	VERB
fumecheng-7267	158	4	as	as	ADP
fumecheng-7267	158	5	:	:	PUNCT
fumecheng-7267	158	6	function	function	NOUN
fumecheng-7267	158	7	praksbrkic(reynolds	praksbrkic(reynold	NOUN
fumecheng-7267	158	8	as	as	ADV
fumecheng-7267	158	9	double	double	ADJ
fumecheng-7267	158	10	,	,	PUNCT
fumecheng-7267	158	11	epsilon	epsilon	PROPN
fumecheng-7267	158	12	as	as	ADV
fumecheng-7267	158	13	double	double	ADJ
fumecheng-7267	158	14	)	)	PUNCT
fumecheng-7267	158	15	as	as	ADV
fumecheng-7267	158	16	double	double	ADJ
fumecheng-7267	158	17	dim	dim	NOUN
fumecheng-7267	158	18	a	a	DET
fumecheng-7267	158	19	,	,	PUNCT
fumecheng-7267	158	20	b	b	NOUN
fumecheng-7267	158	21	,	,	PUNCT
fumecheng-7267	158	22	x	x	NOUN
fumecheng-7267	158	23	,	,	PUNCT
fumecheng-7267	158	24	c	c	X
fumecheng-7267	158	25	,	,	PUNCT
fumecheng-7267	158	26	y	y	PROPN
fumecheng-7267	158	27	,	,	PUNCT
fumecheng-7267	158	28	f	f	PROPN
fumecheng-7267	158	29	as	as	ADV
fumecheng-7267	158	30	double	double	ADV
fumecheng-7267	158	31	if	if	SCONJ
fumecheng-7267	158	32	reynolds	reynold	NOUN
fumecheng-7267	158	33	<	<	X
fumecheng-7267	158	34	2320	2320	NUM
fumecheng-7267	158	35	or	or	CCONJ
fumecheng-7267	158	36	reynolds	reynold	NOUN
fumecheng-7267	158	37	>	>	X
fumecheng-7267	158	38	100000000	100000000	NUM
fumecheng-7267	158	39	#	#	NOUN
fumecheng-7267	158	40	or	or	CCONJ
fumecheng-7267	158	41	epsilon	epsilon	PROPN
fumecheng-7267	158	42	<	<	X
fumecheng-7267	158	43	0	0	NUM
fumecheng-7267	158	44	or	or	CCONJ
fumecheng-7267	158	45	epsilon	epsilon	PROPN
fumecheng-7267	158	46	>	>	X
fumecheng-7267	158	47	0.05	0.05	NUM
fumecheng-7267	158	48	then	then	ADV
fumecheng-7267	158	49	praksbrkic	praksbrkic	PROPN
fumecheng-7267	158	50	=	=	SYM
fumecheng-7267	158	51	cverr(xlerrvalue	cverr(xlerrvalue	PROPN
fumecheng-7267	158	52	)	)	PUNCT
fumecheng-7267	158	53	exit	exit	NOUN
fumecheng-7267	158	54	function	function	NOUN
fumecheng-7267	158	55	end	end	VERB
fumecheng-7267	158	56	if	if	SCONJ
fumecheng-7267	158	57	a	a	DET
fumecheng-7267	158	58	=	=	PUNCT
fumecheng-7267	158	59	reynolds	reynolds	PROPN
fumecheng-7267	158	60	∗	∗	PROPN
fumecheng-7267	158	61	epsilon	epsilon	PROPN
fumecheng-7267	158	62	/	/	SYM
fumecheng-7267	158	63	8.0897	8.0897	NUM
fumecheng-7267	158	64	b	b	X
fumecheng-7267	158	65	=	=	SYM
fumecheng-7267	158	66	log(reynolds	log(reynolds	PROPN
fumecheng-7267	158	67	)	)	PUNCT
fumecheng-7267	158	68	−	−	PROPN
fumecheng-7267	158	69	0.779626	0.779626	NUM
fumecheng-7267	158	70	x	x	X
fumecheng-7267	158	71	=	=	PUNCT
fumecheng-7267	158	72	a	a	PRON
fumecheng-7267	158	73	+	+	NOUN
fumecheng-7267	158	74	b	b	NOUN
fumecheng-7267	158	75	c	c	NOUN
fumecheng-7267	158	76	=	=	SYM
fumecheng-7267	158	77	log(x	log(x	PROPN
fumecheng-7267	158	78	)	)	PUNCT
fumecheng-7267	158	79	y	y	NOUN
fumecheng-7267	158	80	=	=	PUNCT
fumecheng-7267	158	81	c	c	PROPN
fumecheng-7267	158	82	/	/	SYM
fumecheng-7267	158	83	(	(	PUNCT
fumecheng-7267	158	84	x	x	SYM
fumecheng-7267	158	85	−	−	PROPN
fumecheng-7267	158	86	0.5588	0.5588	NUM
fumecheng-7267	158	87	∗	∗	NOUN
fumecheng-7267	158	88	c	c	NOUN
fumecheng-7267	158	89	+	+	NOUN
fumecheng-7267	158	90	1.2079	1.2079	NUM
fumecheng-7267	158	91	)	)	PUNCT
fumecheng-7267	158	92	−	−	PROPN
fumecheng-7267	159	1	c	c	NOUN
fumecheng-7267	159	2	f	f	NOUN
fumecheng-7267	159	3	=	=	SYM
fumecheng-7267	159	4	(	(	PUNCT
fumecheng-7267	159	5	0.8685972	0.8685972	NUM
fumecheng-7267	159	6	∗	∗	NOUN
fumecheng-7267	159	7	(	(	PUNCT
fumecheng-7267	159	8	b	b	PROPN
fumecheng-7267	159	9	+	+	CCONJ
fumecheng-7267	159	10	y	y	NOUN
fumecheng-7267	159	11	)	)	PUNCT
fumecheng-7267	159	12	)	)	PUNCT
fumecheng-7267	159	13	^	^	PUNCT
fumecheng-7267	159	14	−	−	PROPN
fumecheng-7267	159	15	2	2	NUM
fumecheng-7267	159	16	praksbrkic	praksbrkic	NOUN
fumecheng-7267	159	17	=	=	SYM
fumecheng-7267	159	18	f	f	PROPN
fumecheng-7267	159	19	end	end	VERB
fumecheng-7267	159	20	function	function	NOUN
fumecheng-7267	159	21	3.2.2	3.2.2	NUM
fumecheng-7267	159	22	.	.	PUNCT
fumecheng-7267	160	1	serghides	serghide	NOUN
fumecheng-7267	160	2	approximation	approximation	VERB
fumecheng-7267	160	3	the	the	DET
fumecheng-7267	160	4	serghides	serghide	NOUN
fumecheng-7267	160	5	approximation	approximation	NOUN
fumecheng-7267	160	6	[	[	X
fumecheng-7267	160	7	29	29	NUM
fumecheng-7267	160	8	]	]	PUNCT
fumecheng-7267	160	9	is	be	AUX
fumecheng-7267	160	10	based	base	VERB
fumecheng-7267	160	11	on	on	ADP
fumecheng-7267	160	12	steffensen	steffensen	NOUN
fumecheng-7267	160	13	iterative	iterative	NOUN
fumecheng-7267	160	14	scheme	scheme	NOUN
fumecheng-7267	161	1	[	[	X
fumecheng-7267	161	2	4	4	NUM
fumecheng-7267	161	3	]	]	PUNCT
fumecheng-7267	161	4	,	,	PUNCT
fumecheng-7267	161	5	and	and	CCONJ
fumecheng-7267	161	6	the	the	DET
fumecheng-7267	161	7	shown	show	VERB
fumecheng-7267	161	8	version	version	NOUN
fumecheng-7267	161	9	,	,	PUNCT
fumecheng-7267	161	10	eq	eq	NOUN
fumecheng-7267	161	11	.	.	PUNCT
fumecheng-7267	161	12	(	(	PUNCT
fumecheng-7267	161	13	5	5	X
fumecheng-7267	161	14	)	)	PUNCT
fumecheng-7267	161	15	is	be	AUX
fumecheng-7267	161	16	improved	improve	VERB
fumecheng-7267	161	17	by	by	ADP
fumecheng-7267	161	18	genetic	genetic	ADJ
fumecheng-7267	161	19	algorithms	algorithm	NOUN
fumecheng-7267	161	20	[	[	X
fumecheng-7267	161	21	35,45,46	35,45,46	NOUN
fumecheng-7267	161	22	]	]	PUNCT
fumecheng-7267	161	23	.	.	PUNCT
fumecheng-7267	162	1	it	it	PRON
fumecheng-7267	162	2	is	be	AUX
fumecheng-7267	162	3	given	give	VERB
fumecheng-7267	162	4	in	in	ADP
fumecheng-7267	162	5	eq	eq	ADP
fumecheng-7267	162	6	.	.	PUNCT
fumecheng-7267	163	1	(	(	PUNCT
fumecheng-7267	163	2	5	5	NUM
fumecheng-7267	163	3	)	)	PUNCT
fumecheng-7267	163	4	,	,	PUNCT
fumecheng-7267	163	5	with	with	ADP
fumecheng-7267	163	6	related	related	ADJ
fumecheng-7267	163	7	algorithm	algorithm	NOUN
fumecheng-7267	163	8	in	in	ADP
fumecheng-7267	163	9	fig	fig	NOUN
fumecheng-7267	163	10	.	.	PUNCT
fumecheng-7267	164	1	8	8	NUM
fumecheng-7267	164	2	.	.	NOUN
fumecheng-7267	164	3	1	1	NUM
fumecheng-7267	164	4	√f	√f	PRON
fumecheng-7267	164	5	≈	≈	PROPN
fumecheng-7267	164	6	a	a	DET
fumecheng-7267	164	7	−	−	PROPN
fumecheng-7267	164	8	(	(	PUNCT
fumecheng-7267	164	9	b−a)2	b−a)2	PROPN
fumecheng-7267	164	10	c−2·b+a	c−2·b+a	PROPN
fumecheng-7267	164	11	a	a	PROPN
fumecheng-7267	164	12	≈	≈	PROPN
fumecheng-7267	165	1	−0.8686	−0.8686	PRON
fumecheng-7267	165	2	·	·	PUNCT
fumecheng-7267	165	3	ln	ln	X
fumecheng-7267	165	4	(	(	PUNCT
fumecheng-7267	165	5	ε	ε	PROPN
fumecheng-7267	165	6	3.71	3.71	NUM
fumecheng-7267	165	7	+	+	NUM
fumecheng-7267	165	8	12.585	12.585	NUM
fumecheng-7267	165	9	re	re	X
fumecheng-7267	165	10	)	)	PUNCT
fumecheng-7267	165	11	b	b	X
fumecheng-7267	166	1	≈	≈	NOUN
fumecheng-7267	166	2	−0.8686	−0.8686	PRON
fumecheng-7267	166	3	·	·	PUNCT
fumecheng-7267	166	4	ln	ln	X
fumecheng-7267	166	5	(	(	PUNCT
fumecheng-7267	166	6	ε	ε	PROPN
fumecheng-7267	166	7	3.71	3.71	NUM
fumecheng-7267	166	8	+	+	CCONJ
fumecheng-7267	166	9	2.51·a	2.51·a	NUM
fumecheng-7267	166	10	re	re	NOUN
fumecheng-7267	166	11	)	)	PUNCT
fumecheng-7267	166	12	c	c	X
fumecheng-7267	167	1	≈	≈	PROPN
fumecheng-7267	167	2	−0.8686	−0.8686	PRON
fumecheng-7267	167	3	·	·	PUNCT
fumecheng-7267	167	4	ln	ln	X
fumecheng-7267	167	5	(	(	PUNCT
fumecheng-7267	167	6	ε	ε	PROPN
fumecheng-7267	167	7	3.71	3.71	NUM
fumecheng-7267	167	8	+	+	NOUN
fumecheng-7267	167	9	2.51·b	2.51·b	NUM
fumecheng-7267	167	10	re	re	NOUN
fumecheng-7267	167	11	)	)	PUNCT
fumecheng-7267	167	12	}	}	PUNCT
fumecheng-7267	167	13	(	(	PUNCT
fumecheng-7267	167	14	5	5	X
fumecheng-7267	167	15	)	)	PUNCT
fumecheng-7267	167	16	yes	yes	INTJ
fumecheng-7267	168	1	no	no	DET
fumecheng-7267	168	2	error	error	NOUN
fumecheng-7267	168	3	serghides	serghide	VERB
fumecheng-7267	168	4	eq	eq	PRON
fumecheng-7267	168	5	.	.	PUNCT
fumecheng-7267	169	1	(	(	PUNCT
fumecheng-7267	169	2	5	5	X
fumecheng-7267	169	3	)	)	PUNCT
fumecheng-7267	169	4	fig	fig	NOUN
fumecheng-7267	169	5	.	.	PUNCT
fumecheng-7267	170	1	8	8	NUM
fumecheng-7267	170	2	algorithm	algorithm	NOUN
fumecheng-7267	170	3	for	for	ADP
fumecheng-7267	170	4	the	the	DET
fumecheng-7267	170	5	serghides	serghide	NOUN
fumecheng-7267	170	6	approximation	approximation	VERB
fumecheng-7267	170	7	264	264	NUM
fumecheng-7267	170	8	d.	d.	PROPN
fumecheng-7267	170	9	brkić	brkić	PROPN
fumecheng-7267	170	10	,	,	PUNCT
fumecheng-7267	170	11	z.	z.	PROPN
fumecheng-7267	170	12	stajić	stajić	PROPN
fumecheng-7267	170	13	the	the	DET
fumecheng-7267	170	14	vba	vba	PROPN
fumecheng-7267	170	15	code	code	NOUN
fumecheng-7267	170	16	based	base	VERB
fumecheng-7267	170	17	on	on	ADP
fumecheng-7267	170	18	algorithm	algorithm	NOUN
fumecheng-7267	170	19	from	from	ADP
fumecheng-7267	170	20	fig	fig	NOUN
fumecheng-7267	170	21	.	.	PUNCT
fumecheng-7267	170	22	8	8	NUM
fumecheng-7267	170	23	is	be	AUX
fumecheng-7267	170	24	given	give	VERB
fumecheng-7267	170	25	as	as	ADP
fumecheng-7267	170	26	:	:	PUNCT
fumecheng-7267	170	27	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	ADJ
fumecheng-7267	170	28	𝑆𝐸𝑅𝐺𝐻𝐼𝐷𝐸𝑆(𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑆𝐸𝑅𝐺𝐻𝐼𝐷𝐸𝑆(𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	NOUN
fumecheng-7267	170	29	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	170	30	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	170	31	,	,	PUNCT
fumecheng-7267	170	32	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	170	33	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	170	34	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	170	35	)	)	PUNCT
fumecheng-7267	171	1	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	171	2	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	171	3	𝐷𝑖𝑚	𝐷𝑖𝑚	PROPN
fumecheng-7267	171	4	𝐴	𝐴	PROPN
fumecheng-7267	171	5	,	,	PUNCT
fumecheng-7267	171	6	𝐵	𝐵	PROPN
fumecheng-7267	171	7	,	,	PUNCT
fumecheng-7267	171	8	𝐶	𝐶	PROPN
fumecheng-7267	171	9	,	,	PUNCT
fumecheng-7267	171	10	𝑓	𝑓	PROPN
fumecheng-7267	171	11	,	,	PUNCT
fumecheng-7267	171	12	𝑙𝑛	𝑙𝑛	NOUN
fumecheng-7267	172	1	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	172	2	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	172	3	𝐼𝑓	𝐼𝑓	PROPN
fumecheng-7267	172	4	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	NOUN
fumecheng-7267	172	5	<	<	X
fumecheng-7267	172	6	2320	2320	NUM
fumecheng-7267	172	7	𝑂𝑟	𝑂𝑟	NOUN
fumecheng-7267	172	8	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	NOUN
fumecheng-7267	172	9	>	>	X
fumecheng-7267	172	10	100000000	100000000	NUM
fumecheng-7267	172	11	#	#	NOUN
fumecheng-7267	172	12	𝑂𝑟	𝑂𝑟	PROPN
fumecheng-7267	172	13	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	172	14	<	<	X
fumecheng-7267	172	15	0	0	PUNCT
fumecheng-7267	173	1	𝑂𝑟	𝑂𝑟	PROPN
fumecheng-7267	173	2	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	173	3	>	>	X
fumecheng-7267	173	4	0.05	0.05	NUM
fumecheng-7267	173	5	𝑇ℎ𝑒𝑛	𝑇ℎ𝑒𝑛	PROPN
fumecheng-7267	173	6	𝑆𝐸𝑅𝐺𝐻𝐼𝐷𝐸𝑆	𝑆𝐸𝑅𝐺𝐻𝐼𝐷𝐸𝑆	PROPN
fumecheng-7267	173	7	=	=	SYM
fumecheng-7267	173	8	𝐶𝑉𝐸𝑟𝑟(𝑥𝑙𝐸𝑟𝑟𝑉𝑎𝑙𝑢𝑒	𝐶𝑉𝐸𝑟𝑟(𝑥𝑙𝐸𝑟𝑟𝑉𝑎𝑙𝑢𝑒	PROPN
fumecheng-7267	173	9	)	)	PUNCT
fumecheng-7267	174	1	𝐸𝑥𝑖𝑡	𝐸𝑥𝑖𝑡	PROPN
fumecheng-7267	174	2	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	PROPN
fumecheng-7267	174	3	𝐸𝑛𝑑	𝐸𝑛𝑑	PROPN
fumecheng-7267	174	4	𝐼𝑓	𝐼𝑓	PROPN
fumecheng-7267	174	5	𝑙𝑛	𝑙𝑛	NOUN
fumecheng-7267	174	6	=	=	SYM
fumecheng-7267	174	7	2	2	NUM
fumecheng-7267	174	8	/	/	SYM
fumecheng-7267	174	9	𝐿𝑜𝑔(10	𝐿𝑜𝑔(10	NOUN
fumecheng-7267	174	10	)	)	PUNCT
fumecheng-7267	174	11	𝐴	𝐴	NOUN
fumecheng-7267	174	12	=	=	PUNCT
fumecheng-7267	174	13	−𝑙𝑛	−𝑙𝑛	PROPN
fumecheng-7267	174	14	∗	∗	NOUN
fumecheng-7267	174	15	𝐿𝑜𝑔(𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐿𝑜𝑔(𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	174	16	/	/	SYM
fumecheng-7267	174	17	3.71	3.71	NUM
fumecheng-7267	174	18	+	+	NUM
fumecheng-7267	174	19	12.585	12.585	NUM
fumecheng-7267	174	20	/	/	SYM
fumecheng-7267	174	21	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	NOUN
fumecheng-7267	174	22	)	)	PUNCT
fumecheng-7267	174	23	𝐵	𝐵	NOUN
fumecheng-7267	174	24	=	=	PUNCT
fumecheng-7267	174	25	−𝑙𝑛	−𝑙𝑛	PROPN
fumecheng-7267	174	26	∗	∗	NOUN
fumecheng-7267	174	27	𝐿𝑜𝑔(𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐿𝑜𝑔(𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	174	28	/	/	SYM
fumecheng-7267	174	29	3.71	3.71	NUM
fumecheng-7267	174	30	+	+	NUM
fumecheng-7267	174	31	2.51	2.51	NUM
fumecheng-7267	174	32	∗	∗	NOUN
fumecheng-7267	174	33	𝐴	𝐴	PROPN
fumecheng-7267	174	34	/	/	SYM
fumecheng-7267	174	35	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	PROPN
fumecheng-7267	174	36	)	)	PUNCT
fumecheng-7267	174	37	𝐶	𝐶	PROPN
fumecheng-7267	174	38	=	=	PUNCT
fumecheng-7267	174	39	−𝑙𝑛	−𝑙𝑛	PROPN
fumecheng-7267	174	40	∗	∗	NOUN
fumecheng-7267	174	41	𝐿𝑜𝑔(𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐿𝑜𝑔(𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	174	42	/	/	SYM
fumecheng-7267	174	43	3.71	3.71	NUM
fumecheng-7267	174	44	+	+	NUM
fumecheng-7267	174	45	2.51	2.51	NUM
fumecheng-7267	174	46	∗	∗	NOUN
fumecheng-7267	174	47	𝐵	𝐵	NOUN
fumecheng-7267	174	48	/	/	SYM
fumecheng-7267	174	49	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	PROPN
fumecheng-7267	174	50	)	)	PUNCT
fumecheng-7267	174	51	𝑓	𝑓	PROPN
fumecheng-7267	174	52	=	=	PUNCT
fumecheng-7267	174	53	𝐴	𝐴	PROPN
fumecheng-7267	174	54	−	−	PROPN
fumecheng-7267	175	1	(	(	PUNCT
fumecheng-7267	175	2	𝐵	𝐵	NOUN
fumecheng-7267	175	3	−	−	PROPN
fumecheng-7267	175	4	𝐴	𝐴	PROPN
fumecheng-7267	175	5	)	)	PUNCT
fumecheng-7267	175	6	^	^	SYM
fumecheng-7267	175	7	2	2	X
fumecheng-7267	175	8	/	/	SYM
fumecheng-7267	175	9	(	(	PUNCT
fumecheng-7267	175	10	𝐶	𝐶	PROPN
fumecheng-7267	175	11	−	−	PROPN
fumecheng-7267	175	12	2	2	NUM
fumecheng-7267	175	13	∗	∗	NOUN
fumecheng-7267	175	14	𝐵	𝐵	NOUN
fumecheng-7267	175	15	+	+	CCONJ
fumecheng-7267	175	16	𝐴	𝐴	PROPN
fumecheng-7267	175	17	)	)	PUNCT
fumecheng-7267	175	18	𝑓	𝑓	PROPN
fumecheng-7267	175	19	=	=	PUNCT
fumecheng-7267	175	20	𝑓	𝑓	PROPN
fumecheng-7267	175	21	^	^	SYM
fumecheng-7267	175	22	−	−	PROPN
fumecheng-7267	175	23	2	2	NUM
fumecheng-7267	175	24	𝑆𝐸𝑅𝐺𝐻𝐼𝐷𝐸𝑆	𝑆𝐸𝑅𝐺𝐻𝐼𝐷𝐸𝑆	NOUN
fumecheng-7267	175	25	=	=	PUNCT
fumecheng-7267	175	26	𝑓	𝑓	PROPN
fumecheng-7267	175	27	𝐸𝑛𝑑	𝐸𝑛𝑑	PROPN
fumecheng-7267	175	28	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	PROPN
fumecheng-7267	175	29	3.2.3	3.2.3	NUM
fumecheng-7267	175	30	.	.	PUNCT
fumecheng-7267	176	1	vatankhah	vatankhah	PROPN
fumecheng-7267	176	2	approximation	approximation	NOUN
fumecheng-7267	176	3	the	the	DET
fumecheng-7267	176	4	vatankhah	vatankhah	PROPN
fumecheng-7267	176	5	approximation	approximation	NOUN
fumecheng-7267	176	6	[	[	X
fumecheng-7267	176	7	25	25	NUM
fumecheng-7267	176	8	]	]	PUNCT
fumecheng-7267	176	9	is	be	AUX
fumecheng-7267	176	10	given	give	VERB
fumecheng-7267	176	11	in	in	ADP
fumecheng-7267	176	12	eq	eq	ADP
fumecheng-7267	176	13	.	.	PUNCT
fumecheng-7267	177	1	(	(	PUNCT
fumecheng-7267	177	2	6	6	NUM
fumecheng-7267	177	3	)	)	PUNCT
fumecheng-7267	177	4	with	with	ADP
fumecheng-7267	177	5	the	the	DET
fumecheng-7267	177	6	related	related	ADJ
fumecheng-7267	177	7	algorithm	algorithm	NOUN
fumecheng-7267	177	8	in	in	ADP
fumecheng-7267	177	9	fig	fig	NOUN
fumecheng-7267	177	10	.	.	PUNCT
fumecheng-7267	178	1	9	9	NUM
fumecheng-7267	178	2	(	(	PUNCT
fumecheng-7267	178	3	few	few	ADJ
fumecheng-7267	178	4	versions	version	NOUN
fumecheng-7267	178	5	of	of	ADP
fumecheng-7267	178	6	this	this	DET
fumecheng-7267	178	7	approximation	approximation	NOUN
fumecheng-7267	178	8	are	be	AUX
fumecheng-7267	178	9	available	available	ADJ
fumecheng-7267	178	10	in	in	ADP
fumecheng-7267	178	11	[	[	X
fumecheng-7267	178	12	25	25	NUM
fumecheng-7267	178	13	]	]	PUNCT
fumecheng-7267	178	14	,	,	PUNCT
fumecheng-7267	178	15	where	where	SCONJ
fumecheng-7267	178	16	for	for	ADP
fumecheng-7267	178	17	one	one	NUM
fumecheng-7267	178	18	of	of	ADP
fumecheng-7267	178	19	those	those	DET
fumecheng-7267	178	20	approximations	approximation	NOUN
fumecheng-7267	178	21	,	,	PUNCT
fumecheng-7267	178	22	brkić	brkić	ADJ
fumecheng-7267	178	23	and	and	CCONJ
fumecheng-7267	178	24	praks	praks	PRON
fumecheng-7267	178	25	[	[	X
fumecheng-7267	178	26	36	36	NUM
fumecheng-7267	178	27	]	]	PUNCT
fumecheng-7267	178	28	estimate	estimate	VERB
fumecheng-7267	178	29	its	its	PRON
fumecheng-7267	178	30	maximal	maximal	ADJ
fumecheng-7267	178	31	relative	relative	ADJ
fumecheng-7267	178	32	error	error	NOUN
fumecheng-7267	178	33	of	of	ADP
fumecheng-7267	178	34	no	no	DET
fumecheng-7267	178	35	more	more	ADJ
fumecheng-7267	178	36	than	than	ADP
fumecheng-7267	178	37	0.0028	0.0028	NUM
fumecheng-7267	178	38	%	%	NOUN
fumecheng-7267	178	39	)	)	PUNCT
fumecheng-7267	178	40	.	.	PUNCT
fumecheng-7267	179	1	this	this	DET
fumecheng-7267	179	2	approximation	approximation	NOUN
fumecheng-7267	179	3	is	be	AUX
fumecheng-7267	179	4	related	relate	VERB
fumecheng-7267	179	5	to	to	ADP
fumecheng-7267	179	6	[	[	X
fumecheng-7267	179	7	47,48	47,48	NOUN
fumecheng-7267	179	8	]	]	SYM
fumecheng-7267	179	9	.	.	PUNCT
fumecheng-7267	180	1	1	1	NUM
fumecheng-7267	180	2	√f	√f	DET
fumecheng-7267	180	3	≈	≈	PROPN
fumecheng-7267	180	4	0.8686	0.8686	NUM
fumecheng-7267	180	5	·	·	PUNCT
fumecheng-7267	180	6	ln	ln	X
fumecheng-7267	180	7	(	(	PUNCT
fumecheng-7267	180	8	0.3984·re	0.3984·re	NUM
fumecheng-7267	180	9	(	(	PUNCT
fumecheng-7267	180	10	0.8686·a	0.8686·a	NOUN
fumecheng-7267	180	11	)	)	PUNCT
fumecheng-7267	180	12	a	a	DET
fumecheng-7267	180	13	a+b	a+b	PROPN
fumecheng-7267	180	14	)	)	PUNCT
fumecheng-7267	180	15	a	a	DET
fumecheng-7267	180	16	≈	≈	PROPN
fumecheng-7267	180	17	0.12363	0.12363	NUM
fumecheng-7267	180	18	·	·	PUNCT
fumecheng-7267	180	19	re	re	X
fumecheng-7267	180	20	·	·	PUNCT
fumecheng-7267	180	21	ε	ε	PROPN
fumecheng-7267	180	22	+	+	CCONJ
fumecheng-7267	180	23	ln(0.3984	ln(0.3984	PROPN
fumecheng-7267	180	24	·	·	PUNCT
fumecheng-7267	180	25	re	re	ADJ
fumecheng-7267	180	26	)	)	PUNCT
fumecheng-7267	180	27	b	b	PROPN
fumecheng-7267	181	1	≈	≈	PROPN
fumecheng-7267	181	2	1	1	NUM
fumecheng-7267	181	3	+	+	CCONJ
fumecheng-7267	181	4	1	1	NUM
fumecheng-7267	181	5	1+a	1+a	NUM
fumecheng-7267	181	6	0.52·ln(0.8686·a	0.52·ln(0.8686·a	NUM
fumecheng-7267	181	7	)	)	PUNCT
fumecheng-7267	181	8	−	−	NOUN
fumecheng-7267	181	9	a	a	PRON
fumecheng-7267	181	10	1+a	1+a	NUM
fumecheng-7267	181	11	}	}	PUNCT
fumecheng-7267	181	12	(	(	PUNCT
fumecheng-7267	181	13	6	6	NUM
fumecheng-7267	181	14	)	)	PUNCT
fumecheng-7267	181	15	yes	yes	INTJ
fumecheng-7267	181	16	no	no	DET
fumecheng-7267	181	17	error	error	NOUN
fumecheng-7267	181	18	vatankhah	vatankhah	NOUN
fumecheng-7267	181	19	eq	eq	ADJ
fumecheng-7267	181	20	.	.	PUNCT
fumecheng-7267	182	1	(	(	PUNCT
fumecheng-7267	182	2	6	6	NUM
fumecheng-7267	182	3	)	)	PUNCT
fumecheng-7267	182	4	fig	fig	NOUN
fumecheng-7267	182	5	.	.	PUNCT
fumecheng-7267	183	1	9	9	NUM
fumecheng-7267	183	2	algorithm	algorithm	NOUN
fumecheng-7267	183	3	for	for	ADP
fumecheng-7267	183	4	the	the	DET
fumecheng-7267	183	5	vatankhah	vatankhah	PROPN
fumecheng-7267	183	6	approximation	approximation	NOUN
fumecheng-7267	183	7	excel	excel	VERB
fumecheng-7267	183	8	vba	vba	PROPN
fumecheng-7267	183	9	-	-	PUNCT
fumecheng-7267	183	10	based	base	VERB
fumecheng-7267	183	11	user	user	NOUN
fumecheng-7267	183	12	defined	define	VERB
fumecheng-7267	183	13	functions	function	NOUN
fumecheng-7267	183	14	for	for	ADP
fumecheng-7267	183	15	highly	highly	ADV
fumecheng-7267	183	16	precise	precise	ADJ
fumecheng-7267	183	17	colebrook	colebrook	PROPN
fumecheng-7267	183	18	’s	’s	PART
fumecheng-7267	183	19	pipe	pipe	NOUN
fumecheng-7267	183	20	flow	flow	NOUN
fumecheng-7267	183	21	friction	friction	NOUN
fumecheng-7267	183	22	...	...	PUNCT
fumecheng-7267	184	1	265	265	NUM
fumecheng-7267	184	2	the	the	DET
fumecheng-7267	184	3	vba	vba	PROPN
fumecheng-7267	184	4	code	code	NOUN
fumecheng-7267	184	5	based	base	VERB
fumecheng-7267	184	6	on	on	ADP
fumecheng-7267	184	7	algorithm	algorithm	NOUN
fumecheng-7267	184	8	from	from	ADP
fumecheng-7267	184	9	fig	fig	NOUN
fumecheng-7267	184	10	.	.	PUNCT
fumecheng-7267	185	1	9	9	NUM
fumecheng-7267	185	2	is	be	AUX
fumecheng-7267	185	3	given	give	VERB
fumecheng-7267	185	4	as	as	ADP
fumecheng-7267	185	5	:	:	PUNCT
fumecheng-7267	185	6	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	PROPN
fumecheng-7267	185	7	𝑉𝐴𝑇𝐴𝑁𝐾𝐻𝐴𝐻(𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑉𝐴𝑇𝐴𝑁𝐾𝐻𝐴𝐻(𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	VERB
fumecheng-7267	185	8	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	185	9	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	185	10	,	,	PUNCT
fumecheng-7267	185	11	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	185	12	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	185	13	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	185	14	)	)	PUNCT
fumecheng-7267	186	1	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	186	2	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	186	3	𝐷𝑖𝑚	𝐷𝑖𝑚	PROPN
fumecheng-7267	186	4	𝐴	𝐴	PROPN
fumecheng-7267	186	5	,	,	PUNCT
fumecheng-7267	186	6	𝐵	𝐵	PROPN
fumecheng-7267	186	7	,	,	PUNCT
fumecheng-7267	186	8	𝑓	𝑓	PROPN
fumecheng-7267	186	9	,	,	PUNCT
fumecheng-7267	186	10	𝑙𝑛	𝑙𝑛	NOUN
fumecheng-7267	187	1	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	187	2	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	187	3	𝐼𝑓	𝐼𝑓	PROPN
fumecheng-7267	187	4	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	NOUN
fumecheng-7267	187	5	<	<	X
fumecheng-7267	187	6	2320	2320	NUM
fumecheng-7267	187	7	𝑂𝑟	𝑂𝑟	NOUN
fumecheng-7267	187	8	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	NOUN
fumecheng-7267	187	9	>	>	X
fumecheng-7267	187	10	100000000	100000000	NUM
fumecheng-7267	187	11	#	#	NOUN
fumecheng-7267	187	12	𝑂𝑟	𝑂𝑟	PROPN
fumecheng-7267	187	13	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	187	14	<	<	X
fumecheng-7267	187	15	0	0	PUNCT
fumecheng-7267	188	1	𝑂𝑟	𝑂𝑟	PROPN
fumecheng-7267	188	2	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	188	3	>	>	X
fumecheng-7267	188	4	0.05	0.05	NUM
fumecheng-7267	188	5	𝑇ℎ𝑒𝑛	𝑇ℎ𝑒𝑛	PROPN
fumecheng-7267	188	6	𝑉𝐴𝑇𝐴𝑁𝐾𝐻𝐴𝐻	𝑉𝐴𝑇𝐴𝑁𝐾𝐻𝐴𝐻	PROPN
fumecheng-7267	188	7	=	=	SYM
fumecheng-7267	188	8	𝐶𝑉𝐸𝑟𝑟(𝑥𝑙𝐸𝑟𝑟𝑉𝑎𝑙𝑢𝑒	𝐶𝑉𝐸𝑟𝑟(𝑥𝑙𝐸𝑟𝑟𝑉𝑎𝑙𝑢𝑒	PROPN
fumecheng-7267	188	9	)	)	PUNCT
fumecheng-7267	189	1	𝐸𝑥𝑖𝑡	𝐸𝑥𝑖𝑡	PROPN
fumecheng-7267	189	2	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	PROPN
fumecheng-7267	189	3	𝐸𝑛𝑑	𝐸𝑛𝑑	PROPN
fumecheng-7267	189	4	𝐼𝑓	𝐼𝑓	PROPN
fumecheng-7267	189	5	𝑙𝑛	𝑙𝑛	NOUN
fumecheng-7267	189	6	=	=	SYM
fumecheng-7267	189	7	2	2	NUM
fumecheng-7267	189	8	/	/	SYM
fumecheng-7267	189	9	𝐿𝑜𝑔(10	𝐿𝑜𝑔(10	NOUN
fumecheng-7267	189	10	)	)	PUNCT
fumecheng-7267	189	11	𝐴	𝐴	NOUN
fumecheng-7267	189	12	=	=	NOUN
fumecheng-7267	189	13	0.12363	0.12363	NUM
fumecheng-7267	189	14	∗	∗	NOUN
fumecheng-7267	189	15	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	NOUN
fumecheng-7267	189	16	∗	∗	NOUN
fumecheng-7267	189	17	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	189	18	+	+	CCONJ
fumecheng-7267	189	19	𝐿𝑜𝑔(0.3984	𝐿𝑜𝑔(0.3984	PROPN
fumecheng-7267	189	20	∗	∗	NOUN
fumecheng-7267	189	21	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	NOUN
fumecheng-7267	189	22	)	)	PUNCT
fumecheng-7267	189	23	𝐵	𝐵	NOUN
fumecheng-7267	189	24	=	=	SYM
fumecheng-7267	189	25	(	(	PUNCT
fumecheng-7267	189	26	(	(	PUNCT
fumecheng-7267	189	27	1	1	NUM
fumecheng-7267	189	28	+	+	NUM
fumecheng-7267	189	29	𝐴	𝐴	PROPN
fumecheng-7267	189	30	)	)	PUNCT
fumecheng-7267	189	31	/	/	PUNCT
fumecheng-7267	189	32	(	(	PUNCT
fumecheng-7267	189	33	0.52	0.52	NUM
fumecheng-7267	189	34	∗	∗	NOUN
fumecheng-7267	189	35	𝐿𝑜𝑔(𝑙𝑛	𝐿𝑜𝑔(𝑙𝑛	PROPN
fumecheng-7267	189	36	∗	∗	NOUN
fumecheng-7267	189	37	𝐴	𝐴	PROPN
fumecheng-7267	189	38	)	)	PUNCT
fumecheng-7267	189	39	)	)	PUNCT
fumecheng-7267	189	40	)	)	PUNCT
fumecheng-7267	190	1	−	−	PROPN
fumecheng-7267	190	2	(	(	PUNCT
fumecheng-7267	190	3	𝐴	𝐴	PROPN
fumecheng-7267	190	4	/	/	SYM
fumecheng-7267	190	5	(	(	PUNCT
fumecheng-7267	190	6	1	1	NUM
fumecheng-7267	190	7	+	+	NUM
fumecheng-7267	190	8	𝐴	𝐴	PROPN
fumecheng-7267	190	9	)	)	PUNCT
fumecheng-7267	190	10	)	)	PUNCT
fumecheng-7267	191	1	𝐵	𝐵	NOUN
fumecheng-7267	191	2	=	=	NOUN
fumecheng-7267	191	3	1	1	NUM
fumecheng-7267	191	4	+	+	CCONJ
fumecheng-7267	191	5	(	(	PUNCT
fumecheng-7267	191	6	1	1	NUM
fumecheng-7267	191	7	/	/	SYM
fumecheng-7267	191	8	𝐵	𝐵	NOUN
fumecheng-7267	191	9	)	)	PUNCT
fumecheng-7267	191	10	𝑓	𝑓	PROPN
fumecheng-7267	191	11	=	=	X
fumecheng-7267	191	12	𝑙𝑛	𝑙𝑛	PROPN
fumecheng-7267	191	13	∗	∗	PROPN
fumecheng-7267	191	14	𝐿𝑜𝑔(0.3984	𝐿𝑜𝑔(0.3984	PROPN
fumecheng-7267	191	15	∗	∗	VERB
fumecheng-7267	191	16	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	PROPN
fumecheng-7267	191	17	/	/	PUNCT
fumecheng-7267	191	18	(	(	PUNCT
fumecheng-7267	191	19	(	(	PUNCT
fumecheng-7267	191	20	𝑙𝑛	𝑙𝑛	PROPN
fumecheng-7267	191	21	∗	∗	PROPN
fumecheng-7267	191	22	𝐴	𝐴	PROPN
fumecheng-7267	191	23	)	)	PUNCT
fumecheng-7267	191	24	^	^	PUNCT
fumecheng-7267	191	25	(	(	PUNCT
fumecheng-7267	191	26	𝐴	𝐴	PROPN
fumecheng-7267	191	27	/	/	SYM
fumecheng-7267	191	28	(	(	PUNCT
fumecheng-7267	191	29	𝐴	𝐴	PROPN
fumecheng-7267	191	30	+	+	CCONJ
fumecheng-7267	191	31	𝐵	𝐵	NOUN
fumecheng-7267	191	32	)	)	PUNCT
fumecheng-7267	191	33	)	)	PUNCT
fumecheng-7267	191	34	)	)	PUNCT
fumecheng-7267	191	35	)	)	PUNCT
fumecheng-7267	192	1	𝑓	𝑓	X
fumecheng-7267	192	2	=	=	SYM
fumecheng-7267	192	3	𝑓	𝑓	X
fumecheng-7267	192	4	^	^	PUNCT
fumecheng-7267	192	5	−	−	PROPN
fumecheng-7267	192	6	2	2	NUM
fumecheng-7267	192	7	𝑉𝐴𝑇𝐴𝑁𝐾𝐻𝐴𝐻	𝑉𝐴𝑇𝐴𝑁𝐾𝐻𝐴𝐻	PROPN
fumecheng-7267	192	8	=	=	SYM
fumecheng-7267	192	9	𝑓	𝑓	PROPN
fumecheng-7267	192	10	𝐸𝑛𝑑	𝐸𝑛𝑑	PROPN
fumecheng-7267	192	11	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	PROPN
fumecheng-7267	192	12	3.2.4	3.2.4	NUM
fumecheng-7267	192	13	.	.	PUNCT
fumecheng-7267	193	1	romeo	romeo	PROPN
fumecheng-7267	193	2	et	et	PROPN
fumecheng-7267	193	3	al	al	PROPN
fumecheng-7267	193	4	.	.	PROPN
fumecheng-7267	193	5	approximation	approximation	NOUN
fumecheng-7267	193	6	the	the	DET
fumecheng-7267	193	7	romeo	romeo	PROPN
fumecheng-7267	193	8	et	et	PROPN
fumecheng-7267	193	9	al	al	PROPN
fumecheng-7267	193	10	.	.	PROPN
fumecheng-7267	193	11	approximation	approximation	NOUN
fumecheng-7267	194	1	[	[	X
fumecheng-7267	194	2	28	28	NUM
fumecheng-7267	194	3	]	]	PUNCT
fumecheng-7267	194	4	is	be	AUX
fumecheng-7267	194	5	given	give	VERB
fumecheng-7267	194	6	in	in	ADP
fumecheng-7267	194	7	eq	eq	ADP
fumecheng-7267	194	8	.	.	PUNCT
fumecheng-7267	195	1	(	(	PUNCT
fumecheng-7267	195	2	7	7	NUM
fumecheng-7267	195	3	)	)	PUNCT
fumecheng-7267	195	4	with	with	ADP
fumecheng-7267	195	5	the	the	DET
fumecheng-7267	195	6	related	related	ADJ
fumecheng-7267	195	7	algorithm	algorithm	NOUN
fumecheng-7267	195	8	in	in	ADP
fumecheng-7267	195	9	fig	fig	NOUN
fumecheng-7267	195	10	.	.	PUNCT
fumecheng-7267	196	1	10	10	NUM
fumecheng-7267	196	2	.	.	PUNCT
fumecheng-7267	197	1	eq	eq	ADP
fumecheng-7267	197	2	.	.	PUNCT
fumecheng-7267	198	1	(	(	PUNCT
fumecheng-7267	198	2	7	7	X
fumecheng-7267	198	3	)	)	PUNCT
fumecheng-7267	198	4	is	be	AUX
fumecheng-7267	198	5	improved	improve	VERB
fumecheng-7267	198	6	by	by	ADP
fumecheng-7267	198	7	genetic	genetic	ADJ
fumecheng-7267	198	8	algorithms	algorithm	NOUN
fumecheng-7267	199	1	[	[	X
fumecheng-7267	199	2	35,45,46	35,45,46	NOUN
fumecheng-7267	199	3	]	]	PUNCT
fumecheng-7267	199	4	.	.	PUNCT
fumecheng-7267	200	1	1	1	NUM
fumecheng-7267	200	2	√f	√f	PRON
fumecheng-7267	200	3	≈	≈	PROPN
fumecheng-7267	200	4	−0.8686	−0.8686	PRON
fumecheng-7267	200	5	·	·	PUNCT
fumecheng-7267	200	6	ln	ln	X
fumecheng-7267	200	7	(	(	PUNCT
fumecheng-7267	200	8	ε	ε	PROPN
fumecheng-7267	200	9	3.7106	3.7106	NUM
fumecheng-7267	200	10	−	−	NOUN
fumecheng-7267	200	11	5·b	5·b	NUM
fumecheng-7267	200	12	re	re	NOUN
fumecheng-7267	200	13	)	)	PUNCT
fumecheng-7267	200	14	a	a	PRON
fumecheng-7267	201	1	≈	≈	PROPN
fumecheng-7267	201	2	0.4343	0.4343	PROPN
fumecheng-7267	201	3	·	·	PUNCT
fumecheng-7267	202	1	ln	ln	X
fumecheng-7267	202	2	(	(	PUNCT
fumecheng-7267	202	3	(	(	PUNCT
fumecheng-7267	202	4	ε	ε	PROPN
fumecheng-7267	202	5	7.646	7.646	NUM
fumecheng-7267	202	6	)	)	PUNCT
fumecheng-7267	202	7	0.9685	0.9685	NUM
fumecheng-7267	202	8	+	+	CCONJ
fumecheng-7267	202	9	(	(	PUNCT
fumecheng-7267	202	10	4.9755	4.9755	NUM
fumecheng-7267	202	11	206.2795+re	206.2795+re	NUM
fumecheng-7267	202	12	)	)	PUNCT
fumecheng-7267	202	13	0.8759	0.8759	NUM
fumecheng-7267	202	14	)	)	PUNCT
fumecheng-7267	202	15	b	b	PROPN
fumecheng-7267	202	16	≈	≈	PROPN
fumecheng-7267	202	17	0.4343	0.4343	PROPN
fumecheng-7267	202	18	·	·	PUNCT
fumecheng-7267	203	1	ln	ln	INTJ
fumecheng-7267	203	2	(	(	PUNCT
fumecheng-7267	203	3	ε	ε	PROPN
fumecheng-7267	203	4	3.8597	3.8597	NUM
fumecheng-7267	203	5	−	−	NOUN
fumecheng-7267	203	6	4.795·a	4.795·a	NOUN
fumecheng-7267	203	7	re	re	NOUN
fumecheng-7267	203	8	)	)	PUNCT
fumecheng-7267	203	9	}	}	PUNCT
fumecheng-7267	203	10	(	(	PUNCT
fumecheng-7267	203	11	7	7	X
fumecheng-7267	203	12	)	)	PUNCT
fumecheng-7267	203	13	yes	yes	INTJ
fumecheng-7267	204	1	no	no	DET
fumecheng-7267	204	2	error	error	NOUN
fumecheng-7267	204	3	romeo	romeo	NOUN
fumecheng-7267	204	4	et	et	PROPN
fumecheng-7267	204	5	al	al	PROPN
fumecheng-7267	204	6	.	.	PROPN
fumecheng-7267	205	1	eq	eq	X
fumecheng-7267	205	2	.	.	PUNCT
fumecheng-7267	206	1	(	(	PUNCT
fumecheng-7267	206	2	7	7	X
fumecheng-7267	206	3	)	)	PUNCT
fumecheng-7267	206	4	fig	fig	NOUN
fumecheng-7267	206	5	.	.	PUNCT
fumecheng-7267	207	1	10	10	NUM
fumecheng-7267	207	2	algorithm	algorithm	NOUN
fumecheng-7267	207	3	for	for	ADP
fumecheng-7267	207	4	the	the	DET
fumecheng-7267	207	5	romeo	romeo	PROPN
fumecheng-7267	207	6	et	et	PROPN
fumecheng-7267	207	7	al	al	PROPN
fumecheng-7267	207	8	.	.	PROPN
fumecheng-7267	207	9	approximation	approximation	NOUN
fumecheng-7267	207	10	the	the	DET
fumecheng-7267	207	11	vba	vba	PROPN
fumecheng-7267	207	12	code	code	NOUN
fumecheng-7267	207	13	based	base	VERB
fumecheng-7267	207	14	on	on	ADP
fumecheng-7267	207	15	algorithm	algorithm	NOUN
fumecheng-7267	207	16	from	from	ADP
fumecheng-7267	207	17	fig	fig	NOUN
fumecheng-7267	207	18	.	.	PUNCT
fumecheng-7267	208	1	10	10	NUM
fumecheng-7267	208	2	is	be	AUX
fumecheng-7267	208	3	given	give	VERB
fumecheng-7267	208	4	as	as	ADP
fumecheng-7267	208	5	:	:	PUNCT
fumecheng-7267	208	6	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	ADJ
fumecheng-7267	208	7	𝑅𝑂𝑀𝐸𝑂(𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝑂𝑀𝐸𝑂(𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	NOUN
fumecheng-7267	208	8	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	208	9	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	208	10	,	,	PUNCT
fumecheng-7267	208	11	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	208	12	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	208	13	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	208	14	)	)	PUNCT
fumecheng-7267	209	1	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	209	2	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	209	3	𝐷𝑖𝑚	𝐷𝑖𝑚	PROPN
fumecheng-7267	209	4	𝐴	𝐴	PROPN
fumecheng-7267	209	5	,	,	PUNCT
fumecheng-7267	209	6	𝐵	𝐵	PROPN
fumecheng-7267	209	7	,	,	PUNCT
fumecheng-7267	209	8	𝑓	𝑓	PROPN
fumecheng-7267	209	9	,	,	PUNCT
fumecheng-7267	209	10	𝑙𝑛	𝑙𝑛	NOUN
fumecheng-7267	210	1	𝐴𝑠	𝐴𝑠	PROPN
fumecheng-7267	210	2	𝐷𝑜𝑢𝑏𝑙𝑒	𝐷𝑜𝑢𝑏𝑙𝑒	PROPN
fumecheng-7267	210	3	𝐼𝑓	𝐼𝑓	PROPN
fumecheng-7267	210	4	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	NOUN
fumecheng-7267	210	5	<	<	X
fumecheng-7267	210	6	2320	2320	NUM
fumecheng-7267	210	7	𝑂𝑟	𝑂𝑟	NOUN
fumecheng-7267	210	8	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	NOUN
fumecheng-7267	210	9	>	>	X
fumecheng-7267	210	10	100000000	100000000	NUM
fumecheng-7267	210	11	#	#	NOUN
fumecheng-7267	210	12	𝑂𝑟	𝑂𝑟	PROPN
fumecheng-7267	210	13	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	210	14	<	<	X
fumecheng-7267	210	15	0	0	PUNCT
fumecheng-7267	211	1	𝑂𝑟	𝑂𝑟	PROPN
fumecheng-7267	211	2	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	211	3	>	>	X
fumecheng-7267	211	4	0.05	0.05	NUM
fumecheng-7267	211	5	𝑇ℎ𝑒𝑛	𝑇ℎ𝑒𝑛	PROPN
fumecheng-7267	211	6	𝑅𝑂𝑀𝐸𝑂	𝑅𝑂𝑀𝐸𝑂	PROPN
fumecheng-7267	211	7	=	=	SYM
fumecheng-7267	211	8	𝐶𝑉𝐸𝑟𝑟(𝑥𝑙𝐸𝑟𝑟𝑉𝑎𝑙𝑢𝑒	𝐶𝑉𝐸𝑟𝑟(𝑥𝑙𝐸𝑟𝑟𝑉𝑎𝑙𝑢𝑒	ADJ
fumecheng-7267	211	9	)	)	PUNCT
fumecheng-7267	212	1	𝐸𝑥𝑖𝑡	𝐸𝑥𝑖𝑡	PROPN
fumecheng-7267	212	2	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	PROPN
fumecheng-7267	212	3	𝐸𝑛𝑑	𝐸𝑛𝑑	PROPN
fumecheng-7267	212	4	𝐼𝑓	𝐼𝑓	PROPN
fumecheng-7267	212	5	𝑙𝑛	𝑙𝑛	NOUN
fumecheng-7267	212	6	=	=	SYM
fumecheng-7267	212	7	1	1	NUM
fumecheng-7267	212	8	/	/	SYM
fumecheng-7267	212	9	𝐿𝑜𝑔(10	𝐿𝑜𝑔(10	ADJ
fumecheng-7267	212	10	)	)	PUNCT
fumecheng-7267	212	11	𝐴	𝐴	NOUN
fumecheng-7267	212	12	=	=	PUNCT
fumecheng-7267	212	13	𝑙𝑛	𝑙𝑛	PROPN
fumecheng-7267	212	14	∗	∗	NOUN
fumecheng-7267	212	15	𝐿𝑜𝑔((𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐿𝑜𝑔((𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	212	16	/	/	SYM
fumecheng-7267	212	17	7.646	7.646	NUM
fumecheng-7267	212	18	)	)	PUNCT
fumecheng-7267	212	19	^	^	PUNCT
fumecheng-7267	213	1	0.9685	0.9685	NUM
fumecheng-7267	213	2	+	+	CCONJ
fumecheng-7267	213	3	(	(	PUNCT
fumecheng-7267	213	4	4.9755	4.9755	NUM
fumecheng-7267	213	5	/	/	SYM
fumecheng-7267	213	6	(	(	PUNCT
fumecheng-7267	213	7	206.2975	206.2975	NUM
fumecheng-7267	213	8	+	+	CCONJ
fumecheng-7267	213	9	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	NOUN
fumecheng-7267	213	10	)	)	PUNCT
fumecheng-7267	213	11	)	)	PUNCT
fumecheng-7267	213	12	^	^	PUNCT
fumecheng-7267	213	13	0.8759	0.8759	NUM
fumecheng-7267	213	14	)	)	PUNCT
fumecheng-7267	213	15	𝐵	𝐵	NOUN
fumecheng-7267	213	16	=	=	PUNCT
fumecheng-7267	213	17	𝑙𝑛	𝑙𝑛	PROPN
fumecheng-7267	213	18	∗	∗	PROPN
fumecheng-7267	213	19	𝐿𝑜𝑔((𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐿𝑜𝑔((𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	213	20	/	/	SYM
fumecheng-7267	213	21	3.8597	3.8597	NUM
fumecheng-7267	213	22	)	)	PUNCT
fumecheng-7267	213	23	−	−	PROPN
fumecheng-7267	213	24	(	(	PUNCT
fumecheng-7267	213	25	4.795	4.795	NUM
fumecheng-7267	213	26	∗	∗	NOUN
fumecheng-7267	213	27	𝐴	𝐴	PROPN
fumecheng-7267	213	28	/	/	SYM
fumecheng-7267	213	29	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	PROPN
fumecheng-7267	213	30	)	)	PUNCT
fumecheng-7267	213	31	)	)	PUNCT
fumecheng-7267	214	1	𝑓	𝑓	X
fumecheng-7267	214	2	=	=	PUNCT
fumecheng-7267	214	3	−2	−2	PROPN
fumecheng-7267	214	4	∗	∗	NOUN
fumecheng-7267	214	5	𝑙𝑛	𝑙𝑛	ADP
fumecheng-7267	214	6	∗	∗	PROPN
fumecheng-7267	214	7	𝐿𝑜𝑔((𝐸𝑃𝑆𝐼𝐿𝑂𝑁	𝐿𝑜𝑔((𝐸𝑃𝑆𝐼𝐿𝑂𝑁	PROPN
fumecheng-7267	214	8	/	/	SYM
fumecheng-7267	214	9	3.7106	3.7106	NUM
fumecheng-7267	214	10	)	)	PUNCT
fumecheng-7267	214	11	−	−	PROPN
fumecheng-7267	214	12	5	5	NUM
fumecheng-7267	214	13	∗	∗	NOUN
fumecheng-7267	214	14	𝐵	𝐵	NOUN
fumecheng-7267	214	15	/	/	SYM
fumecheng-7267	214	16	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	𝑅𝐸𝑌𝑁𝑂𝐿𝐷𝑆	PROPN
fumecheng-7267	214	17	)	)	PUNCT
fumecheng-7267	215	1	𝑓	𝑓	PROPN
fumecheng-7267	215	2	=	=	PUNCT
fumecheng-7267	215	3	𝑓	𝑓	X
fumecheng-7267	215	4	^	^	SYM
fumecheng-7267	215	5	−	−	PROPN
fumecheng-7267	215	6	2	2	NUM
fumecheng-7267	215	7	𝑅𝑂𝑀𝐸𝑂	𝑅𝑂𝑀𝐸𝑂	PROPN
fumecheng-7267	215	8	=	=	PUNCT
fumecheng-7267	216	1	𝑓	𝑓	PROPN
fumecheng-7267	216	2	𝐸𝑛𝑑	𝐸𝑛𝑑	PROPN
fumecheng-7267	216	3	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛	PROPN
fumecheng-7267	216	4	266	266	NUM
fumecheng-7267	216	5	d.	d.	PROPN
fumecheng-7267	216	6	brkić	brkić	PROPN
fumecheng-7267	216	7	,	,	PUNCT
fumecheng-7267	216	8	z.	z.	PROPN
fumecheng-7267	216	9	stajić	stajić	PROPN
fumecheng-7267	217	1	3.2.5	3.2.5	NUM
fumecheng-7267	217	2	.	.	PUNCT
fumecheng-7267	218	1	buzzelli	buzzelli	PROPN
fumecheng-7267	218	2	approximation	approximation	NOUN
fumecheng-7267	218	3	the	the	DET
fumecheng-7267	218	4	buzzelli	buzzelli	ADJ
fumecheng-7267	218	5	approximation	approximation	NOUN
fumecheng-7267	219	1	[	[	X
fumecheng-7267	219	2	27	27	NUM
fumecheng-7267	219	3	]	]	PUNCT
fumecheng-7267	219	4	is	be	AUX
fumecheng-7267	219	5	given	give	VERB
fumecheng-7267	219	6	in	in	ADP
fumecheng-7267	219	7	eq	eq	ADP
fumecheng-7267	219	8	.	.	PUNCT
fumecheng-7267	220	1	(	(	PUNCT
fumecheng-7267	220	2	8)	8)	NUM
fumecheng-7267	220	3	.	.	NOUN
fumecheng-7267	220	4	1	1	NUM
fumecheng-7267	220	5	√f	√f	PRON
fumecheng-7267	220	6	≈	≈	PROPN
fumecheng-7267	220	7	a	a	DET
fumecheng-7267	220	8	−	−	PROPN
fumecheng-7267	220	9	(	(	PUNCT
fumecheng-7267	220	10	a+0.8686·ln	a+0.8686·ln	PROPN
fumecheng-7267	220	11	(	(	PUNCT
fumecheng-7267	220	12	b	b	NOUN
fumecheng-7267	220	13	re	re	X
fumecheng-7267	220	14	)	)	PUNCT
fumecheng-7267	221	1	1	1	NUM
fumecheng-7267	222	1	+	+	NUM
fumecheng-7267	222	2	2.1018	2.1018	NUM
fumecheng-7267	222	3	b	b	NOUN
fumecheng-7267	222	4	)	)	PUNCT
fumecheng-7267	222	5	a	a	DET
fumecheng-7267	222	6	≈	≈	PROPN
fumecheng-7267	222	7	0.7314·ln(re)−1.3163	0.7314·ln(re)−1.3163	NUM
fumecheng-7267	222	8	1.0025	1.0025	NUM
fumecheng-7267	222	9	+	+	PROPN
fumecheng-7267	222	10	1.2435·√ε	1.2435·√ε	NUM
fumecheng-7267	222	11	b	b	X
fumecheng-7267	222	12	≈	≈	PROPN
fumecheng-7267	222	13	ε	ε	PROPN
fumecheng-7267	222	14	3.71	3.71	NUM
fumecheng-7267	222	15	·	·	PUNCT
fumecheng-7267	222	16	re	re	ADP
fumecheng-7267	222	17	+	+	ADV
fumecheng-7267	222	18	2.51	2.51	NUM
fumecheng-7267	222	19	·	·	PUNCT
fumecheng-7267	222	20	a	a	X
fumecheng-7267	222	21	}	}	PUNCT
fumecheng-7267	222	22	(	(	PUNCT
fumecheng-7267	222	23	8)	8)	NUM
fumecheng-7267	222	24	3.2.6	3.2.6	NUM
fumecheng-7267	222	25	.	.	PUNCT
fumecheng-7267	223	1	praks	prak	NOUN
fumecheng-7267	223	2	and	and	CCONJ
fumecheng-7267	223	3	brkić	brkić	ADJ
fumecheng-7267	223	4	approximation	approximation	NOUN
fumecheng-7267	223	5	based	base	VERB
fumecheng-7267	223	6	on	on	ADP
fumecheng-7267	223	7	the	the	DET
fumecheng-7267	223	8	wright	wright	PROPN
fumecheng-7267	223	9	ω	ω	PROPN
fumecheng-7267	223	10	-	-	PUNCT
fumecheng-7267	223	11	function	function	NOUN
fumecheng-7267	223	12	and	and	CCONJ
fumecheng-7267	223	13	series	series	NOUN
fumecheng-7267	223	14	expansion	expansion	NOUN
fumecheng-7267	223	15	the	the	DET
fumecheng-7267	223	16	praks	prak	NOUN
fumecheng-7267	223	17	and	and	CCONJ
fumecheng-7267	223	18	brkić	brkić	ADJ
fumecheng-7267	223	19	approximation	approximation	NOUN
fumecheng-7267	223	20	[	[	X
fumecheng-7267	223	21	23	23	NUM
fumecheng-7267	223	22	]	]	PUNCT
fumecheng-7267	223	23	are	be	AUX
fumecheng-7267	223	24	based	base	VERB
fumecheng-7267	223	25	on	on	ADP
fumecheng-7267	223	26	the	the	DET
fumecheng-7267	223	27	wright	wright	PROPN
fumecheng-7267	223	28	ω	ω	PROPN
fumecheng-7267	223	29	-	-	PUNCT
fumecheng-7267	223	30	function	function	NOUN
fumecheng-7267	223	31	and	and	CCONJ
fumecheng-7267	223	32	on	on	ADP
fumecheng-7267	223	33	its	its	PRON
fumecheng-7267	223	34	series	series	NOUN
fumecheng-7267	223	35	expansion	expansion	NOUN
fumecheng-7267	223	36	.	.	PUNCT
fumecheng-7267	224	1	it	it	PRON
fumecheng-7267	224	2	is	be	AUX
fumecheng-7267	224	3	given	give	VERB
fumecheng-7267	224	4	in	in	ADP
fumecheng-7267	224	5	eq	eq	ADP
fumecheng-7267	224	6	.	.	PUNCT
fumecheng-7267	225	1	(	(	PUNCT
fumecheng-7267	225	2	9	9	NUM
fumecheng-7267	225	3	)	)	PUNCT
fumecheng-7267	225	4	.	.	PUNCT
fumecheng-7267	226	1	1	1	NUM
fumecheng-7267	226	2	√f	√f	DET
fumecheng-7267	226	3	≈	≈	PROPN
fumecheng-7267	226	4	0.8686	0.8686	NUM
fumecheng-7267	226	5	·	·	PUNCT
fumecheng-7267	226	6	(	(	PUNCT
fumecheng-7267	226	7	b	b	X
fumecheng-7267	226	8	+	+	CCONJ
fumecheng-7267	226	9	y	y	NOUN
fumecheng-7267	226	10	)	)	PUNCT
fumecheng-7267	227	1	a	a	PRON
fumecheng-7267	227	2	≈	≈	PROPN
fumecheng-7267	227	3	re·ε	re·ε	PROPN
fumecheng-7267	227	4	8.0897	8.0897	NUM
fumecheng-7267	227	5	b	b	PROPN
fumecheng-7267	227	6	≈	≈	PROPN
fumecheng-7267	227	7	ln(re	ln(re	PROPN
fumecheng-7267	227	8	)	)	PUNCT
fumecheng-7267	227	9	−0.779626	−0.779626	X
fumecheng-7267	228	1	x	x	X
fumecheng-7267	229	1	≈	≈	NOUN
fumecheng-7267	229	2	a	a	DET
fumecheng-7267	229	3	+	+	X
fumecheng-7267	229	4	b	b	PROPN
fumecheng-7267	229	5	c	c	X
fumecheng-7267	229	6	≈	≈	PROPN
fumecheng-7267	229	7	ln(x	ln(x	X
fumecheng-7267	229	8	)	)	PUNCT
fumecheng-7267	230	1	y	y	PROPN
fumecheng-7267	230	2	≈	≈	PROPN
fumecheng-7267	230	3	c	c	PROPN
fumecheng-7267	230	4	·	·	PUNCT
fumecheng-7267	230	5	(	(	PUNCT
fumecheng-7267	230	6	1	1	NUM
fumecheng-7267	230	7	x−1	x−1	X
fumecheng-7267	230	8	+	+	CCONJ
fumecheng-7267	230	9	c−2	c−2	PROPN
fumecheng-7267	230	10	2·x2	2·x2	NUM
fumecheng-7267	230	11	)	)	PUNCT
fumecheng-7267	231	1	−	−	ADP
fumecheng-7267	231	2	0.0014	0.0014	NUM
fumecheng-7267	231	3	}	}	PUNCT
fumecheng-7267	231	4	(	(	PUNCT
fumecheng-7267	231	5	9	9	NUM
fumecheng-7267	231	6	)	)	SYM
fumecheng-7267	231	7	3.2.7	3.2.7	NUM
fumecheng-7267	231	8	.	.	PUNCT
fumecheng-7267	232	1	offor	offor	ADP
fumecheng-7267	232	2	and	and	CCONJ
fumecheng-7267	232	3	alabi	alabi	NOUN
fumecheng-7267	232	4	approximation	approximation	NOUN
fumecheng-7267	232	5	the	the	DET
fumecheng-7267	232	6	offor	offor	NOUN
fumecheng-7267	232	7	and	and	CCONJ
fumecheng-7267	232	8	alabi	alabi	NOUN
fumecheng-7267	232	9	approximation	approximation	NOUN
fumecheng-7267	233	1	[	[	X
fumecheng-7267	233	2	26	26	NUM
fumecheng-7267	233	3	]	]	PUNCT
fumecheng-7267	233	4	is	be	AUX
fumecheng-7267	233	5	given	give	VERB
fumecheng-7267	233	6	in	in	ADP
fumecheng-7267	233	7	eq	eq	ADP
fumecheng-7267	233	8	.	.	PUNCT
fumecheng-7267	234	1	(	(	PUNCT
fumecheng-7267	234	2	10	10	NUM
fumecheng-7267	234	3	)	)	PUNCT
fumecheng-7267	234	4	.	.	PUNCT
fumecheng-7267	235	1	1	1	NUM
fumecheng-7267	235	2	√f	√f	PRON
fumecheng-7267	235	3	≈	≈	PROPN
fumecheng-7267	235	4	−0.8686	−0.8686	PRON
fumecheng-7267	235	5	·	·	PUNCT
fumecheng-7267	235	6	ln	ln	X
fumecheng-7267	235	7	(	(	PUNCT
fumecheng-7267	235	8	ε	ε	PROPN
fumecheng-7267	235	9	3.71	3.71	NUM
fumecheng-7267	235	10	−	−	PROPN
fumecheng-7267	235	11	1.975·a	1.975·a	NUM
fumecheng-7267	235	12	re	re	X
fumecheng-7267	235	13	)	)	PUNCT
fumecheng-7267	235	14	a	a	PRON
fumecheng-7267	236	1	≈	≈	PROPN
fumecheng-7267	236	2	ln	ln	NOUN
fumecheng-7267	236	3	(	(	PUNCT
fumecheng-7267	236	4	(	(	PUNCT
fumecheng-7267	236	5	ε	ε	PROPN
fumecheng-7267	236	6	3.93	3.93	NUM
fumecheng-7267	236	7	)	)	PUNCT
fumecheng-7267	236	8	1.092	1.092	NUM
fumecheng-7267	236	9	+	+	CCONJ
fumecheng-7267	236	10	7.627	7.627	NUM
fumecheng-7267	236	11	re+395.9	re+395.9	NOUN
fumecheng-7267	236	12	)	)	PUNCT
fumecheng-7267	236	13	}	}	PUNCT
fumecheng-7267	236	14	(	(	PUNCT
fumecheng-7267	236	15	10	10	NUM
fumecheng-7267	236	16	)	)	PUNCT
fumecheng-7267	236	17	3.2.8	3.2.8	NUM
fumecheng-7267	236	18	.	.	PUNCT
fumecheng-7267	237	1	shacham	shacham	PROPN
fumecheng-7267	237	2	approximation	approximation	NOUN
fumecheng-7267	237	3	the	the	DET
fumecheng-7267	237	4	shacham	shacham	PROPN
fumecheng-7267	237	5	approximation	approximation	NOUN
fumecheng-7267	238	1	[	[	X
fumecheng-7267	238	2	30	30	NUM
fumecheng-7267	238	3	]	]	PUNCT
fumecheng-7267	238	4	is	be	AUX
fumecheng-7267	238	5	given	give	VERB
fumecheng-7267	238	6	in	in	ADP
fumecheng-7267	238	7	eq	eq	ADP
fumecheng-7267	238	8	.	.	PUNCT
fumecheng-7267	239	1	(	(	PUNCT
fumecheng-7267	239	2	11	11	NUM
fumecheng-7267	239	3	)	)	PUNCT
fumecheng-7267	239	4	and	and	CCONJ
fumecheng-7267	239	5	is	be	AUX
fumecheng-7267	239	6	known	know	VERB
fumecheng-7267	239	7	also	also	ADV
fumecheng-7267	239	8	as	as	ADP
fumecheng-7267	239	9	zigrang	zigrang	PROPN
fumecheng-7267	239	10	and	and	CCONJ
fumecheng-7267	239	11	sylvester	sylvest	ADJ
fumecheng-7267	239	12	approximation	approximation	NOUN
fumecheng-7267	240	1	[	[	X
fumecheng-7267	240	2	49	49	NUM
fumecheng-7267	240	3	]	]	PUNCT
fumecheng-7267	240	4	.	.	PUNCT
fumecheng-7267	241	1	1	1	NUM
fumecheng-7267	241	2	√f	√f	PRON
fumecheng-7267	241	3	≈	≈	PROPN
fumecheng-7267	241	4	−08691	−08691	PROPN
fumecheng-7267	241	5	·	·	PUNCT
fumecheng-7267	241	6	ln	ln	NOUN
fumecheng-7267	241	7	(	(	PUNCT
fumecheng-7267	241	8	ε	ε	PROPN
fumecheng-7267	241	9	3.7027	3.7027	NUM
fumecheng-7267	241	10	+	+	CCONJ
fumecheng-7267	241	11	5.0605·b	5.0605·b	PROPN
fumecheng-7267	241	12	re	re	NOUN
fumecheng-7267	241	13	)	)	PUNCT
fumecheng-7267	241	14	a	a	DET
fumecheng-7267	241	15	≈	≈	PROPN
fumecheng-7267	241	16	0.4343	0.4343	PROPN
fumecheng-7267	241	17	·	·	PUNCT
fumecheng-7267	241	18	ln	ln	INTJ
fumecheng-7267	241	19	(	(	PUNCT
fumecheng-7267	241	20	ε	ε	PROPN
fumecheng-7267	241	21	3.7027	3.7027	NUM
fumecheng-7267	241	22	+	+	CCONJ
fumecheng-7267	241	23	12.543	12.543	NUM
fumecheng-7267	241	24	re	re	X
fumecheng-7267	241	25	)	)	PUNCT
fumecheng-7267	241	26	b	b	PROPN
fumecheng-7267	242	1	≈	≈	PROPN
fumecheng-7267	242	2	0.4343	0.4343	PROPN
fumecheng-7267	242	3	·	·	PUNCT
fumecheng-7267	243	1	ln	ln	INTJ
fumecheng-7267	243	2	(	(	PUNCT
fumecheng-7267	243	3	ε	ε	PROPN
fumecheng-7267	243	4	3.7027	3.7027	NUM
fumecheng-7267	243	5	+	+	CCONJ
fumecheng-7267	243	6	5.0605·a	5.0605·a	NUM
fumecheng-7267	243	7	re	re	NOUN
fumecheng-7267	243	8	)	)	PUNCT
fumecheng-7267	243	9	}	}	PUNCT
fumecheng-7267	243	10	(	(	PUNCT
fumecheng-7267	243	11	11	11	NUM
fumecheng-7267	243	12	)	)	PUNCT
fumecheng-7267	243	13	3.2.9	3.2.9	NUM
fumecheng-7267	243	14	.	.	PUNCT
fumecheng-7267	244	1	lamri	lamri	PROPN
fumecheng-7267	244	2	approximation	approximation	NOUN
fumecheng-7267	244	3	the	the	DET
fumecheng-7267	244	4	lamri	lamri	NOUN
fumecheng-7267	244	5	approximation	approximation	NOUN
fumecheng-7267	245	1	[	[	X
fumecheng-7267	245	2	24	24	NUM
fumecheng-7267	245	3	]	]	PUNCT
fumecheng-7267	245	4	is	be	AUX
fumecheng-7267	245	5	given	give	VERB
fumecheng-7267	245	6	in	in	ADP
fumecheng-7267	245	7	eq	eq	ADP
fumecheng-7267	245	8	.	.	PUNCT
fumecheng-7267	246	1	(	(	PUNCT
fumecheng-7267	246	2	12	12	NUM
fumecheng-7267	246	3	)	)	PUNCT
fumecheng-7267	246	4	.	.	PUNCT
fumecheng-7267	247	1	excel	excel	VERB
fumecheng-7267	247	2	vba	vba	PROPN
fumecheng-7267	247	3	-	-	PUNCT
fumecheng-7267	247	4	based	base	VERB
fumecheng-7267	247	5	user	user	NOUN
fumecheng-7267	247	6	defined	define	VERB
fumecheng-7267	247	7	functions	function	NOUN
fumecheng-7267	247	8	for	for	ADP
fumecheng-7267	247	9	highly	highly	ADV
fumecheng-7267	247	10	precise	precise	ADJ
fumecheng-7267	247	11	colebrook	colebrook	PROPN
fumecheng-7267	247	12	’s	’s	PART
fumecheng-7267	247	13	pipe	pipe	NOUN
fumecheng-7267	247	14	flow	flow	NOUN
fumecheng-7267	247	15	friction	friction	NOUN
fumecheng-7267	247	16	...	...	PUNCT
fumecheng-7267	248	1	267	267	NUM
fumecheng-7267	248	2	1	1	NUM
fumecheng-7267	248	3	√f	√f	PRON
fumecheng-7267	248	4	≈	≈	PROPN
fumecheng-7267	248	5	a	a	DET
fumecheng-7267	248	6	+	+	NOUN
fumecheng-7267	248	7	0.8686	0.8686	NUM
fumecheng-7267	248	8	·	·	PUNCT
fumecheng-7267	248	9	(	(	PUNCT
fumecheng-7267	248	10	0.8686	0.8686	NUM
fumecheng-7267	248	11	b	b	NOUN
fumecheng-7267	248	12	−	−	NOUN
fumecheng-7267	248	13	1	1	NUM
fumecheng-7267	248	14	)	)	PUNCT
fumecheng-7267	248	15	·	·	PUNCT
fumecheng-7267	248	16	ln(b	ln(b	X
fumecheng-7267	248	17	)	)	PUNCT
fumecheng-7267	248	18	a	a	PRON
fumecheng-7267	248	19	≈	≈	PROPN
fumecheng-7267	248	20	0.8686	0.8686	NUM
fumecheng-7267	248	21	·	·	PUNCT
fumecheng-7267	248	22	ln	ln	X
fumecheng-7267	248	23	(	(	PUNCT
fumecheng-7267	248	24	re	re	NOUN
fumecheng-7267	248	25	2.51	2.51	NUM
fumecheng-7267	248	26	)	)	PUNCT
fumecheng-7267	248	27	b	b	PROPN
fumecheng-7267	249	1	≈	≈	PROPN
fumecheng-7267	249	2	a	a	DET
fumecheng-7267	249	3	+	+	X
fumecheng-7267	249	4	re·ε	re·ε	PROPN
fumecheng-7267	249	5	9.3125	9.3125	NUM
fumecheng-7267	249	6	}	}	PUNCT
fumecheng-7267	249	7	(	(	PUNCT
fumecheng-7267	249	8	12	12	NUM
fumecheng-7267	249	9	)	)	PUNCT
fumecheng-7267	249	10	4	4	NUM
fumecheng-7267	249	11	.	.	PUNCT
fumecheng-7267	249	12	conclusions	conclusion	NOUN
fumecheng-7267	249	13	nine	nine	NUM
fumecheng-7267	249	14	explicit	explicit	ADJ
fumecheng-7267	249	15	approximations	approximation	NOUN
fumecheng-7267	249	16	of	of	ADP
fumecheng-7267	249	17	the	the	DET
fumecheng-7267	249	18	colebrook	colebrook	PROPN
fumecheng-7267	249	19	equation	equation	NOUN
fumecheng-7267	249	20	are	be	AUX
fumecheng-7267	249	21	examined	examine	VERB
fumecheng-7267	249	22	in	in	ADP
fumecheng-7267	249	23	this	this	DET
fumecheng-7267	249	24	review	review	NOUN
fumecheng-7267	249	25	paper	paper	NOUN
fumecheng-7267	249	26	.	.	PUNCT
fumecheng-7267	250	1	they	they	PRON
fumecheng-7267	250	2	are	be	AUX
fumecheng-7267	250	3	divided	divide	VERB
fumecheng-7267	250	4	in	in	ADP
fumecheng-7267	250	5	two	two	NUM
fumecheng-7267	250	6	groups	group	NOUN
fumecheng-7267	250	7	:	:	PUNCT
fumecheng-7267	250	8	1	1	X
fumecheng-7267	250	9	)	)	PUNCT
fumecheng-7267	250	10	extremely	extremely	ADV
fumecheng-7267	250	11	accurate	accurate	ADJ
fumecheng-7267	250	12	approximations	approximation	NOUN
fumecheng-7267	250	13	with	with	ADP
fumecheng-7267	250	14	the	the	DET
fumecheng-7267	250	15	relative	relative	ADJ
fumecheng-7267	250	16	error	error	NOUN
fumecheng-7267	250	17	of	of	ADP
fumecheng-7267	250	18	no	no	DET
fumecheng-7267	250	19	more	more	ADJ
fumecheng-7267	250	20	than	than	ADP
fumecheng-7267	250	21	0.01	0.01	NUM
fumecheng-7267	250	22	%	%	NOUN
fumecheng-7267	250	23	and	and	CCONJ
fumecheng-7267	250	24	2	2	NUM
fumecheng-7267	250	25	)	)	PUNCT
fumecheng-7267	250	26	very	very	ADV
fumecheng-7267	250	27	accurate	accurate	ADJ
fumecheng-7267	250	28	approximations	approximation	NOUN
fumecheng-7267	250	29	with	with	ADP
fumecheng-7267	250	30	the	the	DET
fumecheng-7267	250	31	relative	relative	ADJ
fumecheng-7267	250	32	error	error	NOUN
fumecheng-7267	250	33	between	between	ADP
fumecheng-7267	250	34	0.01	0.01	NUM
fumecheng-7267	250	35	%	%	NOUN
fumecheng-7267	250	36	and	and	CCONJ
fumecheng-7267	250	37	0.1	0.1	NUM
fumecheng-7267	250	38	%	%	NOUN
fumecheng-7267	250	39	.	.	PUNCT
fumecheng-7267	251	1	the	the	DET
fumecheng-7267	251	2	most	most	ADV
fumecheng-7267	251	3	complex	complex	ADJ
fumecheng-7267	251	4	approximation	approximation	NOUN
fumecheng-7267	251	5	is	be	AUX
fumecheng-7267	251	6	executed	execute	VERB
fumecheng-7267	251	7	using	use	VERB
fumecheng-7267	251	8	the	the	DET
fumecheng-7267	251	9	here	here	ADV
fumecheng-7267	251	10	presented	present	VERB
fumecheng-7267	251	11	vbaexcel	vbaexcel	ADP
fumecheng-7267	251	12	code	code	NOUN
fumecheng-7267	251	13	only	only	ADV
fumecheng-7267	251	14	2.06	2.06	NUM
fumecheng-7267	251	15	times	time	NOUN
fumecheng-7267	251	16	slower	slow	ADJ
fumecheng-7267	251	17	compared	compare	VERB
fumecheng-7267	251	18	with	with	ADP
fumecheng-7267	251	19	the	the	DET
fumecheng-7267	251	20	code	code	NOUN
fumecheng-7267	251	21	for	for	ADP
fumecheng-7267	251	22	the	the	DET
fumecheng-7267	251	23	simplest	simple	ADJ
fumecheng-7267	251	24	approximation	approximation	NOUN
fumecheng-7267	251	25	of	of	ADP
fumecheng-7267	251	26	nine	nine	NUM
fumecheng-7267	251	27	presented	present	VERB
fumecheng-7267	251	28	in	in	ADP
fumecheng-7267	251	29	this	this	DET
fumecheng-7267	251	30	review	review	NOUN
fumecheng-7267	251	31	paper	paper	NOUN
fumecheng-7267	251	32	.	.	PUNCT
fumecheng-7267	252	1	therefore	therefore	ADV
fumecheng-7267	252	2	,	,	PUNCT
fumecheng-7267	252	3	using	use	VERB
fumecheng-7267	252	4	balance	balance	NOUN
fumecheng-7267	252	5	between	between	ADP
fumecheng-7267	252	6	the	the	DET
fumecheng-7267	252	7	smallest	small	ADJ
fumecheng-7267	252	8	relative	relative	ADJ
fumecheng-7267	252	9	error	error	NOUN
fumecheng-7267	252	10	and	and	CCONJ
fumecheng-7267	252	11	the	the	DET
fumecheng-7267	252	12	speed	speed	NOUN
fumecheng-7267	252	13	of	of	ADP
fumecheng-7267	252	14	execution	execution	NOUN
fumecheng-7267	252	15	in	in	ADP
fumecheng-7267	252	16	computers	computer	NOUN
fumecheng-7267	252	17	as	as	ADP
fumecheng-7267	252	18	a	a	DET
fumecheng-7267	252	19	criterion	criterion	NOUN
fumecheng-7267	252	20	for	for	ADP
fumecheng-7267	252	21	choosing	choose	VERB
fumecheng-7267	252	22	the	the	DET
fumecheng-7267	252	23	appropriate	appropriate	ADJ
fumecheng-7267	252	24	approximation	approximation	NOUN
fumecheng-7267	252	25	for	for	ADP
fumecheng-7267	252	26	use	use	NOUN
fumecheng-7267	252	27	in	in	ADP
fumecheng-7267	252	28	large	large	ADJ
fumecheng-7267	252	29	computing	computing	NOUN
fumecheng-7267	252	30	simulations	simulation	NOUN
fumecheng-7267	252	31	,	,	PUNCT
fumecheng-7267	252	32	the	the	DET
fumecheng-7267	252	33	praks	prak	NOUN
fumecheng-7267	252	34	and	and	CCONJ
fumecheng-7267	252	35	brkić	brkić	ADJ
fumecheng-7267	252	36	approximation	approximation	NOUN
fumecheng-7267	252	37	[	[	X
fumecheng-7267	252	38	23	23	NUM
fumecheng-7267	252	39	]	]	PUNCT
fumecheng-7267	252	40	based	base	VERB
fumecheng-7267	252	41	on	on	ADP
fumecheng-7267	252	42	the	the	DET
fumecheng-7267	252	43	wright	wright	PROPN
fumecheng-7267	252	44	ω	ω	PROPN
fumecheng-7267	252	45	-	-	PUNCT
fumecheng-7267	252	46	function	function	NOUN
fumecheng-7267	252	47	and	and	CCONJ
fumecheng-7267	252	48	on	on	ADP
fumecheng-7267	252	49	symbolic	symbolic	ADJ
fumecheng-7267	252	50	regression	regression	NOUN
fumecheng-7267	252	51	,	,	PUNCT
fumecheng-7267	252	52	given	give	VERB
fumecheng-7267	252	53	in	in	ADP
fumecheng-7267	252	54	this	this	DET
fumecheng-7267	252	55	review	review	NOUN
fumecheng-7267	252	56	paper	paper	NOUN
fumecheng-7267	252	57	in	in	ADP
fumecheng-7267	252	58	eq	eq	ADP
fumecheng-7267	252	59	.	.	PUNCT
fumecheng-7267	253	1	(	(	PUNCT
fumecheng-7267	253	2	4	4	NUM
fumecheng-7267	253	3	)	)	PUNCT
fumecheng-7267	253	4	,	,	PUNCT
fumecheng-7267	253	5	is	be	AUX
fumecheng-7267	253	6	the	the	DET
fumecheng-7267	253	7	most	most	ADV
fumecheng-7267	253	8	suitable	suitable	ADJ
fumecheng-7267	253	9	and	and	CCONJ
fumecheng-7267	253	10	can	can	AUX
fumecheng-7267	253	11	be	be	AUX
fumecheng-7267	253	12	recommended	recommend	VERB
fumecheng-7267	253	13	for	for	ADP
fumecheng-7267	253	14	use	use	NOUN
fumecheng-7267	253	15	.	.	PUNCT
fumecheng-7267	254	1	almost	almost	ADV
fumecheng-7267	254	2	equally	equally	ADV
fumecheng-7267	254	3	suitable	suitable	ADJ
fumecheng-7267	254	4	are	be	AUX
fumecheng-7267	254	5	approximations	approximation	NOUN
fumecheng-7267	254	6	by	by	ADP
fumecheng-7267	254	7	serghides	serghide	NOUN
fumecheng-7267	254	8	[	[	X
fumecheng-7267	254	9	29	29	NUM
fumecheng-7267	254	10	]	]	PUNCT
fumecheng-7267	254	11	,	,	PUNCT
fumecheng-7267	254	12	vatankhah	vatankhah	PROPN
fumecheng-7267	255	1	[	[	X
fumecheng-7267	255	2	25	25	NUM
fumecheng-7267	255	3	]	]	PUNCT
fumecheng-7267	255	4	,	,	PUNCT
fumecheng-7267	255	5	and	and	CCONJ
fumecheng-7267	255	6	romeo	romeo	PROPN
fumecheng-7267	255	7	et	et	PROPN
fumecheng-7267	255	8	al	al	PROPN
fumecheng-7267	255	9	.	.	PUNCT
fumecheng-7267	256	1	[	[	X
fumecheng-7267	256	2	28	28	NUM
fumecheng-7267	256	3	]	]	PUNCT
fumecheng-7267	256	4	.	.	PUNCT
fumecheng-7267	257	1	udfs	udfs	PROPN
fumecheng-7267	257	2	written	write	VERB
fumecheng-7267	257	3	in	in	ADP
fumecheng-7267	257	4	the	the	DET
fumecheng-7267	257	5	vba	vba	NOUN
fumecheng-7267	257	6	,	,	PUNCT
fumecheng-7267	257	7	a	a	DET
fumecheng-7267	257	8	common	common	ADJ
fumecheng-7267	257	9	programming	programming	NOUN
fumecheng-7267	257	10	language	language	NOUN
fumecheng-7267	257	11	for	for	ADP
fumecheng-7267	257	12	ms	ms	PROPN
fumecheng-7267	257	13	excel	excel	PROPN
fumecheng-7267	257	14	spreadsheet	spreadsheet	PROPN
fumecheng-7267	257	15	solver	solver	PROPN
fumecheng-7267	257	16	prepared	prepare	VERB
fumecheng-7267	257	17	for	for	ADP
fumecheng-7267	257	18	the	the	DET
fumecheng-7267	257	19	presented	present	VERB
fumecheng-7267	257	20	approximations	approximation	NOUN
fumecheng-7267	257	21	to	to	ADP
fumecheng-7267	257	22	the	the	DET
fumecheng-7267	257	23	colebrook	colebrook	PROPN
fumecheng-7267	257	24	equation	equation	NOUN
fumecheng-7267	257	25	are	be	AUX
fumecheng-7267	257	26	suitable	suitable	ADJ
fumecheng-7267	257	27	for	for	ADP
fumecheng-7267	257	28	use	use	NOUN
fumecheng-7267	257	29	of	of	ADP
fumecheng-7267	257	30	those	those	DET
fumecheng-7267	257	31	engineers	engineer	NOUN
fumecheng-7267	257	32	who	who	PRON
fumecheng-7267	257	33	use	use	VERB
fumecheng-7267	257	34	spreadsheet	spreadsheet	NOUN
fumecheng-7267	257	35	solvers	solver	NOUN
fumecheng-7267	257	36	in	in	ADP
fumecheng-7267	257	37	their	their	PRON
fumecheng-7267	257	38	everyday	everyday	ADJ
fumecheng-7267	257	39	work	work	NOUN
fumecheng-7267	257	40	.	.	PUNCT
fumecheng-7267	258	1	also	also	ADV
fumecheng-7267	258	2	,	,	PUNCT
fumecheng-7267	258	3	the	the	DET
fumecheng-7267	258	4	shown	show	VERB
fumecheng-7267	258	5	udf	udf	NOUN
fumecheng-7267	258	6	for	for	ADP
fumecheng-7267	258	7	the	the	DET
fumecheng-7267	258	8	principal	principal	ADJ
fumecheng-7267	258	9	branch	branch	NOUN
fumecheng-7267	258	10	of	of	ADP
fumecheng-7267	258	11	the	the	DET
fumecheng-7267	258	12	lambert	lambert	PROPN
fumecheng-7267	258	13	w	w	PROPN
fumecheng-7267	258	14	-	-	PUNCT
fumecheng-7267	258	15	function	function	NOUN
fumecheng-7267	258	16	[	[	X
fumecheng-7267	258	17	50	50	NUM
fumecheng-7267	258	18	]	]	PUNCT
fumecheng-7267	258	19	can	can	AUX
fumecheng-7267	258	20	find	find	VERB
fumecheng-7267	258	21	much	much	ADV
fumecheng-7267	258	22	wider	wide	ADJ
fumecheng-7267	258	23	use	use	NOUN
fumecheng-7267	258	24	in	in	ADP
fumecheng-7267	258	25	engineering	engineering	NOUN
fumecheng-7267	258	26	than	than	ADP
fumecheng-7267	258	27	those	those	PRON
fumecheng-7267	258	28	for	for	ADP
fumecheng-7267	258	29	solving	solving	NOUN
fumecheng-7267	258	30	of	of	ADP
fumecheng-7267	258	31	the	the	DET
fumecheng-7267	258	32	colebrook	colebrook	PROPN
fumecheng-7267	258	33	equation	equation	NOUN
fumecheng-7267	258	34	.	.	PUNCT
fumecheng-7267	259	1	acknowledgement	acknowledgement	NOUN
fumecheng-7267	259	2	:	:	PUNCT
fumecheng-7267	259	3	the	the	DET
fumecheng-7267	259	4	authors	author	NOUN
fumecheng-7267	259	5	acknowledge	acknowledge	VERB
fumecheng-7267	259	6	a	a	DET
fumecheng-7267	259	7	support	support	NOUN
fumecheng-7267	259	8	from	from	ADP
fumecheng-7267	259	9	the	the	DET
fumecheng-7267	259	10	technology	technology	NOUN
fumecheng-7267	259	11	agency	agency	NOUN
fumecheng-7267	259	12	of	of	ADP
fumecheng-7267	259	13	the	the	DET
fumecheng-7267	259	14	czech	czech	PROPN
fumecheng-7267	259	15	republic	republic	NOUN
fumecheng-7267	259	16	through	through	ADP
fumecheng-7267	259	17	the	the	DET
fumecheng-7267	259	18	project	project	NOUN
fumecheng-7267	259	19	ceet	ceet	NOUN
fumecheng-7267	259	20	–	–	PUNCT
fumecheng-7267	259	21	“	"	PUNCT
fumecheng-7267	259	22	center	center	NOUN
fumecheng-7267	259	23	of	of	ADP
fumecheng-7267	259	24	energy	energy	NOUN
fumecheng-7267	259	25	and	and	CCONJ
fumecheng-7267	259	26	environmental	environmental	ADJ
fumecheng-7267	259	27	technologies	technology	NOUN
fumecheng-7267	259	28	”	"	PUNCT
fumecheng-7267	259	29	tk03020027	tk03020027	PROPN
fumecheng-7267	259	30	and	and	CCONJ
fumecheng-7267	259	31	the	the	DET
fumecheng-7267	259	32	ministry	ministry	PROPN
fumecheng-7267	259	33	of	of	ADP
fumecheng-7267	259	34	education	education	PROPN
fumecheng-7267	259	35	,	,	PUNCT
fumecheng-7267	259	36	science	science	NOUN
fumecheng-7267	259	37	,	,	PUNCT
fumecheng-7267	259	38	and	and	CCONJ
fumecheng-7267	259	39	technological	technological	ADJ
fumecheng-7267	259	40	development	development	NOUN
fumecheng-7267	259	41	of	of	ADP
fumecheng-7267	259	42	the	the	DET
fumecheng-7267	259	43	republic	republic	NOUN
fumecheng-7267	259	44	of	of	ADP
fumecheng-7267	259	45	serbia	serbia	PROPN
fumecheng-7267	259	46	.	.	PUNCT
fumecheng-7267	260	1	references	reference	NOUN
fumecheng-7267	260	2	1	1	NUM
fumecheng-7267	260	3	.	.	PUNCT
fumecheng-7267	261	1	colebrook	colebrook	PROPN
fumecheng-7267	261	2	,	,	PUNCT
fumecheng-7267	261	3	c.f	c.f	PROPN
fumecheng-7267	261	4	.	.	PROPN
fumecheng-7267	261	5	,	,	PUNCT
fumecheng-7267	261	6	1939	1939	NUM
fumecheng-7267	261	7	,	,	PUNCT
fumecheng-7267	261	8	turbulent	turbulent	ADJ
fumecheng-7267	261	9	flow	flow	NOUN
fumecheng-7267	261	10	in	in	ADP
fumecheng-7267	261	11	pipes	pipe	NOUN
fumecheng-7267	261	12	,	,	PUNCT
fumecheng-7267	261	13	with	with	ADP
fumecheng-7267	261	14	particular	particular	ADJ
fumecheng-7267	261	15	reference	reference	NOUN
fumecheng-7267	261	16	to	to	ADP
fumecheng-7267	261	17	the	the	DET
fumecheng-7267	261	18	transition	transition	NOUN
fumecheng-7267	261	19	region	region	NOUN
fumecheng-7267	261	20	between	between	ADP
fumecheng-7267	261	21	the	the	DET
fumecheng-7267	261	22	smooth	smooth	ADJ
fumecheng-7267	261	23	and	and	CCONJ
fumecheng-7267	261	24	rough	rough	ADJ
fumecheng-7267	261	25	pipe	pipe	NOUN
fumecheng-7267	261	26	laws	law	NOUN
fumecheng-7267	261	27	,	,	PUNCT
fumecheng-7267	261	28	journal	journal	NOUN
fumecheng-7267	261	29	of	of	ADP
fumecheng-7267	261	30	the	the	DET
fumecheng-7267	261	31	institution	institution	NOUN
fumecheng-7267	261	32	of	of	ADP
fumecheng-7267	261	33	civil	civil	ADJ
fumecheng-7267	261	34	engineers	engineer	NOUN
fumecheng-7267	261	35	,	,	PUNCT
fumecheng-7267	261	36	11(4	11(4	NUM
fumecheng-7267	261	37	)	)	PUNCT
fumecheng-7267	261	38	,	,	PUNCT
fumecheng-7267	261	39	pp	pp	PROPN
fumecheng-7267	261	40	.	.	PUNCT
fumecheng-7267	262	1	133	133	NUM
fumecheng-7267	262	2	-	-	SYM
fumecheng-7267	262	3	156	156	NUM
fumecheng-7267	262	4	.	.	PUNCT
fumecheng-7267	263	1	2	2	NUM
fumecheng-7267	263	2	.	.	X
fumecheng-7267	263	3	colebrook	colebrook	PROPN
fumecheng-7267	263	4	,	,	PUNCT
fumecheng-7267	263	5	c.f	c.f	PROPN
fumecheng-7267	263	6	.	.	PROPN
fumecheng-7267	263	7	,	,	PUNCT
fumecheng-7267	263	8	white	white	PROPN
fumecheng-7267	263	9	,	,	PUNCT
fumecheng-7267	263	10	c.m	c.m	PROPN
fumecheng-7267	263	11	.	.	PROPN
fumecheng-7267	263	12	,	,	PUNCT
fumecheng-7267	263	13	1937	1937	NUM
fumecheng-7267	263	14	,	,	PUNCT
fumecheng-7267	263	15	experiments	experiment	NOUN
fumecheng-7267	263	16	with	with	ADP
fumecheng-7267	263	17	fluid	fluid	ADJ
fumecheng-7267	263	18	friction	friction	NOUN
fumecheng-7267	263	19	in	in	ADP
fumecheng-7267	263	20	roughened	roughen	VERB
fumecheng-7267	263	21	pipes	pipe	NOUN
fumecheng-7267	263	22	,	,	PUNCT
fumecheng-7267	263	23	proceedings	proceeding	NOUN
fumecheng-7267	263	24	of	of	ADP
fumecheng-7267	263	25	the	the	DET
fumecheng-7267	263	26	royal	royal	ADJ
fumecheng-7267	263	27	society	society	NOUN
fumecheng-7267	263	28	of	of	ADP
fumecheng-7267	263	29	london	london	PROPN
fumecheng-7267	263	30	.	.	PUNCT
fumecheng-7267	264	1	series	series	PROPN
fumecheng-7267	264	2	a	a	PROPN
fumecheng-7267	264	3	-	-	PUNCT
fumecheng-7267	264	4	mathematical	mathematical	ADJ
fumecheng-7267	264	5	and	and	CCONJ
fumecheng-7267	264	6	physical	physical	ADJ
fumecheng-7267	264	7	sciences	science	NOUN
fumecheng-7267	264	8	,	,	PUNCT
fumecheng-7267	264	9	161(906	161(906	NUM
fumecheng-7267	264	10	)	)	PUNCT
fumecheng-7267	264	11	,	,	PUNCT
fumecheng-7267	264	12	pp	pp	PROPN
fumecheng-7267	264	13	.	.	PUNCT
fumecheng-7267	265	1	367	367	NUM
fumecheng-7267	265	2	-	-	SYM
fumecheng-7267	265	3	381	381	NUM
fumecheng-7267	265	4	.	.	PUNCT
fumecheng-7267	266	1	3	3	X
fumecheng-7267	266	2	.	.	X
fumecheng-7267	266	3	moody	moody	PROPN
fumecheng-7267	266	4	,	,	PUNCT
fumecheng-7267	266	5	l.	l.	PROPN
fumecheng-7267	266	6	,	,	PUNCT
fumecheng-7267	266	7	1944	1944	NUM
fumecheng-7267	266	8	,	,	PUNCT
fumecheng-7267	266	9	friction	friction	NOUN
fumecheng-7267	266	10	factors	factor	NOUN
fumecheng-7267	266	11	for	for	ADP
fumecheng-7267	266	12	pipe	pipe	NOUN
fumecheng-7267	266	13	flow	flow	NOUN
fumecheng-7267	266	14	,	,	PUNCT
fumecheng-7267	266	15	transactions	transaction	NOUN
fumecheng-7267	266	16	of	of	ADP
fumecheng-7267	266	17	the	the	DET
fumecheng-7267	266	18	a.s.m.e	a.s.m.e	PROPN
fumecheng-7267	266	19	.	.	PROPN
fumecheng-7267	266	20	,	,	PUNCT
fumecheng-7267	266	21	66(8	66(8	NOUN
fumecheng-7267	266	22	)	)	PUNCT
fumecheng-7267	266	23	,	,	PUNCT
fumecheng-7267	266	24	pp	pp	ADP
fumecheng-7267	266	25	.	.	PUNCT
fumecheng-7267	267	1	671–684	671–684	NUM
fumecheng-7267	267	2	.	.	PUNCT
fumecheng-7267	268	1	4	4	NUM
fumecheng-7267	268	2	.	.	X
fumecheng-7267	269	1	praks	prak	NOUN
fumecheng-7267	269	2	,	,	PUNCT
fumecheng-7267	269	3	p.	p.	NOUN
fumecheng-7267	269	4	,	,	PUNCT
fumecheng-7267	269	5	brkić	brkić	PROPN
fumecheng-7267	269	6	,	,	PUNCT
fumecheng-7267	269	7	d.	d.	PROPN
fumecheng-7267	269	8	,	,	PUNCT
fumecheng-7267	269	9	2018	2018	NUM
fumecheng-7267	269	10	,	,	PUNCT
fumecheng-7267	269	11	choosing	choose	VERB
fumecheng-7267	269	12	the	the	DET
fumecheng-7267	269	13	optimal	optimal	ADJ
fumecheng-7267	269	14	multi	multi	ADJ
fumecheng-7267	269	15	-	-	ADJ
fumecheng-7267	269	16	point	point	ADJ
fumecheng-7267	269	17	iterative	iterative	NOUN
fumecheng-7267	269	18	method	method	NOUN
fumecheng-7267	269	19	for	for	ADP
fumecheng-7267	269	20	the	the	DET
fumecheng-7267	269	21	colebrook	colebrook	PROPN
fumecheng-7267	269	22	flow	flow	PROPN
fumecheng-7267	269	23	friction	friction	NOUN
fumecheng-7267	269	24	equation	equation	NOUN
fumecheng-7267	269	25	,	,	PUNCT
fumecheng-7267	269	26	processes	process	NOUN
fumecheng-7267	269	27	,	,	PUNCT
fumecheng-7267	269	28	6(8	6(8	NUM
fumecheng-7267	269	29	)	)	PUNCT
fumecheng-7267	269	30	,	,	PUNCT
fumecheng-7267	269	31	130	130	NUM
fumecheng-7267	269	32	.	.	NOUN
fumecheng-7267	270	1	5	5	NUM
fumecheng-7267	270	2	.	.	X
fumecheng-7267	270	3	praks	prak	NOUN
fumecheng-7267	270	4	,	,	PUNCT
fumecheng-7267	270	5	p.	p.	NOUN
fumecheng-7267	270	6	,	,	PUNCT
fumecheng-7267	270	7	brkić	brkić	PROPN
fumecheng-7267	270	8	,	,	PUNCT
fumecheng-7267	270	9	d.	d.	PROPN
fumecheng-7267	270	10	,	,	PUNCT
fumecheng-7267	270	11	2018	2018	NUM
fumecheng-7267	270	12	,	,	PUNCT
fumecheng-7267	270	13	advanced	advanced	ADJ
fumecheng-7267	270	14	iterative	iterative	NOUN
fumecheng-7267	270	15	procedures	procedure	NOUN
fumecheng-7267	270	16	for	for	ADP
fumecheng-7267	270	17	solving	solve	VERB
fumecheng-7267	270	18	the	the	DET
fumecheng-7267	270	19	implicit	implicit	ADJ
fumecheng-7267	270	20	colebrook	colebrook	ADJ
fumecheng-7267	270	21	equation	equation	NOUN
fumecheng-7267	270	22	for	for	ADP
fumecheng-7267	270	23	fluid	fluid	ADJ
fumecheng-7267	270	24	flow	flow	NOUN
fumecheng-7267	270	25	friction	friction	NOUN
fumecheng-7267	270	26	,	,	PUNCT
fumecheng-7267	270	27	advances	advance	NOUN
fumecheng-7267	270	28	in	in	ADP
fumecheng-7267	270	29	civil	civil	ADJ
fumecheng-7267	270	30	engineering	engineering	NOUN
fumecheng-7267	270	31	,	,	PUNCT
fumecheng-7267	270	32	2018	2018	NUM
fumecheng-7267	270	33	,	,	PUNCT
fumecheng-7267	270	34	5451034	5451034	NUM
fumecheng-7267	270	35	.	.	PUNCT
fumecheng-7267	271	1	6	6	NUM
fumecheng-7267	271	2	.	.	X
fumecheng-7267	271	3	pimenta	pimenta	PROPN
fumecheng-7267	271	4	,	,	PUNCT
fumecheng-7267	271	5	b.d	b.d	PROPN
fumecheng-7267	271	6	.	.	PROPN
fumecheng-7267	271	7	,	,	PUNCT
fumecheng-7267	271	8	robaina	robaina	PROPN
fumecheng-7267	271	9	,	,	PUNCT
fumecheng-7267	271	10	a.d	a.d	PROPN
fumecheng-7267	271	11	.	.	PROPN
fumecheng-7267	271	12	,	,	PUNCT
fumecheng-7267	271	13	peiter	peiter	NOUN
fumecheng-7267	271	14	,	,	PUNCT
fumecheng-7267	271	15	m.x	m.x	PROPN
fumecheng-7267	271	16	.	.	PROPN
fumecheng-7267	271	17	,	,	PUNCT
fumecheng-7267	271	18	mezzomo	mezzomo	NOUN
fumecheng-7267	271	19	,	,	PUNCT
fumecheng-7267	271	20	w.	w.	PROPN
fumecheng-7267	271	21	,	,	PUNCT
fumecheng-7267	271	22	kirchner	kirchner	PROPN
fumecheng-7267	271	23	,	,	PUNCT
fumecheng-7267	271	24	j.h	j.h	PROPN
fumecheng-7267	271	25	.	.	PROPN
fumecheng-7267	271	26	,	,	PUNCT
fumecheng-7267	271	27	ben	ben	PROPN
fumecheng-7267	271	28	,	,	PUNCT
fumecheng-7267	271	29	l.h	l.h	PROPN
fumecheng-7267	271	30	.	.	PROPN
fumecheng-7267	271	31	,	,	PUNCT
fumecheng-7267	271	32	2018	2018	NUM
fumecheng-7267	271	33	,	,	PUNCT
fumecheng-7267	271	34	performance	performance	NOUN
fumecheng-7267	271	35	of	of	ADP
fumecheng-7267	271	36	explicit	explicit	ADJ
fumecheng-7267	271	37	approximations	approximation	NOUN
fumecheng-7267	271	38	of	of	ADP
fumecheng-7267	271	39	the	the	DET
fumecheng-7267	271	40	coefficient	coefficient	NOUN
fumecheng-7267	271	41	of	of	ADP
fumecheng-7267	271	42	head	head	NOUN
fumecheng-7267	271	43	loss	loss	NOUN
fumecheng-7267	271	44	for	for	ADP
fumecheng-7267	271	45	pressurized	pressurized	ADJ
fumecheng-7267	271	46	conduits	conduit	NOUN
fumecheng-7267	271	47	,	,	PUNCT
fumecheng-7267	271	48	revista	revista	PROPN
fumecheng-7267	271	49	brasileira	brasileira	PROPN
fumecheng-7267	271	50	de	de	PROPN
fumecheng-7267	271	51	engenharia	engenharia	PROPN
fumecheng-7267	271	52	agrícola	agrícola	PROPN
fumecheng-7267	271	53	e	e	PROPN
fumecheng-7267	271	54	ambiental	ambiental	PROPN
fumecheng-7267	271	55	,	,	PUNCT
fumecheng-7267	271	56	22(5	22(5	NOUN
fumecheng-7267	271	57	)	)	PUNCT
fumecheng-7267	271	58	,	,	PUNCT
fumecheng-7267	271	59	pp	pp	PROPN
fumecheng-7267	271	60	.	.	PUNCT
fumecheng-7267	272	1	301	301	NUM
fumecheng-7267	272	2	-	-	SYM
fumecheng-7267	272	3	307	307	NUM
fumecheng-7267	272	4	.	.	PUNCT
fumecheng-7267	273	1	7	7	X
fumecheng-7267	273	2	.	.	X
fumecheng-7267	273	3	winning	win	VERB
fumecheng-7267	273	4	,	,	PUNCT
fumecheng-7267	273	5	h.k	h.k	PROPN
fumecheng-7267	273	6	.	.	PROPN
fumecheng-7267	273	7	,	,	PUNCT
fumecheng-7267	273	8	coole	coole	NOUN
fumecheng-7267	273	9	,	,	PUNCT
fumecheng-7267	273	10	t.	t.	NOUN
fumecheng-7267	273	11	,	,	PUNCT
fumecheng-7267	273	12	2013	2013	NUM
fumecheng-7267	273	13	,	,	PUNCT
fumecheng-7267	273	14	explicit	explicit	ADJ
fumecheng-7267	273	15	friction	friction	NOUN
fumecheng-7267	273	16	factor	factor	NOUN
fumecheng-7267	273	17	accuracy	accuracy	NOUN
fumecheng-7267	273	18	and	and	CCONJ
fumecheng-7267	273	19	computational	computational	ADJ
fumecheng-7267	273	20	efficiency	efficiency	NOUN
fumecheng-7267	273	21	for	for	ADP
fumecheng-7267	273	22	turbulent	turbulent	ADJ
fumecheng-7267	273	23	flow	flow	NOUN
fumecheng-7267	273	24	in	in	ADP
fumecheng-7267	273	25	pipes	pipe	NOUN
fumecheng-7267	273	26	,	,	PUNCT
fumecheng-7267	273	27	flow	flow	NOUN
fumecheng-7267	273	28	,	,	PUNCT
fumecheng-7267	273	29	turbulence	turbulence	NOUN
fumecheng-7267	273	30	and	and	CCONJ
fumecheng-7267	273	31	combustion	combustion	NOUN
fumecheng-7267	273	32	,	,	PUNCT
fumecheng-7267	273	33	90(1	90(1	NUM
fumecheng-7267	273	34	)	)	PUNCT
fumecheng-7267	273	35	,	,	PUNCT
fumecheng-7267	273	36	pp	pp	ADJ
fumecheng-7267	273	37	.	.	PUNCT
fumecheng-7267	274	1	1	1	NUM
fumecheng-7267	274	2	-	-	SYM
fumecheng-7267	274	3	27	27	NUM
fumecheng-7267	274	4	.	.	NOUN
fumecheng-7267	275	1	8	8	NUM
fumecheng-7267	275	2	.	.	X
fumecheng-7267	276	1	brkić	brkić	NOUN
fumecheng-7267	276	2	,	,	PUNCT
fumecheng-7267	276	3	d.	d.	PROPN
fumecheng-7267	276	4	,	,	PUNCT
fumecheng-7267	276	5	2012	2012	NUM
fumecheng-7267	276	6	,	,	PUNCT
fumecheng-7267	276	7	determining	determine	VERB
fumecheng-7267	276	8	friction	friction	NOUN
fumecheng-7267	276	9	factors	factor	NOUN
fumecheng-7267	276	10	in	in	ADP
fumecheng-7267	276	11	turbulent	turbulent	ADJ
fumecheng-7267	276	12	pipe	pipe	NOUN
fumecheng-7267	276	13	flow	flow	NOUN
fumecheng-7267	276	14	,	,	PUNCT
fumecheng-7267	276	15	chemical	chemical	NOUN
fumecheng-7267	276	16	engineering	engineering	NOUN
fumecheng-7267	276	17	(	(	PUNCT
fumecheng-7267	276	18	new	new	PROPN
fumecheng-7267	276	19	york	york	PROPN
fumecheng-7267	276	20	)	)	PUNCT
fumecheng-7267	276	21	,	,	PUNCT
fumecheng-7267	276	22	119	119	NUM
fumecheng-7267	276	23	,	,	PUNCT
fumecheng-7267	276	24	pp	pp	ADJ
fumecheng-7267	276	25	.	.	PUNCT
fumecheng-7267	277	1	34	34	NUM
fumecheng-7267	277	2	-	-	SYM
fumecheng-7267	277	3	39	39	NUM
fumecheng-7267	277	4	.	.	PUNCT
fumecheng-7267	278	1	9	9	X
fumecheng-7267	278	2	.	.	X
fumecheng-7267	278	3	brkić	brkić	NOUN
fumecheng-7267	278	4	,	,	PUNCT
fumecheng-7267	278	5	d.	d.	PROPN
fumecheng-7267	278	6	,	,	PUNCT
fumecheng-7267	278	7	2011	2011	NUM
fumecheng-7267	278	8	,	,	PUNCT
fumecheng-7267	278	9	review	review	NOUN
fumecheng-7267	278	10	of	of	ADP
fumecheng-7267	278	11	explicit	explicit	ADJ
fumecheng-7267	278	12	approximations	approximation	NOUN
fumecheng-7267	278	13	to	to	ADP
fumecheng-7267	278	14	the	the	DET
fumecheng-7267	278	15	colebrook	colebrook	PROPN
fumecheng-7267	278	16	relation	relation	PROPN
fumecheng-7267	278	17	for	for	ADP
fumecheng-7267	278	18	flow	flow	NOUN
fumecheng-7267	278	19	friction	friction	NOUN
fumecheng-7267	278	20	,	,	PUNCT
fumecheng-7267	278	21	journal	journal	NOUN
fumecheng-7267	278	22	of	of	ADP
fumecheng-7267	278	23	petroleum	petroleum	NOUN
fumecheng-7267	278	24	science	science	NOUN
fumecheng-7267	278	25	and	and	CCONJ
fumecheng-7267	278	26	engineering	engineering	NOUN
fumecheng-7267	278	27	,	,	PUNCT
fumecheng-7267	278	28	77(1	77(1	NUM
fumecheng-7267	278	29	)	)	PUNCT
fumecheng-7267	278	30	,	,	PUNCT
fumecheng-7267	278	31	pp	pp	PROPN
fumecheng-7267	278	32	.	.	PUNCT
fumecheng-7267	279	1	34	34	NUM
fumecheng-7267	279	2	-	-	SYM
fumecheng-7267	279	3	48	48	NUM
fumecheng-7267	279	4	.	.	PUNCT
fumecheng-7267	280	1	268	268	NUM
fumecheng-7267	280	2	d.	d.	PROPN
fumecheng-7267	280	3	brkić	brkić	PROPN
fumecheng-7267	280	4	,	,	PUNCT
fumecheng-7267	280	5	z.	z.	PROPN
fumecheng-7267	280	6	stajić	stajić	PROPN
fumecheng-7267	280	7	10	10	NUM
fumecheng-7267	280	8	.	.	PUNCT
fumecheng-7267	281	1	zigrang	zigrang	PROPN
fumecheng-7267	281	2	,	,	PUNCT
fumecheng-7267	281	3	d.j	d.j	PROPN
fumecheng-7267	281	4	.	.	PROPN
fumecheng-7267	281	5	,	,	PUNCT
fumecheng-7267	281	6	sylvester	sylvester	PROPN
fumecheng-7267	281	7	,	,	PUNCT
fumecheng-7267	281	8	n.d	n.d	PROPN
fumecheng-7267	281	9	.	.	PROPN
fumecheng-7267	281	10	,	,	PUNCT
fumecheng-7267	281	11	1985	1985	NUM
fumecheng-7267	281	12	,	,	PUNCT
fumecheng-7267	281	13	a	a	DET
fumecheng-7267	281	14	review	review	NOUN
fumecheng-7267	281	15	of	of	ADP
fumecheng-7267	281	16	explicit	explicit	ADJ
fumecheng-7267	281	17	friction	friction	NOUN
fumecheng-7267	281	18	factor	factor	NOUN
fumecheng-7267	281	19	equations	equation	NOUN
fumecheng-7267	281	20	,	,	PUNCT
fumecheng-7267	281	21	journal	journal	NOUN
fumecheng-7267	281	22	of	of	ADP
fumecheng-7267	281	23	energy	energy	NOUN
fumecheng-7267	281	24	resources	resource	NOUN
fumecheng-7267	281	25	technology	technology	NOUN
fumecheng-7267	281	26	,	,	PUNCT
fumecheng-7267	281	27	107(2	107(2	NUM
fumecheng-7267	281	28	)	)	PUNCT
fumecheng-7267	281	29	,	,	PUNCT
fumecheng-7267	281	30	pp	pp	PROPN
fumecheng-7267	281	31	.	.	PUNCT
fumecheng-7267	282	1	280	280	NUM
fumecheng-7267	282	2	-	-	SYM
fumecheng-7267	282	3	283	283	NUM
fumecheng-7267	282	4	.	.	PUNCT
fumecheng-7267	283	1	11	11	NUM
fumecheng-7267	283	2	.	.	PUNCT
fumecheng-7267	284	1	gregory	gregory	PROPN
fumecheng-7267	284	2	,	,	PUNCT
fumecheng-7267	284	3	g.a	g.a	PROPN
fumecheng-7267	284	4	.	.	PROPN
fumecheng-7267	284	5	,	,	PUNCT
fumecheng-7267	284	6	fogarasi	fogarasi	PROPN
fumecheng-7267	284	7	,	,	PUNCT
fumecheng-7267	284	8	m.	m.	NOUN
fumecheng-7267	284	9	,	,	PUNCT
fumecheng-7267	284	10	1985	1985	NUM
fumecheng-7267	284	11	,	,	PUNCT
fumecheng-7267	284	12	alternate	alternate	ADJ
fumecheng-7267	284	13	to	to	ADP
fumecheng-7267	284	14	standard	standard	ADJ
fumecheng-7267	284	15	friction	friction	NOUN
fumecheng-7267	284	16	factor	factor	NOUN
fumecheng-7267	284	17	equation	equation	NOUN
fumecheng-7267	284	18	,	,	PUNCT
fumecheng-7267	284	19	oil	oil	NOUN
fumecheng-7267	284	20	&	&	CCONJ
fumecheng-7267	284	21	gas	gas	NOUN
fumecheng-7267	284	22	journal	journal	NOUN
fumecheng-7267	284	23	,	,	PUNCT
fumecheng-7267	284	24	83(13	83(13	NUM
fumecheng-7267	284	25	)	)	PUNCT
fumecheng-7267	284	26	,	,	PUNCT
fumecheng-7267	284	27	pp	pp	ADP
fumecheng-7267	284	28	.	.	PUNCT
fumecheng-7267	285	1	120	120	NUM
fumecheng-7267	285	2	-	-	SYM
fumecheng-7267	285	3	127	127	NUM
fumecheng-7267	285	4	.	.	PUNCT
fumecheng-7267	286	1	12	12	NUM
fumecheng-7267	286	2	.	.	PUNCT
fumecheng-7267	287	1	zeyu	zeyu	NOUN
fumecheng-7267	287	2	,	,	PUNCT
fumecheng-7267	287	3	z.	z.	PROPN
fumecheng-7267	287	4	,	,	PUNCT
fumecheng-7267	287	5	junrui	junrui	PROPN
fumecheng-7267	287	6	,	,	PUNCT
fumecheng-7267	287	7	c.	c.	PROPN
fumecheng-7267	287	8	,	,	PUNCT
fumecheng-7267	287	9	zhanbin	zhanbin	PROPN
fumecheng-7267	287	10	,	,	PUNCT
fumecheng-7267	287	11	l.	l.	PROPN
fumecheng-7267	287	12	,	,	PUNCT
fumecheng-7267	287	13	zengguang	zengguang	PROPN
fumecheng-7267	287	14	,	,	PUNCT
fumecheng-7267	287	15	x.	x.	PROPN
fumecheng-7267	287	16	,	,	PUNCT
fumecheng-7267	287	17	peng	peng	PROPN
fumecheng-7267	287	18	,	,	PUNCT
fumecheng-7267	287	19	l.	l.	PROPN
fumecheng-7267	287	20	,	,	PUNCT
fumecheng-7267	287	21	2020	2020	NUM
fumecheng-7267	287	22	,	,	PUNCT
fumecheng-7267	287	23	approximations	approximation	NOUN
fumecheng-7267	287	24	of	of	ADP
fumecheng-7267	287	25	the	the	DET
fumecheng-7267	287	26	darcy	darcy	NOUN
fumecheng-7267	287	27	–	–	PUNCT
fumecheng-7267	287	28	weisbach	weisbach	NOUN
fumecheng-7267	287	29	friction	friction	NOUN
fumecheng-7267	287	30	factor	factor	NOUN
fumecheng-7267	287	31	in	in	ADP
fumecheng-7267	287	32	a	a	DET
fumecheng-7267	287	33	vertical	vertical	ADJ
fumecheng-7267	287	34	pipe	pipe	NOUN
fumecheng-7267	287	35	with	with	ADP
fumecheng-7267	287	36	full	full	ADJ
fumecheng-7267	287	37	flow	flow	NOUN
fumecheng-7267	287	38	regime	regime	NOUN
fumecheng-7267	287	39	,	,	PUNCT
fumecheng-7267	287	40	water	water	NOUN
fumecheng-7267	287	41	supply	supply	NOUN
fumecheng-7267	287	42	,	,	PUNCT
fumecheng-7267	287	43	20(4	20(4	NOUN
fumecheng-7267	287	44	)	)	PUNCT
fumecheng-7267	287	45	,	,	PUNCT
fumecheng-7267	287	46	pp	pp	ADP
fumecheng-7267	287	47	.	.	PUNCT
fumecheng-7267	288	1	1321	1321	NUM
fumecheng-7267	288	2	-	-	SYM
fumecheng-7267	288	3	1333	1333	NUM
fumecheng-7267	288	4	.	.	PUNCT
fumecheng-7267	289	1	13	13	NUM
fumecheng-7267	289	2	.	.	X
fumecheng-7267	290	1	niazkar	niazkar	PROPN
fumecheng-7267	290	2	,	,	PUNCT
fumecheng-7267	290	3	m.	m.	NOUN
fumecheng-7267	290	4	,	,	PUNCT
fumecheng-7267	290	5	eryılmaz	eryılmaz	PROPN
fumecheng-7267	290	6	türkkan	türkkan	PROPN
fumecheng-7267	290	7	,	,	PUNCT
fumecheng-7267	290	8	g.	g.	PROPN
fumecheng-7267	290	9	,	,	PUNCT
fumecheng-7267	290	10	2021	2021	NUM
fumecheng-7267	290	11	,	,	PUNCT
fumecheng-7267	290	12	application	application	NOUN
fumecheng-7267	290	13	of	of	ADP
fumecheng-7267	290	14	third	third	ADJ
fumecheng-7267	290	15	-	-	PUNCT
fumecheng-7267	290	16	order	order	NOUN
fumecheng-7267	290	17	schemes	scheme	NOUN
fumecheng-7267	290	18	to	to	PART
fumecheng-7267	290	19	improve	improve	VERB
fumecheng-7267	290	20	the	the	DET
fumecheng-7267	290	21	convergence	convergence	NOUN
fumecheng-7267	290	22	of	of	ADP
fumecheng-7267	290	23	the	the	DET
fumecheng-7267	290	24	hardy	hardy	PROPN
fumecheng-7267	290	25	cross	cross	NOUN
fumecheng-7267	290	26	method	method	NOUN
fumecheng-7267	290	27	in	in	ADP
fumecheng-7267	290	28	pipe	pipe	NOUN
fumecheng-7267	290	29	network	network	NOUN
fumecheng-7267	290	30	analysis	analysis	NOUN
fumecheng-7267	290	31	,	,	PUNCT
fumecheng-7267	290	32	advances	advance	NOUN
fumecheng-7267	290	33	in	in	ADP
fumecheng-7267	290	34	mathematical	mathematical	ADJ
fumecheng-7267	290	35	physics	physics	NOUN
fumecheng-7267	290	36	,	,	PUNCT
fumecheng-7267	290	37	2021	2021	NUM
fumecheng-7267	290	38	,	,	PUNCT
fumecheng-7267	290	39	6692067	6692067	NUM
fumecheng-7267	290	40	.	.	PUNCT
fumecheng-7267	291	1	14	14	NUM
fumecheng-7267	291	2	.	.	PUNCT
fumecheng-7267	292	1	praks	prak	NOUN
fumecheng-7267	292	2	,	,	PUNCT
fumecheng-7267	292	3	p.	p.	NOUN
fumecheng-7267	292	4	,	,	PUNCT
fumecheng-7267	292	5	brkić	brkić	PROPN
fumecheng-7267	292	6	,	,	PUNCT
fumecheng-7267	292	7	d.	d.	PROPN
fumecheng-7267	292	8	,	,	PUNCT
fumecheng-7267	292	9	2020	2020	NUM
fumecheng-7267	292	10	,	,	PUNCT
fumecheng-7267	292	11	suitability	suitability	NOUN
fumecheng-7267	292	12	for	for	ADP
fumecheng-7267	292	13	coding	code	VERB
fumecheng-7267	292	14	of	of	ADP
fumecheng-7267	292	15	the	the	DET
fumecheng-7267	292	16	colebrook	colebrook	PROPN
fumecheng-7267	292	17	’s	’s	PART
fumecheng-7267	292	18	flow	flow	PROPN
fumecheng-7267	292	19	friction	friction	NOUN
fumecheng-7267	292	20	relation	relation	NOUN
fumecheng-7267	292	21	expressed	express	VERB
fumecheng-7267	292	22	through	through	ADP
fumecheng-7267	292	23	the	the	DET
fumecheng-7267	292	24	wright	wright	PROPN
fumecheng-7267	292	25	ω	ω	PROPN
fumecheng-7267	292	26	-	-	PUNCT
fumecheng-7267	292	27	function	function	NOUN
fumecheng-7267	292	28	,	,	PUNCT
fumecheng-7267	292	29	reports	report	NOUN
fumecheng-7267	292	30	in	in	ADP
fumecheng-7267	292	31	mechanical	mechanical	ADJ
fumecheng-7267	292	32	engineering	engineering	NOUN
fumecheng-7267	292	33	,	,	PUNCT
fumecheng-7267	292	34	1(1	1(1	NUM
fumecheng-7267	292	35	)	)	PUNCT
fumecheng-7267	292	36	,	,	PUNCT
fumecheng-7267	292	37	pp	pp	PROPN
fumecheng-7267	292	38	.	.	PUNCT
fumecheng-7267	293	1	174	174	NUM
fumecheng-7267	293	2	-	-	SYM
fumecheng-7267	293	3	179	179	NUM
fumecheng-7267	293	4	.	.	PUNCT
fumecheng-7267	294	1	15	15	NUM
fumecheng-7267	294	2	.	.	PUNCT
fumecheng-7267	295	1	brkić	brkić	NOUN
fumecheng-7267	295	2	,	,	PUNCT
fumecheng-7267	295	3	d.	d.	PROPN
fumecheng-7267	295	4	,	,	PUNCT
fumecheng-7267	295	5	2012	2012	NUM
fumecheng-7267	295	6	,	,	PUNCT
fumecheng-7267	295	7	lambert	lambert	PROPN
fumecheng-7267	295	8	w	w	PROPN
fumecheng-7267	295	9	function	function	PROPN
fumecheng-7267	295	10	in	in	ADP
fumecheng-7267	295	11	hydraulic	hydraulic	ADJ
fumecheng-7267	295	12	problems	problem	NOUN
fumecheng-7267	295	13	,	,	PUNCT
fumecheng-7267	295	14	mathematica	mathematica	PROPN
fumecheng-7267	295	15	balkanica	balkanica	PROPN
fumecheng-7267	296	1	(	(	PUNCT
fumecheng-7267	296	2	new	new	ADJ
fumecheng-7267	296	3	series	series	NOUN
fumecheng-7267	296	4	)	)	PUNCT
fumecheng-7267	296	5	,	,	PUNCT
fumecheng-7267	296	6	26(34	26(34	NUM
fumecheng-7267	296	7	)	)	PUNCT
fumecheng-7267	296	8	,	,	PUNCT
fumecheng-7267	296	9	pp	pp	PROPN
fumecheng-7267	296	10	.	.	PUNCT
fumecheng-7267	297	1	285	285	NUM
fumecheng-7267	297	2	-	-	SYM
fumecheng-7267	297	3	292	292	NUM
fumecheng-7267	297	4	.	.	PUNCT
fumecheng-7267	298	1	16	16	NUM
fumecheng-7267	298	2	.	.	PUNCT
fumecheng-7267	299	1	viccione	viccione	NOUN
fumecheng-7267	299	2	,	,	PUNCT
fumecheng-7267	299	3	g.	g.	PROPN
fumecheng-7267	299	4	,	,	PUNCT
fumecheng-7267	299	5	tibullo	tibullo	PROPN
fumecheng-7267	299	6	,	,	PUNCT
fumecheng-7267	299	7	v.	v.	ADP
fumecheng-7267	299	8	,	,	PUNCT
fumecheng-7267	299	9	2012	2012	NUM
fumecheng-7267	299	10	,	,	PUNCT
fumecheng-7267	299	11	an	an	DET
fumecheng-7267	299	12	effective	effective	ADJ
fumecheng-7267	299	13	approach	approach	NOUN
fumecheng-7267	299	14	for	for	ADP
fumecheng-7267	299	15	designing	design	VERB
fumecheng-7267	299	16	circular	circular	ADJ
fumecheng-7267	299	17	pipes	pipe	NOUN
fumecheng-7267	299	18	with	with	ADP
fumecheng-7267	299	19	the	the	DET
fumecheng-7267	299	20	colebrookwhite	colebrookwhite	ADJ
fumecheng-7267	299	21	formula	formula	NOUN
fumecheng-7267	299	22	,	,	PUNCT
fumecheng-7267	299	23	american	american	PROPN
fumecheng-7267	299	24	institute	institute	PROPN
fumecheng-7267	299	25	of	of	ADP
fumecheng-7267	299	26	physics	physics	PROPN
fumecheng-7267	299	27	conference	conference	NOUN
fumecheng-7267	299	28	proceedings	proceeding	NOUN
fumecheng-7267	299	29	,	,	PUNCT
fumecheng-7267	299	30	1479(1	1479(1	NUM
fumecheng-7267	299	31	)	)	PUNCT
fumecheng-7267	299	32	,	,	PUNCT
fumecheng-7267	300	1	pp	pp	PROPN
fumecheng-7267	300	2	.	.	PUNCT
fumecheng-7267	301	1	205	205	NUM
fumecheng-7267	301	2	-	-	SYM
fumecheng-7267	301	3	208	208	NUM
fumecheng-7267	301	4	.	.	PUNCT
fumecheng-7267	302	1	17	17	NUM
fumecheng-7267	302	2	.	.	PUNCT
fumecheng-7267	303	1	brkić	brkić	NOUN
fumecheng-7267	303	2	,	,	PUNCT
fumecheng-7267	303	3	d.	d.	PROPN
fumecheng-7267	303	4	,	,	PUNCT
fumecheng-7267	303	5	2011	2011	NUM
fumecheng-7267	303	6	,	,	PUNCT
fumecheng-7267	303	7	w	w	NOUN
fumecheng-7267	303	8	solutions	solution	NOUN
fumecheng-7267	303	9	of	of	ADP
fumecheng-7267	303	10	the	the	DET
fumecheng-7267	303	11	cw	cw	NOUN
fumecheng-7267	303	12	equation	equation	NOUN
fumecheng-7267	303	13	for	for	ADP
fumecheng-7267	303	14	flow	flow	NOUN
fumecheng-7267	303	15	friction	friction	NOUN
fumecheng-7267	303	16	,	,	PUNCT
fumecheng-7267	303	17	applied	apply	VERB
fumecheng-7267	303	18	mathematics	mathematics	NOUN
fumecheng-7267	303	19	letters	letter	NOUN
fumecheng-7267	303	20	,	,	PUNCT
fumecheng-7267	303	21	24(8	24(8	NUM
fumecheng-7267	303	22	)	)	PUNCT
fumecheng-7267	303	23	,	,	PUNCT
fumecheng-7267	303	24	pp	pp	PROPN
fumecheng-7267	303	25	.	.	PUNCT
fumecheng-7267	303	26	1379	1379	NUM
fumecheng-7267	303	27	-	-	SYM
fumecheng-7267	303	28	1383	1383	NUM
fumecheng-7267	303	29	.	.	PUNCT
fumecheng-7267	304	1	18	18	NUM
fumecheng-7267	304	2	.	.	X
fumecheng-7267	305	1	keady	keady	PROPN
fumecheng-7267	305	2	,	,	PUNCT
fumecheng-7267	305	3	g.	g.	PROPN
fumecheng-7267	305	4	,	,	PUNCT
fumecheng-7267	305	5	1998	1998	NUM
fumecheng-7267	305	6	,	,	PUNCT
fumecheng-7267	305	7	colebrook	colebrook	PROPN
fumecheng-7267	305	8	-	-	PUNCT
fumecheng-7267	305	9	white	white	ADJ
fumecheng-7267	305	10	formula	formula	NOUN
fumecheng-7267	305	11	for	for	ADP
fumecheng-7267	305	12	pipe	pipe	NOUN
fumecheng-7267	305	13	flows	flow	NOUN
fumecheng-7267	305	14	,	,	PUNCT
fumecheng-7267	305	15	journal	journal	NOUN
fumecheng-7267	305	16	of	of	ADP
fumecheng-7267	305	17	hydraulic	hydraulic	ADJ
fumecheng-7267	305	18	engineering	engineering	NOUN
fumecheng-7267	305	19	,	,	PUNCT
fumecheng-7267	305	20	124(1	124(1	NUM
fumecheng-7267	305	21	)	)	PUNCT
fumecheng-7267	305	22	,	,	PUNCT
fumecheng-7267	305	23	pp	pp	ADP
fumecheng-7267	305	24	.	.	PUNCT
fumecheng-7267	306	1	96	96	NUM
fumecheng-7267	306	2	-	-	SYM
fumecheng-7267	306	3	97	97	NUM
fumecheng-7267	306	4	.	.	NOUN
fumecheng-7267	307	1	19	19	NUM
fumecheng-7267	307	2	.	.	PUNCT
fumecheng-7267	308	1	hayes	hayes	PROPN
fumecheng-7267	308	2	,	,	PUNCT
fumecheng-7267	308	3	b.	b.	PROPN
fumecheng-7267	308	4	,	,	PUNCT
fumecheng-7267	308	5	2005	2005	NUM
fumecheng-7267	308	6	,	,	PUNCT
fumecheng-7267	308	7	why	why	SCONJ
fumecheng-7267	308	8	w	w	X
fumecheng-7267	308	9	?	?	PUNCT
fumecheng-7267	308	10	american	american	ADJ
fumecheng-7267	308	11	scientist	scientist	NOUN
fumecheng-7267	308	12	,	,	PUNCT
fumecheng-7267	308	13	93(2	93(2	NOUN
fumecheng-7267	308	14	)	)	PUNCT
fumecheng-7267	308	15	,	,	PUNCT
fumecheng-7267	308	16	pp	pp	ADP
fumecheng-7267	308	17	.	.	PUNCT
fumecheng-7267	309	1	104	104	NUM
fumecheng-7267	309	2	-	-	SYM
fumecheng-7267	309	3	108	108	NUM
fumecheng-7267	309	4	.	.	PUNCT
fumecheng-7267	310	1	20	20	NUM
fumecheng-7267	310	2	.	.	PUNCT
fumecheng-7267	311	1	corless	corless	PROPN
fumecheng-7267	311	2	,	,	PUNCT
fumecheng-7267	311	3	r.m	r.m	PROPN
fumecheng-7267	311	4	.	.	PROPN
fumecheng-7267	311	5	,	,	PUNCT
fumecheng-7267	311	6	gonnet	gonnet	NOUN
fumecheng-7267	311	7	,	,	PUNCT
fumecheng-7267	311	8	g.h	g.h	PROPN
fumecheng-7267	311	9	.	.	PROPN
fumecheng-7267	311	10	,	,	PUNCT
fumecheng-7267	311	11	hare	hare	PROPN
fumecheng-7267	311	12	,	,	PUNCT
fumecheng-7267	311	13	d.e	d.e	PROPN
fumecheng-7267	311	14	.	.	PROPN
fumecheng-7267	311	15	,	,	PUNCT
fumecheng-7267	311	16	jeffrey	jeffrey	PROPN
fumecheng-7267	311	17	,	,	PUNCT
fumecheng-7267	311	18	d.j	d.j	PROPN
fumecheng-7267	311	19	.	.	PROPN
fumecheng-7267	311	20	,	,	PUNCT
fumecheng-7267	311	21	knuth	knuth	PROPN
fumecheng-7267	311	22	,	,	PUNCT
fumecheng-7267	311	23	d.e	d.e	PROPN
fumecheng-7267	311	24	.	.	PROPN
fumecheng-7267	311	25	,	,	PUNCT
fumecheng-7267	311	26	1996	1996	NUM
fumecheng-7267	311	27	,	,	PUNCT
fumecheng-7267	311	28	on	on	ADP
fumecheng-7267	311	29	the	the	DET
fumecheng-7267	311	30	lambertw	lambertw	NOUN
fumecheng-7267	311	31	function	function	NOUN
fumecheng-7267	311	32	.	.	PUNCT
fumecheng-7267	312	1	advances	advance	NOUN
fumecheng-7267	312	2	in	in	ADP
fumecheng-7267	312	3	computational	computational	ADJ
fumecheng-7267	312	4	mathematics	mathematic	NOUN
fumecheng-7267	312	5	,	,	PUNCT
fumecheng-7267	312	6	5(1	5(1	NUM
fumecheng-7267	312	7	)	)	PUNCT
fumecheng-7267	312	8	,	,	PUNCT
fumecheng-7267	312	9	pp	pp	PROPN
fumecheng-7267	312	10	.	.	PUNCT
fumecheng-7267	312	11	329	329	NUM
fumecheng-7267	312	12	-	-	SYM
fumecheng-7267	312	13	359	359	NUM
fumecheng-7267	312	14	.	.	PUNCT
fumecheng-7267	313	1	21	21	NUM
fumecheng-7267	313	2	.	.	PUNCT
fumecheng-7267	313	3	alfaro	alfaro	PROPN
fumecheng-7267	313	4	-	-	PUNCT
fumecheng-7267	313	5	guerra	guerra	PROPN
fumecheng-7267	313	6	,	,	PUNCT
fumecheng-7267	313	7	m.	m.	NOUN
fumecheng-7267	313	8	,	,	PUNCT
fumecheng-7267	313	9	guerra	guerra	NOUN
fumecheng-7267	313	10	-	-	PUNCT
fumecheng-7267	313	11	rojas	rojas	PROPN
fumecheng-7267	313	12	,	,	PUNCT
fumecheng-7267	313	13	r.	r.	PROPN
fumecheng-7267	313	14	,	,	PUNCT
fumecheng-7267	313	15	olivares	olivare	NOUN
fumecheng-7267	313	16	-	-	PUNCT
fumecheng-7267	313	17	gallardo	gallardo	PROPN
fumecheng-7267	313	18	,	,	PUNCT
fumecheng-7267	313	19	a.	a.	NOUN
fumecheng-7267	313	20	,	,	PUNCT
fumecheng-7267	313	21	2020	2020	NUM
fumecheng-7267	313	22	.	.	PUNCT
fumecheng-7267	314	1	evaluación	evaluación	PROPN
fumecheng-7267	314	2	de	de	PROPN
fumecheng-7267	314	3	la	la	PROPN
fumecheng-7267	314	4	profundidad	profundidad	PROPN
fumecheng-7267	314	5	de	de	X
fumecheng-7267	314	6	recursión	recursión	PROPN
fumecheng-7267	314	7	de	de	X
fumecheng-7267	314	8	la	la	X
fumecheng-7267	314	9	solución	solución	X
fumecheng-7267	314	10	analítica	analítica	X
fumecheng-7267	314	11	de	de	X
fumecheng-7267	314	12	la	la	PROPN
fumecheng-7267	314	13	ecuación	ecuación	PROPN
fumecheng-7267	314	14	de	de	PROPN
fumecheng-7267	314	15	colebrook	colebrook	PROPN
fumecheng-7267	314	16	-	-	PUNCT
fumecheng-7267	314	17	white	white	PROPN
fumecheng-7267	314	18	en	en	X
fumecheng-7267	314	19	la	la	X
fumecheng-7267	314	20	exactitud	exactitud	X
fumecheng-7267	314	21	de	de	X
fumecheng-7267	314	22	la	la	PROPN
fumecheng-7267	314	23	predicción	predicción	NOUN
fumecheng-7267	314	24	del	del	PROPN
fumecheng-7267	314	25	factor	factor	PROPN
fumecheng-7267	314	26	de	de	PROPN
fumecheng-7267	314	27	fricción	fricción	PROPN
fumecheng-7267	314	28	,	,	PUNCT
fumecheng-7267	314	29	ingeniería	ingeniería	PROPN
fumecheng-7267	314	30	,	,	PUNCT
fumecheng-7267	314	31	investigación	investigación	PROPN
fumecheng-7267	314	32	y	y	PROPN
fumecheng-7267	314	33	tecnología	tecnología	PROPN
fumecheng-7267	314	34	,	,	PUNCT
fumecheng-7267	314	35	21(4	21(4	NUM
fumecheng-7267	314	36	)	)	PUNCT
fumecheng-7267	314	37	,	,	PUNCT
fumecheng-7267	314	38	epub	epub	PROPN
fumecheng-7267	314	39	20	20	NUM
fumecheng-7267	314	40	-	-	PUNCT
fumecheng-7267	314	41	nov-2020	nov-2020	NOUN
fumecheng-7267	314	42	.	.	PUNCT
fumecheng-7267	315	1	22	22	NUM
fumecheng-7267	315	2	.	.	PUNCT
fumecheng-7267	316	1	brkić	brkić	NOUN
fumecheng-7267	316	2	,	,	PUNCT
fumecheng-7267	316	3	d.	d.	PROPN
fumecheng-7267	316	4	,	,	PUNCT
fumecheng-7267	316	5	2017	2017	NUM
fumecheng-7267	316	6	,	,	PUNCT
fumecheng-7267	316	7	solution	solution	NOUN
fumecheng-7267	316	8	of	of	ADP
fumecheng-7267	316	9	the	the	DET
fumecheng-7267	316	10	implicit	implicit	ADJ
fumecheng-7267	316	11	colebrook	colebrook	ADJ
fumecheng-7267	316	12	equation	equation	NOUN
fumecheng-7267	316	13	for	for	ADP
fumecheng-7267	316	14	flow	flow	NOUN
fumecheng-7267	316	15	friction	friction	NOUN
fumecheng-7267	316	16	using	use	VERB
fumecheng-7267	316	17	excel	excel	NOUN
fumecheng-7267	316	18	,	,	PUNCT
fumecheng-7267	316	19	spreadsheets	spreadsheet	NOUN
fumecheng-7267	316	20	in	in	ADP
fumecheng-7267	316	21	education	education	NOUN
fumecheng-7267	316	22	,	,	PUNCT
fumecheng-7267	316	23	10(2	10(2	NUM
fumecheng-7267	316	24	)	)	PUNCT
fumecheng-7267	316	25	.	.	PUNCT
fumecheng-7267	317	1	4663	4663	NUM
fumecheng-7267	317	2	.	.	PUNCT
fumecheng-7267	318	1	23	23	NUM
fumecheng-7267	318	2	.	.	PUNCT
fumecheng-7267	319	1	praks	prak	NOUN
fumecheng-7267	319	2	,	,	PUNCT
fumecheng-7267	319	3	p.	p.	NOUN
fumecheng-7267	319	4	,	,	PUNCT
fumecheng-7267	319	5	brkić	brkić	PROPN
fumecheng-7267	319	6	,	,	PUNCT
fumecheng-7267	319	7	d.	d.	PROPN
fumecheng-7267	319	8	,	,	PUNCT
fumecheng-7267	319	9	2020	2020	NUM
fumecheng-7267	319	10	,	,	PUNCT
fumecheng-7267	319	11	review	review	NOUN
fumecheng-7267	319	12	of	of	ADP
fumecheng-7267	319	13	new	new	ADJ
fumecheng-7267	319	14	flow	flow	NOUN
fumecheng-7267	319	15	friction	friction	NOUN
fumecheng-7267	319	16	equations	equation	NOUN
fumecheng-7267	319	17	:	:	PUNCT
fumecheng-7267	319	18	constructing	construct	VERB
fumecheng-7267	319	19	colebrook	colebrook	PROPN
fumecheng-7267	319	20	explicit	explicit	ADJ
fumecheng-7267	319	21	correlations	correlation	NOUN
fumecheng-7267	319	22	accurately	accurately	ADV
fumecheng-7267	319	23	,	,	PUNCT
fumecheng-7267	319	24	revista	revista	PROPN
fumecheng-7267	319	25	internacional	internacional	PROPN
fumecheng-7267	319	26	de	de	PROPN
fumecheng-7267	319	27	métodos	métodos	PROPN
fumecheng-7267	319	28	numéricos	numéricos	PROPN
fumecheng-7267	319	29	para	para	PROPN
fumecheng-7267	319	30	cálculo	cálculo	PROPN
fumecheng-7267	319	31	y	y	PROPN
fumecheng-7267	319	32	diseño	diseño	PROPN
fumecheng-7267	319	33	en	en	PROPN
fumecheng-7267	319	34	ingeniería	ingeniería	PROPN
fumecheng-7267	319	35	,	,	PUNCT
fumecheng-7267	319	36	36(3	36(3	NUM
fumecheng-7267	319	37	)	)	PUNCT
fumecheng-7267	319	38	,	,	PUNCT
fumecheng-7267	319	39	41	41	NUM
fumecheng-7267	319	40	.	.	NOUN
fumecheng-7267	320	1	24	24	NUM
fumecheng-7267	320	2	.	.	PUNCT
fumecheng-7267	320	3	lamri	lamri	PROPN
fumecheng-7267	320	4	,	,	PUNCT
fumecheng-7267	320	5	a.a	a.a	PROPN
fumecheng-7267	320	6	.	.	PROPN
fumecheng-7267	320	7	,	,	PUNCT
fumecheng-7267	320	8	2020	2020	NUM
fumecheng-7267	320	9	,	,	PUNCT
fumecheng-7267	320	10	discussion	discussion	NOUN
fumecheng-7267	320	11	of	of	ADP
fumecheng-7267	320	12	“	"	PUNCT
fumecheng-7267	320	13	approximate	approximate	ADJ
fumecheng-7267	320	14	analytical	analytical	ADJ
fumecheng-7267	320	15	solutions	solution	NOUN
fumecheng-7267	320	16	for	for	ADP
fumecheng-7267	320	17	the	the	DET
fumecheng-7267	320	18	colebrook	colebrook	PROPN
fumecheng-7267	320	19	equation	equation	NOUN
fumecheng-7267	320	20	”	"	PUNCT
fumecheng-7267	320	21	,	,	PUNCT
fumecheng-7267	320	22	journal	journal	NOUN
fumecheng-7267	320	23	of	of	ADP
fumecheng-7267	320	24	hydraulic	hydraulic	ADJ
fumecheng-7267	320	25	engineering	engineering	NOUN
fumecheng-7267	320	26	,	,	PUNCT
fumecheng-7267	320	27	146(2	146(2	NUM
fumecheng-7267	320	28	)	)	PUNCT
fumecheng-7267	320	29	,	,	PUNCT
fumecheng-7267	320	30	07019012	07019012	NUM
fumecheng-7267	320	31	.	.	PUNCT
fumecheng-7267	321	1	25	25	NUM
fumecheng-7267	321	2	.	.	PUNCT
fumecheng-7267	322	1	vatankhah	vatankhah	PROPN
fumecheng-7267	322	2	,	,	PUNCT
fumecheng-7267	322	3	a.r	a.r	PROPN
fumecheng-7267	322	4	.	.	PROPN
fumecheng-7267	322	5	,	,	PUNCT
fumecheng-7267	322	6	2018	2018	NUM
fumecheng-7267	322	7	,	,	PUNCT
fumecheng-7267	322	8	approximate	approximate	ADJ
fumecheng-7267	322	9	analytical	analytical	ADJ
fumecheng-7267	322	10	solutions	solution	NOUN
fumecheng-7267	322	11	for	for	ADP
fumecheng-7267	322	12	the	the	DET
fumecheng-7267	322	13	colebrook	colebrook	PROPN
fumecheng-7267	322	14	equation	equation	PROPN
fumecheng-7267	322	15	,	,	PUNCT
fumecheng-7267	322	16	journal	journal	NOUN
fumecheng-7267	322	17	of	of	ADP
fumecheng-7267	322	18	hydraulic	hydraulic	ADJ
fumecheng-7267	322	19	engineering	engineering	NOUN
fumecheng-7267	322	20	,	,	PUNCT
fumecheng-7267	322	21	144(5	144(5	NUM
fumecheng-7267	322	22	)	)	PUNCT
fumecheng-7267	322	23	,	,	PUNCT
fumecheng-7267	322	24	06018007	06018007	NUM
fumecheng-7267	322	25	.	.	PUNCT
fumecheng-7267	323	1	26	26	NUM
fumecheng-7267	323	2	.	.	PUNCT
fumecheng-7267	324	1	offor	offor	PROPN
fumecheng-7267	324	2	,	,	PUNCT
fumecheng-7267	324	3	u.h	u.h	PROPN
fumecheng-7267	324	4	.	.	PROPN
fumecheng-7267	324	5	,	,	PUNCT
fumecheng-7267	324	6	alabi	alabi	PROPN
fumecheng-7267	324	7	,	,	PUNCT
fumecheng-7267	324	8	s.b	s.b	PROPN
fumecheng-7267	324	9	.	.	PROPN
fumecheng-7267	324	10	,	,	PUNCT
fumecheng-7267	324	11	2016	2016	NUM
fumecheng-7267	324	12	,	,	PUNCT
fumecheng-7267	324	13	an	an	DET
fumecheng-7267	324	14	accurate	accurate	ADJ
fumecheng-7267	324	15	and	and	CCONJ
fumecheng-7267	324	16	computationally	computationally	ADV
fumecheng-7267	324	17	efficient	efficient	ADJ
fumecheng-7267	324	18	explicit	explicit	ADJ
fumecheng-7267	324	19	friction	friction	NOUN
fumecheng-7267	324	20	factor	factor	NOUN
fumecheng-7267	324	21	model	model	NOUN
fumecheng-7267	324	22	,	,	PUNCT
fumecheng-7267	324	23	advances	advance	NOUN
fumecheng-7267	324	24	in	in	ADP
fumecheng-7267	324	25	chemical	chemical	ADJ
fumecheng-7267	324	26	engineering	engineering	NOUN
fumecheng-7267	324	27	and	and	CCONJ
fumecheng-7267	324	28	science	science	NOUN
fumecheng-7267	324	29	,	,	PUNCT
fumecheng-7267	324	30	6(3	6(3	NUM
fumecheng-7267	324	31	)	)	PUNCT
fumecheng-7267	324	32	,	,	PUNCT
fumecheng-7267	324	33	pp	pp	ADP
fumecheng-7267	324	34	.	.	PUNCT
fumecheng-7267	325	1	237	237	NUM
fumecheng-7267	325	2	-	-	SYM
fumecheng-7267	325	3	245	245	NUM
fumecheng-7267	325	4	.	.	PUNCT
fumecheng-7267	326	1	27	27	NUM
fumecheng-7267	326	2	.	.	PUNCT
fumecheng-7267	327	1	buzzelli	buzzelli	PROPN
fumecheng-7267	327	2	,	,	PUNCT
fumecheng-7267	327	3	d.	d.	PROPN
fumecheng-7267	327	4	,	,	PUNCT
fumecheng-7267	327	5	2008	2008	NUM
fumecheng-7267	327	6	,	,	PUNCT
fumecheng-7267	327	7	calculating	calculate	VERB
fumecheng-7267	327	8	friction	friction	NOUN
fumecheng-7267	327	9	in	in	ADP
fumecheng-7267	327	10	one	one	NUM
fumecheng-7267	327	11	step	step	NOUN
fumecheng-7267	327	12	,	,	PUNCT
fumecheng-7267	327	13	machine	machine	NOUN
fumecheng-7267	327	14	design	design	NOUN
fumecheng-7267	327	15	80(12	80(12	NUM
fumecheng-7267	327	16	)	)	PUNCT
fumecheng-7267	327	17	,	,	PUNCT
fumecheng-7267	327	18	pp	pp	ADP
fumecheng-7267	327	19	.	.	PUNCT
fumecheng-7267	328	1	54–55	54–55	NUM
fumecheng-7267	328	2	.	.	PUNCT
fumecheng-7267	329	1	28	28	NUM
fumecheng-7267	329	2	.	.	PUNCT
fumecheng-7267	330	1	romeo	romeo	PROPN
fumecheng-7267	330	2	,	,	PUNCT
fumecheng-7267	330	3	e.	e.	PROPN
fumecheng-7267	330	4	,	,	PUNCT
fumecheng-7267	330	5	royo	royo	PROPN
fumecheng-7267	330	6	,	,	PUNCT
fumecheng-7267	330	7	c.	c.	PROPN
fumecheng-7267	330	8	,	,	PUNCT
fumecheng-7267	330	9	monzón	monzón	NOUN
fumecheng-7267	330	10	,	,	PUNCT
fumecheng-7267	330	11	a.	a.	NOUN
fumecheng-7267	330	12	,	,	PUNCT
fumecheng-7267	330	13	2002	2002	NUM
fumecheng-7267	330	14	,	,	PUNCT
fumecheng-7267	330	15	improved	improve	VERB
fumecheng-7267	330	16	explicit	explicit	ADJ
fumecheng-7267	330	17	equations	equation	NOUN
fumecheng-7267	330	18	for	for	ADP
fumecheng-7267	330	19	estimation	estimation	NOUN
fumecheng-7267	330	20	of	of	ADP
fumecheng-7267	330	21	the	the	DET
fumecheng-7267	330	22	friction	friction	NOUN
fumecheng-7267	330	23	factor	factor	NOUN
fumecheng-7267	330	24	in	in	ADP
fumecheng-7267	330	25	rough	rough	ADJ
fumecheng-7267	330	26	and	and	CCONJ
fumecheng-7267	330	27	smooth	smooth	ADJ
fumecheng-7267	330	28	pipes	pipe	NOUN
fumecheng-7267	330	29	,	,	PUNCT
fumecheng-7267	330	30	chemical	chemical	ADJ
fumecheng-7267	330	31	engineering	engineering	NOUN
fumecheng-7267	330	32	journal	journal	PROPN
fumecheng-7267	330	33	,	,	PUNCT
fumecheng-7267	330	34	86(3	86(3	PROPN
fumecheng-7267	330	35	)	)	PUNCT
fumecheng-7267	330	36	,	,	PUNCT
fumecheng-7267	330	37	pp	pp	PROPN
fumecheng-7267	330	38	.	.	PUNCT
fumecheng-7267	331	1	369	369	NUM
fumecheng-7267	331	2	-	-	SYM
fumecheng-7267	331	3	374	374	NUM
fumecheng-7267	331	4	.	.	NOUN
fumecheng-7267	332	1	29	29	NUM
fumecheng-7267	332	2	.	.	PUNCT
fumecheng-7267	333	1	serghides	serghide	NOUN
fumecheng-7267	333	2	,	,	PUNCT
fumecheng-7267	333	3	t.k	t.k	PROPN
fumecheng-7267	333	4	.	.	PROPN
fumecheng-7267	333	5	,	,	PUNCT
fumecheng-7267	333	6	1984	1984	NUM
fumecheng-7267	333	7	,	,	PUNCT
fumecheng-7267	333	8	estimate	estimate	VERB
fumecheng-7267	333	9	friction	friction	NOUN
fumecheng-7267	333	10	factor	factor	NOUN
fumecheng-7267	333	11	accurately	accurately	ADV
fumecheng-7267	333	12	,	,	PUNCT
fumecheng-7267	333	13	chemical	chemical	ADJ
fumecheng-7267	333	14	engineering	engineering	NOUN
fumecheng-7267	333	15	(	(	PUNCT
fumecheng-7267	333	16	new	new	PROPN
fumecheng-7267	333	17	york	york	PROPN
fumecheng-7267	333	18	)	)	PUNCT
fumecheng-7267	333	19	,	,	PUNCT
fumecheng-7267	333	20	91(5	91(5	NUM
fumecheng-7267	333	21	)	)	PUNCT
fumecheng-7267	333	22	,	,	PUNCT
fumecheng-7267	333	23	pp	pp	ADP
fumecheng-7267	333	24	.	.	PUNCT
fumecheng-7267	334	1	63–64	63–64	NOUN
fumecheng-7267	334	2	.	.	PUNCT
fumecheng-7267	335	1	30	30	NUM
fumecheng-7267	335	2	.	.	PUNCT
fumecheng-7267	335	3	schorle	schorle	NOUN
fumecheng-7267	335	4	,	,	PUNCT
fumecheng-7267	335	5	b.j	b.j	PROPN
fumecheng-7267	335	6	.	.	PROPN
fumecheng-7267	335	7	,	,	PUNCT
fumecheng-7267	335	8	churchill	churchill	PROPN
fumecheng-7267	335	9	,	,	PUNCT
fumecheng-7267	335	10	s.w	s.w	PROPN
fumecheng-7267	335	11	.	.	PROPN
fumecheng-7267	335	12	,	,	PUNCT
fumecheng-7267	335	13	shacham	shacham	PROPN
fumecheng-7267	335	14	,	,	PUNCT
fumecheng-7267	335	15	m.	m.	NOUN
fumecheng-7267	335	16	,	,	PUNCT
fumecheng-7267	335	17	1980	1980	NUM
fumecheng-7267	335	18	,	,	PUNCT
fumecheng-7267	335	19	comments	comment	VERB
fumecheng-7267	335	20	on	on	ADP
fumecheng-7267	335	21	:	:	PUNCT
fumecheng-7267	335	22	“	"	PUNCT
fumecheng-7267	335	23	an	an	DET
fumecheng-7267	335	24	explicit	explicit	ADJ
fumecheng-7267	335	25	equation	equation	NOUN
fumecheng-7267	335	26	for	for	ADP
fumecheng-7267	335	27	friction	friction	NOUN
fumecheng-7267	335	28	factor	factor	NOUN
fumecheng-7267	335	29	in	in	ADP
fumecheng-7267	335	30	pipe	pipe	NOUN
fumecheng-7267	335	31	”	"	PUNCT
fumecheng-7267	335	32	,	,	PUNCT
fumecheng-7267	335	33	industrial	industrial	PROPN
fumecheng-7267	335	34	&	&	CCONJ
fumecheng-7267	335	35	engineering	engineering	NOUN
fumecheng-7267	335	36	chemistry	chemistry	NOUN
fumecheng-7267	335	37	fundamentals	fundamental	NOUN
fumecheng-7267	335	38	,	,	PUNCT
fumecheng-7267	335	39	19(2	19(2	NUM
fumecheng-7267	335	40	)	)	PUNCT
fumecheng-7267	335	41	,	,	PUNCT
fumecheng-7267	335	42	pp	pp	ADJ
fumecheng-7267	335	43	.	.	PUNCT
fumecheng-7267	336	1	228–230	228–230	NUM
fumecheng-7267	336	2	.	.	PUNCT
fumecheng-7267	337	1	31	31	NUM
fumecheng-7267	337	2	.	.	PUNCT
fumecheng-7267	338	1	gross	gross	PROPN
fumecheng-7267	338	2	,	,	PUNCT
fumecheng-7267	338	3	c.j	c.j	PROPN
fumecheng-7267	338	4	.	.	PROPN
fumecheng-7267	338	5	,	,	PUNCT
fumecheng-7267	338	6	campbell	campbell	PROPN
fumecheng-7267	338	7	,	,	PUNCT
fumecheng-7267	338	8	j.	j.	PROPN
fumecheng-7267	338	9	,	,	PUNCT
fumecheng-7267	338	10	becker	becker	PROPN
fumecheng-7267	338	11	,	,	PUNCT
fumecheng-7267	338	12	a.j	a.j	PROPN
fumecheng-7267	338	13	.	.	PROPN
fumecheng-7267	338	14	,	,	PUNCT
fumecheng-7267	338	15	russo	russo	PROPN
fumecheng-7267	338	16	,	,	PUNCT
fumecheng-7267	338	17	c.v	c.v	PROPN
fumecheng-7267	338	18	.	.	PROPN
fumecheng-7267	338	19	microsoft	microsoft	PROPN
fumecheng-7267	338	20	technology	technology	PROPN
fumecheng-7267	338	21	licensing	licensing	PROPN
fumecheng-7267	338	22	llc	llc	PROPN
fumecheng-7267	338	23	,	,	PUNCT
fumecheng-7267	338	24	2020	2020	NUM
fumecheng-7267	338	25	,	,	PUNCT
fumecheng-7267	338	26	automatically	automatically	ADV
fumecheng-7267	338	27	creating	create	VERB
fumecheng-7267	338	28	lambda	lambda	ADJ
fumecheng-7267	338	29	functions	function	NOUN
fumecheng-7267	338	30	in	in	ADP
fumecheng-7267	338	31	spreadsheet	spreadsheet	NOUN
fumecheng-7267	338	32	applications	application	NOUN
fumecheng-7267	338	33	,	,	PUNCT
fumecheng-7267	338	34	u.s	u.s	PROPN
fumecheng-7267	338	35	.	.	PROPN
fumecheng-7267	338	36	patent	patent	NOUN
fumecheng-7267	338	37	appl	appl	PROPN
fumecheng-7267	338	38	.	.	PUNCT
fumecheng-7267	339	1	16/024,580	16/024,580	NUM
fumecheng-7267	339	2	.	.	NOUN
fumecheng-7267	339	3	32	32	NUM
fumecheng-7267	339	4	.	.	PUNCT
fumecheng-7267	340	1	sonnad	sonnad	PROPN
fumecheng-7267	340	2	,	,	PUNCT
fumecheng-7267	340	3	j.r	j.r	PROPN
fumecheng-7267	340	4	.	.	PROPN
fumecheng-7267	340	5	,	,	PUNCT
fumecheng-7267	340	6	goudar	goudar	PROPN
fumecheng-7267	340	7	,	,	PUNCT
fumecheng-7267	340	8	c.t	c.t	PROPN
fumecheng-7267	340	9	.	.	PROPN
fumecheng-7267	340	10	,	,	PUNCT
fumecheng-7267	340	11	2004	2004	NUM
fumecheng-7267	340	12	,	,	PUNCT
fumecheng-7267	340	13	constraints	constraint	NOUN
fumecheng-7267	340	14	for	for	ADP
fumecheng-7267	340	15	using	use	VERB
fumecheng-7267	340	16	lambert	lambert	PROPN
fumecheng-7267	340	17	w	w	PROPN
fumecheng-7267	340	18	function	function	NOUN
fumecheng-7267	340	19	-	-	PUNCT
fumecheng-7267	340	20	based	base	VERB
fumecheng-7267	340	21	explicit	explicit	ADJ
fumecheng-7267	340	22	colebrook	colebrook	PROPN
fumecheng-7267	340	23	–	–	PUNCT
fumecheng-7267	340	24	white	white	ADJ
fumecheng-7267	340	25	equation	equation	NOUN
fumecheng-7267	340	26	,	,	PUNCT
fumecheng-7267	340	27	journal	journal	NOUN
fumecheng-7267	340	28	of	of	ADP
fumecheng-7267	340	29	hydraulic	hydraulic	ADJ
fumecheng-7267	340	30	engineering	engineering	NOUN
fumecheng-7267	340	31	,	,	PUNCT
fumecheng-7267	340	32	130(9	130(9	NUM
fumecheng-7267	340	33	)	)	PUNCT
fumecheng-7267	340	34	,	,	PUNCT
fumecheng-7267	340	35	pp	pp	ADP
fumecheng-7267	340	36	.	.	PUNCT
fumecheng-7267	341	1	929	929	NUM
fumecheng-7267	341	2	-	-	SYM
fumecheng-7267	341	3	931	931	NUM
fumecheng-7267	341	4	.	.	PUNCT
fumecheng-7267	342	1	33	33	NUM
fumecheng-7267	342	2	.	.	PUNCT
fumecheng-7267	343	1	brkić	brkić	PROPN
fumecheng-7267	343	2	,	,	PUNCT
fumecheng-7267	343	3	d.	d.	PROPN
fumecheng-7267	343	4	,	,	PUNCT
fumecheng-7267	343	5	2012	2012	NUM
fumecheng-7267	343	6	,	,	PUNCT
fumecheng-7267	343	7	comparison	comparison	NOUN
fumecheng-7267	343	8	of	of	ADP
fumecheng-7267	343	9	the	the	DET
fumecheng-7267	343	10	lambert	lambert	PROPN
fumecheng-7267	343	11	w‐function	w‐function	PUNCT
fumecheng-7267	343	12	based	base	VERB
fumecheng-7267	343	13	solutions	solution	NOUN
fumecheng-7267	343	14	to	to	ADP
fumecheng-7267	343	15	the	the	DET
fumecheng-7267	343	16	colebrook	colebrook	PROPN
fumecheng-7267	343	17	equation	equation	NOUN
fumecheng-7267	343	18	,	,	PUNCT
fumecheng-7267	343	19	engineering	engineering	NOUN
fumecheng-7267	343	20	computations	computation	NOUN
fumecheng-7267	343	21	,	,	PUNCT
fumecheng-7267	343	22	29(6	29(6	NUM
fumecheng-7267	343	23	)	)	PUNCT
fumecheng-7267	343	24	,	,	PUNCT
fumecheng-7267	343	25	pp	pp	ADP
fumecheng-7267	343	26	.	.	PUNCT
fumecheng-7267	344	1	617–630	617–630	NUM
fumecheng-7267	344	2	.	.	PUNCT
fumecheng-7267	345	1	34	34	NUM
fumecheng-7267	345	2	.	.	X
fumecheng-7267	345	3	barry	barry	PROPN
fumecheng-7267	345	4	,	,	PUNCT
fumecheng-7267	345	5	d.a	d.a	PROPN
fumecheng-7267	345	6	.	.	PROPN
fumecheng-7267	345	7	,	,	PUNCT
fumecheng-7267	345	8	parlange	parlange	PROPN
fumecheng-7267	345	9	,	,	PUNCT
fumecheng-7267	345	10	j.y	j.y	PROPN
fumecheng-7267	345	11	.	.	PROPN
fumecheng-7267	345	12	,	,	PUNCT
fumecheng-7267	345	13	li	li	PROPN
fumecheng-7267	345	14	,	,	PUNCT
fumecheng-7267	345	15	l.	l.	PROPN
fumecheng-7267	345	16	,	,	PUNCT
fumecheng-7267	345	17	prommer	prommer	PROPN
fumecheng-7267	345	18	,	,	PUNCT
fumecheng-7267	345	19	h.	h.	PROPN
fumecheng-7267	345	20	,	,	PUNCT
fumecheng-7267	345	21	cunningham	cunningham	PROPN
fumecheng-7267	345	22	,	,	PUNCT
fumecheng-7267	345	23	c.j	c.j	PROPN
fumecheng-7267	345	24	.	.	PROPN
fumecheng-7267	345	25	,	,	PUNCT
fumecheng-7267	345	26	stagnitti	stagnitti	PROPN
fumecheng-7267	345	27	,	,	PUNCT
fumecheng-7267	345	28	f.	f.	PROPN
fumecheng-7267	345	29	,	,	PUNCT
fumecheng-7267	345	30	2000	2000	NUM
fumecheng-7267	345	31	,	,	PUNCT
fumecheng-7267	345	32	analytical	analytical	ADJ
fumecheng-7267	345	33	approximations	approximation	NOUN
fumecheng-7267	345	34	for	for	ADP
fumecheng-7267	345	35	real	real	ADJ
fumecheng-7267	345	36	values	value	NOUN
fumecheng-7267	345	37	of	of	ADP
fumecheng-7267	345	38	the	the	DET
fumecheng-7267	345	39	lambert	lambert	PROPN
fumecheng-7267	345	40	w	w	PROPN
fumecheng-7267	345	41	-	-	PUNCT
fumecheng-7267	345	42	function	function	NOUN
fumecheng-7267	345	43	,	,	PUNCT
fumecheng-7267	345	44	mathematics	mathematic	NOUN
fumecheng-7267	345	45	and	and	CCONJ
fumecheng-7267	345	46	computers	computer	NOUN
fumecheng-7267	345	47	in	in	ADP
fumecheng-7267	345	48	simulation	simulation	NOUN
fumecheng-7267	345	49	,	,	PUNCT
fumecheng-7267	345	50	53(1	53(1	PROPN
fumecheng-7267	345	51	-	-	SYM
fumecheng-7267	345	52	2	2	NUM
fumecheng-7267	345	53	)	)	PUNCT
fumecheng-7267	345	54	,	,	PUNCT
fumecheng-7267	345	55	pp	pp	ADP
fumecheng-7267	345	56	.	.	PUNCT
fumecheng-7267	346	1	95	95	NUM
fumecheng-7267	346	2	-	-	SYM
fumecheng-7267	346	3	103	103	NUM
fumecheng-7267	346	4	.	.	PUNCT
fumecheng-7267	347	1	35	35	NUM
fumecheng-7267	347	2	.	.	PUNCT
fumecheng-7267	348	1	brkić	brkić	NOUN
fumecheng-7267	348	2	,	,	PUNCT
fumecheng-7267	348	3	d.	d.	PROPN
fumecheng-7267	348	4	,	,	PUNCT
fumecheng-7267	348	5	ćojbašić	ćojbašić	PROPN
fumecheng-7267	348	6	,	,	PUNCT
fumecheng-7267	348	7	ž	ž	PROPN
fumecheng-7267	348	8	.	.	PROPN
fumecheng-7267	348	9	,	,	PUNCT
fumecheng-7267	348	10	2017	2017	NUM
fumecheng-7267	348	11	,	,	PUNCT
fumecheng-7267	348	12	evolutionary	evolutionary	ADJ
fumecheng-7267	348	13	optimization	optimization	NOUN
fumecheng-7267	348	14	of	of	ADP
fumecheng-7267	348	15	colebrook	colebrook	PROPN
fumecheng-7267	348	16	’s	’s	PART
fumecheng-7267	348	17	turbulent	turbulent	ADJ
fumecheng-7267	348	18	flow	flow	NOUN
fumecheng-7267	348	19	friction	friction	NOUN
fumecheng-7267	348	20	approximations	approximation	NOUN
fumecheng-7267	348	21	,	,	PUNCT
fumecheng-7267	348	22	fluids	fluid	NOUN
fumecheng-7267	348	23	,	,	PUNCT
fumecheng-7267	348	24	2(2	2(2	NUM
fumecheng-7267	348	25	)	)	PUNCT
fumecheng-7267	348	26	,	,	PUNCT
fumecheng-7267	348	27	15	15	NUM
fumecheng-7267	348	28	.	.	NOUN
fumecheng-7267	348	29	36	36	NUM
fumecheng-7267	348	30	.	.	PUNCT
fumecheng-7267	349	1	brkić	brkić	NOUN
fumecheng-7267	349	2	,	,	PUNCT
fumecheng-7267	349	3	d.	d.	PROPN
fumecheng-7267	349	4	,	,	PUNCT
fumecheng-7267	349	5	praks	praks	PROPN
fumecheng-7267	349	6	,	,	PUNCT
fumecheng-7267	349	7	p.	p.	NOUN
fumecheng-7267	349	8	,	,	PUNCT
fumecheng-7267	349	9	2019	2019	NUM
fumecheng-7267	349	10	,	,	PUNCT
fumecheng-7267	349	11	accurate	accurate	ADJ
fumecheng-7267	349	12	and	and	CCONJ
fumecheng-7267	349	13	efficient	efficient	ADJ
fumecheng-7267	349	14	explicit	explicit	ADJ
fumecheng-7267	349	15	approximations	approximation	NOUN
fumecheng-7267	349	16	of	of	ADP
fumecheng-7267	349	17	the	the	DET
fumecheng-7267	349	18	colebrook	colebrook	PROPN
fumecheng-7267	349	19	flow	flow	PROPN
fumecheng-7267	349	20	friction	friction	NOUN
fumecheng-7267	349	21	equation	equation	NOUN
fumecheng-7267	349	22	based	base	VERB
fumecheng-7267	349	23	on	on	ADP
fumecheng-7267	349	24	the	the	DET
fumecheng-7267	349	25	wright	wright	PROPN
fumecheng-7267	349	26	ω	ω	PROPN
fumecheng-7267	349	27	-	-	PUNCT
fumecheng-7267	349	28	function	function	NOUN
fumecheng-7267	349	29	.	.	PUNCT
fumecheng-7267	350	1	mathematics	mathematic	NOUN
fumecheng-7267	350	2	,	,	PUNCT
fumecheng-7267	350	3	7(1	7(1	NUM
fumecheng-7267	350	4	)	)	PUNCT
fumecheng-7267	350	5	,	,	PUNCT
fumecheng-7267	350	6	34	34	NUM
fumecheng-7267	350	7	.	.	NOUN
fumecheng-7267	350	8	37	37	NUM
fumecheng-7267	350	9	.	.	PUNCT
fumecheng-7267	351	1	olivares	olivare	NOUN
fumecheng-7267	351	2	,	,	PUNCT
fumecheng-7267	351	3	a.	a.	PROPN
fumecheng-7267	351	4	,	,	PUNCT
fumecheng-7267	351	5	guerra	guerra	PROPN
fumecheng-7267	351	6	,	,	PUNCT
fumecheng-7267	351	7	r.	r.	PROPN
fumecheng-7267	351	8	,	,	PUNCT
fumecheng-7267	351	9	alfaro	alfaro	PROPN
fumecheng-7267	351	10	,	,	PUNCT
fumecheng-7267	351	11	m.	m.	NOUN
fumecheng-7267	351	12	,	,	PUNCT
fumecheng-7267	351	13	notte	notte	NOUN
fumecheng-7267	351	14	-	-	PUNCT
fumecheng-7267	351	15	cuello	cuello	PROPN
fumecheng-7267	351	16	,	,	PUNCT
fumecheng-7267	351	17	e.	e.	PROPN
fumecheng-7267	351	18	,	,	PUNCT
fumecheng-7267	351	19	puentes	puentes	PROPN
fumecheng-7267	351	20	,	,	PUNCT
fumecheng-7267	351	21	l.	l.	PROPN
fumecheng-7267	351	22	,	,	PUNCT
fumecheng-7267	351	23	2019	2019	NUM
fumecheng-7267	351	24	,	,	PUNCT
fumecheng-7267	351	25	evaluación	evaluación	PROPN
fumecheng-7267	351	26	experimental	experimental	PROPN
fumecheng-7267	351	27	de	de	PROPN
fumecheng-7267	351	28	correlaciones	correlaciones	PROPN
fumecheng-7267	351	29	para	para	PROPN
fumecheng-7267	351	30	el	el	PROPN
fumecheng-7267	351	31	cálculo	cálculo	PROPN
fumecheng-7267	351	32	del	del	PROPN
fumecheng-7267	351	33	factor	factor	PROPN
fumecheng-7267	351	34	de	de	PROPN
fumecheng-7267	351	35	fricción	fricción	PROPN
fumecheng-7267	351	36	para	para	PROPN
fumecheng-7267	351	37	flujo	flujo	PROPN
fumecheng-7267	351	38	turbulento	turbulento	PROPN
fumecheng-7267	351	39	en	en	ADP
fumecheng-7267	351	40	tuberías	tuberías	NOUN
fumecheng-7267	351	41	cilíndricas	cilíndricas	NOUN
fumecheng-7267	351	42	,	,	PUNCT
fumecheng-7267	351	43	revista	revista	PROPN
fumecheng-7267	351	44	internacional	internacional	PROPN
fumecheng-7267	351	45	de	de	PROPN
fumecheng-7267	351	46	métodos	métodos	PROPN
fumecheng-7267	351	47	numéricos	numéricos	PROPN
fumecheng-7267	351	48	para	para	PROPN
fumecheng-7267	351	49	cálculo	cálculo	PROPN
fumecheng-7267	351	50	y	y	PROPN
fumecheng-7267	351	51	diseño	diseño	PROPN
fumecheng-7267	351	52	en	en	PROPN
fumecheng-7267	351	53	ingeniería	ingeniería	PROPN
fumecheng-7267	351	54	,	,	PUNCT
fumecheng-7267	351	55	35(1	35(1	NUM
fumecheng-7267	351	56	)	)	PUNCT
fumecheng-7267	351	57	,	,	PUNCT
fumecheng-7267	351	58	15	15	NUM
fumecheng-7267	351	59	.	.	X
fumecheng-7267	351	60	excel	excel	VERB
fumecheng-7267	351	61	vba	vba	PROPN
fumecheng-7267	351	62	-	-	PUNCT
fumecheng-7267	351	63	based	base	VERB
fumecheng-7267	351	64	user	user	NOUN
fumecheng-7267	351	65	defined	define	VERB
fumecheng-7267	351	66	functions	function	NOUN
fumecheng-7267	351	67	for	for	ADP
fumecheng-7267	351	68	highly	highly	ADV
fumecheng-7267	351	69	precise	precise	ADJ
fumecheng-7267	351	70	colebrook	colebrook	PROPN
fumecheng-7267	351	71	’s	’s	PART
fumecheng-7267	351	72	pipe	pipe	NOUN
fumecheng-7267	351	73	flow	flow	NOUN
fumecheng-7267	351	74	friction	friction	NOUN
fumecheng-7267	351	75	...	...	PUNCT
fumecheng-7267	352	1	269	269	NUM
fumecheng-7267	352	2	38	38	NUM
fumecheng-7267	352	3	.	.	PUNCT
fumecheng-7267	353	1	mileikovskyi	mileikovskyi	PROPN
fumecheng-7267	353	2	v.	v.	PROPN
fumecheng-7267	353	3	,	,	PUNCT
fumecheng-7267	353	4	tkachenko	tkachenko	PROPN
fumecheng-7267	353	5	t.	t.	PROPN
fumecheng-7267	353	6	,	,	PUNCT
fumecheng-7267	353	7	2020	2020	NUM
fumecheng-7267	353	8	,	,	PUNCT
fumecheng-7267	353	9	precise	precise	ADJ
fumecheng-7267	353	10	explicit	explicit	ADJ
fumecheng-7267	353	11	approximations	approximation	NOUN
fumecheng-7267	353	12	of	of	ADP
fumecheng-7267	353	13	the	the	DET
fumecheng-7267	353	14	colebrook	colebrook	PROPN
fumecheng-7267	353	15	-	-	PUNCT
fumecheng-7267	353	16	white	white	ADJ
fumecheng-7267	353	17	equation	equation	NOUN
fumecheng-7267	353	18	for	for	ADP
fumecheng-7267	353	19	engineering	engineering	NOUN
fumecheng-7267	353	20	systems	system	NOUN
fumecheng-7267	353	21	,	,	PUNCT
fumecheng-7267	353	22	proceedings	proceeding	NOUN
fumecheng-7267	353	23	of	of	ADP
fumecheng-7267	353	24	ecocomfort	ecocomfort	NOUN
fumecheng-7267	353	25	,	,	PUNCT
fumecheng-7267	353	26	lecture	lecture	NOUN
fumecheng-7267	353	27	notes	note	NOUN
fumecheng-7267	353	28	in	in	ADP
fumecheng-7267	353	29	civil	civil	ADJ
fumecheng-7267	353	30	engineering	engineering	NOUN
fumecheng-7267	353	31	39	39	NUM
fumecheng-7267	353	32	.	.	PUNCT
fumecheng-7267	354	1	muzzo	muzzo	PROPN
fumecheng-7267	354	2	l.e	l.e	PROPN
fumecheng-7267	354	3	.	.	PROPN
fumecheng-7267	354	4	,	,	PUNCT
fumecheng-7267	354	5	pinho	pinho	PROPN
fumecheng-7267	354	6	d.	d.	PROPN
fumecheng-7267	354	7	,	,	PUNCT
fumecheng-7267	354	8	lima	lima	PROPN
fumecheng-7267	354	9	l.e.m	l.e.m	NOUN
fumecheng-7267	354	10	.	.	PUNCT
fumecheng-7267	354	11	,	,	PUNCT
fumecheng-7267	354	12	ribeiro	ribeiro	PROPN
fumecheng-7267	354	13	l.f	l.f	PROPN
fumecheng-7267	354	14	.	.	PROPN
fumecheng-7267	354	15	2019	2019	NUM
fumecheng-7267	354	16	,	,	PUNCT
fumecheng-7267	354	17	accuracy	accuracy	NOUN
fumecheng-7267	354	18	/	/	SYM
fumecheng-7267	354	19	speed	speed	NOUN
fumecheng-7267	354	20	analysis	analysis	NOUN
fumecheng-7267	354	21	of	of	ADP
fumecheng-7267	354	22	pipe	pipe	NOUN
fumecheng-7267	354	23	friction	friction	NOUN
fumecheng-7267	354	24	factor	factor	NOUN
fumecheng-7267	354	25	correlations	correlation	NOUN
fumecheng-7267	354	26	,	,	PUNCT
fumecheng-7267	354	27	proceedings	proceeding	NOUN
fumecheng-7267	354	28	of	of	ADP
fumecheng-7267	354	29	increase	increase	NOUN
fumecheng-7267	354	30	2019	2019	NUM
fumecheng-7267	354	31	40	40	NUM
fumecheng-7267	354	32	.	.	PUNCT
fumecheng-7267	355	1	biberg	biberg	PROPN
fumecheng-7267	355	2	,	,	PUNCT
fumecheng-7267	355	3	d.	d.	PROPN
fumecheng-7267	355	4	,	,	PUNCT
fumecheng-7267	355	5	2017	2017	NUM
fumecheng-7267	355	6	,	,	PUNCT
fumecheng-7267	355	7	fast	fast	ADJ
fumecheng-7267	355	8	and	and	CCONJ
fumecheng-7267	355	9	accurate	accurate	ADJ
fumecheng-7267	355	10	approximations	approximation	NOUN
fumecheng-7267	355	11	for	for	ADP
fumecheng-7267	355	12	the	the	DET
fumecheng-7267	355	13	colebrook	colebrook	PROPN
fumecheng-7267	355	14	equation	equation	PROPN
fumecheng-7267	355	15	,	,	PUNCT
fumecheng-7267	355	16	journal	journal	NOUN
fumecheng-7267	355	17	of	of	ADP
fumecheng-7267	355	18	fluids	fluid	NOUN
fumecheng-7267	355	19	engineering	engineering	NOUN
fumecheng-7267	355	20	,	,	PUNCT
fumecheng-7267	355	21	139(3	139(3	NUM
fumecheng-7267	355	22	)	)	PUNCT
fumecheng-7267	355	23	,	,	PUNCT
fumecheng-7267	355	24	031401	031401	NUM
fumecheng-7267	355	25	.	.	PUNCT
fumecheng-7267	356	1	41	41	NUM
fumecheng-7267	356	2	.	.	PUNCT
fumecheng-7267	357	1	clamond	clamond	PROPN
fumecheng-7267	357	2	,	,	PUNCT
fumecheng-7267	357	3	d.	d.	PROPN
fumecheng-7267	357	4	,	,	PUNCT
fumecheng-7267	357	5	2009	2009	NUM
fumecheng-7267	357	6	.	.	PUNCT
fumecheng-7267	358	1	efficient	efficient	ADJ
fumecheng-7267	358	2	resolution	resolution	NOUN
fumecheng-7267	358	3	of	of	ADP
fumecheng-7267	358	4	the	the	DET
fumecheng-7267	358	5	colebrook	colebrook	PROPN
fumecheng-7267	358	6	equation	equation	NOUN
fumecheng-7267	358	7	,	,	PUNCT
fumecheng-7267	358	8	industrial	industrial	PROPN
fumecheng-7267	358	9	&	&	CCONJ
fumecheng-7267	358	10	engineering	engineer	VERB
fumecheng-7267	358	11	chemistry	chemistry	NOUN
fumecheng-7267	358	12	research	research	NOUN
fumecheng-7267	358	13	,	,	PUNCT
fumecheng-7267	358	14	48(7	48(7	PROPN
fumecheng-7267	358	15	)	)	PUNCT
fumecheng-7267	358	16	,	,	PUNCT
fumecheng-7267	358	17	pp	pp	PROPN
fumecheng-7267	358	18	.	.	PUNCT
fumecheng-7267	358	19	3665	3665	NUM
fumecheng-7267	358	20	-	-	SYM
fumecheng-7267	358	21	3671	3671	NUM
fumecheng-7267	358	22	.	.	PUNCT
fumecheng-7267	359	1	42	42	NUM
fumecheng-7267	359	2	.	.	PUNCT
fumecheng-7267	360	1	winning	win	VERB
fumecheng-7267	360	2	,	,	PUNCT
fumecheng-7267	360	3	h.k	h.k	PROPN
fumecheng-7267	360	4	.	.	PROPN
fumecheng-7267	360	5	,	,	PUNCT
fumecheng-7267	360	6	coole	coole	NOUN
fumecheng-7267	360	7	,	,	PUNCT
fumecheng-7267	360	8	t.	t.	NOUN
fumecheng-7267	360	9	,	,	PUNCT
fumecheng-7267	360	10	2015	2015	NUM
fumecheng-7267	360	11	,	,	PUNCT
fumecheng-7267	360	12	improved	improve	VERB
fumecheng-7267	360	13	method	method	NOUN
fumecheng-7267	360	14	of	of	ADP
fumecheng-7267	360	15	determining	determine	VERB
fumecheng-7267	360	16	friction	friction	NOUN
fumecheng-7267	360	17	factor	factor	NOUN
fumecheng-7267	360	18	in	in	ADP
fumecheng-7267	360	19	pipes	pipe	NOUN
fumecheng-7267	360	20	,	,	PUNCT
fumecheng-7267	360	21	international	international	ADJ
fumecheng-7267	360	22	journal	journal	NOUN
fumecheng-7267	360	23	of	of	ADP
fumecheng-7267	360	24	numerical	numerical	ADJ
fumecheng-7267	360	25	methods	method	NOUN
fumecheng-7267	360	26	for	for	ADP
fumecheng-7267	360	27	heat	heat	NOUN
fumecheng-7267	360	28	&	&	CCONJ
fumecheng-7267	360	29	fluid	fluid	ADJ
fumecheng-7267	360	30	flow	flow	NOUN
fumecheng-7267	360	31	,	,	PUNCT
fumecheng-7267	360	32	25(4	25(4	NOUN
fumecheng-7267	360	33	)	)	PUNCT
fumecheng-7267	360	34	,	,	PUNCT
fumecheng-7267	360	35	pp	pp	ADP
fumecheng-7267	360	36	.	.	PUNCT
fumecheng-7267	361	1	941–949	941–949	NUM
fumecheng-7267	361	2	.	.	X
fumecheng-7267	362	1	43	43	NUM
fumecheng-7267	362	2	.	.	PUNCT
fumecheng-7267	362	3	pérez	pérez	NOUN
fumecheng-7267	362	4	-	-	PUNCT
fumecheng-7267	362	5	pupo	pupo	NOUN
fumecheng-7267	362	6	,	,	PUNCT
fumecheng-7267	362	7	j.r	j.r	PROPN
fumecheng-7267	362	8	.	.	PROPN
fumecheng-7267	362	9	,	,	PUNCT
fumecheng-7267	362	10	navarro	navarro	PROPN
fumecheng-7267	362	11	-	-	PUNCT
fumecheng-7267	362	12	ojeda	ojeda	PROPN
fumecheng-7267	362	13	,	,	PUNCT
fumecheng-7267	362	14	m.n	m.n	PROPN
fumecheng-7267	362	15	.	.	PROPN
fumecheng-7267	362	16	,	,	PUNCT
fumecheng-7267	362	17	pérez	pérez	NOUN
fumecheng-7267	362	18	-	-	PUNCT
fumecheng-7267	362	19	guerrero	guerrero	NOUN
fumecheng-7267	362	20	,	,	PUNCT
fumecheng-7267	362	21	j.n	j.n	PROPN
fumecheng-7267	362	22	.	.	PROPN
fumecheng-7267	362	23	,	,	PUNCT
fumecheng-7267	362	24	batista	batista	PROPN
fumecheng-7267	362	25	-	-	PUNCT
fumecheng-7267	362	26	zaldívar	zaldívar	PROPN
fumecheng-7267	362	27	,	,	PUNCT
fumecheng-7267	362	28	m.a	m.a	PROPN
fumecheng-7267	362	29	.	.	PROPN
fumecheng-7267	362	30	,	,	PUNCT
fumecheng-7267	362	31	2020	2020	NUM
fumecheng-7267	362	32	,	,	PUNCT
fumecheng-7267	362	33	on	on	ADP
fumecheng-7267	362	34	the	the	DET
fumecheng-7267	362	35	explicit	explicit	ADJ
fumecheng-7267	362	36	expressions	expression	NOUN
fumecheng-7267	362	37	for	for	ADP
fumecheng-7267	362	38	the	the	DET
fumecheng-7267	362	39	determination	determination	NOUN
fumecheng-7267	362	40	of	of	ADP
fumecheng-7267	362	41	the	the	DET
fumecheng-7267	362	42	friction	friction	NOUN
fumecheng-7267	362	43	factor	factor	NOUN
fumecheng-7267	362	44	in	in	ADP
fumecheng-7267	362	45	turbulent	turbulent	ADJ
fumecheng-7267	362	46	regime	regime	NOUN
fumecheng-7267	362	47	,	,	PUNCT
fumecheng-7267	362	48	revista	revista	NOUN
fumecheng-7267	362	49	mexicana	mexicana	PROPN
fumecheng-7267	362	50	de	de	PROPN
fumecheng-7267	362	51	ingeniería	ingeniería	PROPN
fumecheng-7267	362	52	química	química	PROPN
fumecheng-7267	362	53	,	,	PUNCT
fumecheng-7267	362	54	19(1	19(1	NUM
fumecheng-7267	362	55	)	)	PUNCT
fumecheng-7267	362	56	,	,	PUNCT
fumecheng-7267	362	57	pp	pp	PROPN
fumecheng-7267	362	58	.	.	PUNCT
fumecheng-7267	363	1	313	313	NUM
fumecheng-7267	363	2	-	-	SYM
fumecheng-7267	363	3	334	334	NUM
fumecheng-7267	363	4	.	.	PUNCT
fumecheng-7267	364	1	44	44	NUM
fumecheng-7267	364	2	.	.	PUNCT
fumecheng-7267	365	1	brkić	brkić	PROPN
fumecheng-7267	365	2	,	,	PUNCT
fumecheng-7267	365	3	d.	d.	PROPN
fumecheng-7267	365	4	,	,	PUNCT
fumecheng-7267	365	5	praks	praks	PROPN
fumecheng-7267	365	6	,	,	PUNCT
fumecheng-7267	365	7	p.	p.	NOUN
fumecheng-7267	365	8	,	,	PUNCT
fumecheng-7267	365	9	2019	2019	NUM
fumecheng-7267	365	10	,	,	PUNCT
fumecheng-7267	365	11	what	what	PRON
fumecheng-7267	365	12	can	can	AUX
fumecheng-7267	365	13	students	student	NOUN
fumecheng-7267	365	14	learn	learn	VERB
fumecheng-7267	365	15	while	while	SCONJ
fumecheng-7267	365	16	solving	solve	VERB
fumecheng-7267	365	17	colebrook	colebrook	PROPN
fumecheng-7267	365	18	’s	’s	PART
fumecheng-7267	365	19	flow	flow	NOUN
fumecheng-7267	365	20	friction	friction	NOUN
fumecheng-7267	365	21	equation	equation	NOUN
fumecheng-7267	365	22	?	?	PUNCT
fumecheng-7267	366	1	fluids	fluid	NOUN
fumecheng-7267	366	2	,	,	PUNCT
fumecheng-7267	366	3	4(3	4(3	NUM
fumecheng-7267	366	4	)	)	PUNCT
fumecheng-7267	366	5	,	,	PUNCT
fumecheng-7267	366	6	114	114	NUM
fumecheng-7267	366	7	.	.	X
fumecheng-7267	366	8	45	45	NUM
fumecheng-7267	366	9	.	.	PUNCT
fumecheng-7267	367	1	ćojbašić	ćojbašić	PROPN
fumecheng-7267	367	2	,	,	PUNCT
fumecheng-7267	367	3	ž	ž	PROPN
fumecheng-7267	367	4	.	.	PROPN
fumecheng-7267	367	5	,	,	PUNCT
fumecheng-7267	367	6	brkić	brkić	NOUN
fumecheng-7267	367	7	,	,	PUNCT
fumecheng-7267	367	8	d.	d.	PROPN
fumecheng-7267	367	9	,	,	PUNCT
fumecheng-7267	367	10	2013	2013	NUM
fumecheng-7267	367	11	,	,	PUNCT
fumecheng-7267	367	12	very	very	ADV
fumecheng-7267	367	13	accurate	accurate	ADJ
fumecheng-7267	367	14	explicit	explicit	ADJ
fumecheng-7267	367	15	approximations	approximation	NOUN
fumecheng-7267	367	16	for	for	ADP
fumecheng-7267	367	17	calculation	calculation	NOUN
fumecheng-7267	367	18	of	of	ADP
fumecheng-7267	367	19	the	the	DET
fumecheng-7267	367	20	colebrook	colebrook	PROPN
fumecheng-7267	367	21	friction	friction	NOUN
fumecheng-7267	367	22	factor	factor	NOUN
fumecheng-7267	367	23	,	,	PUNCT
fumecheng-7267	367	24	international	international	ADJ
fumecheng-7267	367	25	journal	journal	NOUN
fumecheng-7267	367	26	of	of	ADP
fumecheng-7267	367	27	mechanical	mechanical	ADJ
fumecheng-7267	367	28	sciences	science	NOUN
fumecheng-7267	367	29	,	,	PUNCT
fumecheng-7267	367	30	67	67	NUM
fumecheng-7267	367	31	,	,	PUNCT
fumecheng-7267	367	32	pp	pp	ADJ
fumecheng-7267	367	33	.	.	PUNCT
fumecheng-7267	368	1	10	10	NUM
fumecheng-7267	368	2	-	-	SYM
fumecheng-7267	368	3	13	13	NUM
fumecheng-7267	368	4	.	.	PUNCT
fumecheng-7267	369	1	46	46	NUM
fumecheng-7267	369	2	.	.	PUNCT
fumecheng-7267	369	3	petrović	petrović	PROPN
fumecheng-7267	369	4	,	,	PUNCT
fumecheng-7267	369	5	g.	g.	PROPN
fumecheng-7267	369	6	,	,	PUNCT
fumecheng-7267	369	7	mihajlović	mihajlović	PROPN
fumecheng-7267	369	8	,	,	PUNCT
fumecheng-7267	369	9	j.	j.	PROPN
fumecheng-7267	369	10	,	,	PUNCT
fumecheng-7267	369	11	ćojbašić	ćojbašić	PROPN
fumecheng-7267	369	12	,	,	PUNCT
fumecheng-7267	369	13	ž	ž	PROPN
fumecheng-7267	369	14	.	.	PROPN
fumecheng-7267	369	15	,	,	PUNCT
fumecheng-7267	369	16	madić	madić	NOUN
fumecheng-7267	369	17	,	,	PUNCT
fumecheng-7267	369	18	m.	m.	NOUN
fumecheng-7267	369	19	,	,	PUNCT
fumecheng-7267	369	20	marinković	marinković	PROPN
fumecheng-7267	369	21	,	,	PUNCT
fumecheng-7267	369	22	d.	d.	PROPN
fumecheng-7267	369	23	,	,	PUNCT
fumecheng-7267	369	24	2019	2019	NUM
fumecheng-7267	369	25	,	,	PUNCT
fumecheng-7267	369	26	comparison	comparison	NOUN
fumecheng-7267	369	27	of	of	ADP
fumecheng-7267	369	28	three	three	NUM
fumecheng-7267	369	29	fuzzy	fuzzy	ADJ
fumecheng-7267	369	30	mcdm	mcdm	ADJ
fumecheng-7267	369	31	methods	method	NOUN
fumecheng-7267	369	32	for	for	ADP
fumecheng-7267	369	33	solving	solve	VERB
fumecheng-7267	369	34	the	the	DET
fumecheng-7267	369	35	supplier	supplier	NOUN
fumecheng-7267	369	36	selection	selection	NOUN
fumecheng-7267	369	37	problem	problem	NOUN
fumecheng-7267	369	38	,	,	PUNCT
fumecheng-7267	369	39	facta	facta	PROPN
fumecheng-7267	369	40	universitatis	universitatis	PROPN
fumecheng-7267	369	41	-	-	PUNCT
fumecheng-7267	369	42	series	series	NOUN
fumecheng-7267	369	43	mechanical	mechanical	ADJ
fumecheng-7267	369	44	engineering	engineering	NOUN
fumecheng-7267	369	45	,	,	PUNCT
fumecheng-7267	369	46	17(3	17(3	NUM
fumecheng-7267	369	47	)	)	PUNCT
fumecheng-7267	369	48	,	,	PUNCT
fumecheng-7267	369	49	pp	pp	ADP
fumecheng-7267	369	50	.	.	PUNCT
fumecheng-7267	370	1	455	455	NUM
fumecheng-7267	370	2	-	-	SYM
fumecheng-7267	370	3	469	469	NUM
fumecheng-7267	370	4	.	.	PUNCT
fumecheng-7267	371	1	47	47	NUM
fumecheng-7267	371	2	.	.	PUNCT
fumecheng-7267	372	1	sonnad	sonnad	PROPN
fumecheng-7267	372	2	,	,	PUNCT
fumecheng-7267	372	3	j.r	j.r	PROPN
fumecheng-7267	372	4	.	.	PROPN
fumecheng-7267	372	5	,	,	PUNCT
fumecheng-7267	372	6	goudar	goudar	PROPN
fumecheng-7267	372	7	,	,	PUNCT
fumecheng-7267	372	8	c.t	c.t	PROPN
fumecheng-7267	372	9	.	.	PROPN
fumecheng-7267	372	10	,	,	PUNCT
fumecheng-7267	372	11	2006	2006	NUM
fumecheng-7267	372	12	,	,	PUNCT
fumecheng-7267	372	13	turbulent	turbulent	ADJ
fumecheng-7267	372	14	flow	flow	NOUN
fumecheng-7267	372	15	friction	friction	NOUN
fumecheng-7267	372	16	factor	factor	NOUN
fumecheng-7267	372	17	calculation	calculation	NOUN
fumecheng-7267	372	18	using	use	VERB
fumecheng-7267	372	19	a	a	DET
fumecheng-7267	372	20	mathematically	mathematically	ADV
fumecheng-7267	372	21	exact	exact	ADJ
fumecheng-7267	372	22	alternative	alternative	NOUN
fumecheng-7267	372	23	to	to	ADP
fumecheng-7267	372	24	the	the	DET
fumecheng-7267	372	25	colebrook	colebrook	PROPN
fumecheng-7267	372	26	–	–	PUNCT
fumecheng-7267	372	27	white	white	ADJ
fumecheng-7267	372	28	equation	equation	NOUN
fumecheng-7267	372	29	,	,	PUNCT
fumecheng-7267	372	30	journal	journal	NOUN
fumecheng-7267	372	31	of	of	ADP
fumecheng-7267	372	32	hydraulic	hydraulic	ADJ
fumecheng-7267	372	33	engineering	engineering	NOUN
fumecheng-7267	372	34	,	,	PUNCT
fumecheng-7267	372	35	132(8	132(8	NUM
fumecheng-7267	372	36	)	)	PUNCT
fumecheng-7267	372	37	,	,	PUNCT
fumecheng-7267	372	38	pp	pp	PROPN
fumecheng-7267	372	39	.	.	PUNCT
fumecheng-7267	373	1	863	863	NUM
fumecheng-7267	373	2	-	-	SYM
fumecheng-7267	373	3	867	867	NUM
fumecheng-7267	373	4	.	.	PUNCT
fumecheng-7267	374	1	48	48	NUM
fumecheng-7267	374	2	.	.	PUNCT
fumecheng-7267	375	1	mikata	mikata	ADJ
fumecheng-7267	375	2	,	,	PUNCT
fumecheng-7267	375	3	y.	y.	NOUN
fumecheng-7267	375	4	,	,	PUNCT
fumecheng-7267	375	5	walczak	walczak	ADJ
fumecheng-7267	375	6	,	,	PUNCT
fumecheng-7267	375	7	w.s	w.s	PROPN
fumecheng-7267	375	8	.	.	PROPN
fumecheng-7267	375	9	,	,	PUNCT
fumecheng-7267	375	10	2016	2016	NUM
fumecheng-7267	375	11	,	,	PUNCT
fumecheng-7267	375	12	exact	exact	ADJ
fumecheng-7267	375	13	analytical	analytical	ADJ
fumecheng-7267	375	14	solutions	solution	NOUN
fumecheng-7267	375	15	of	of	ADP
fumecheng-7267	375	16	the	the	DET
fumecheng-7267	375	17	colebrook	colebrook	PROPN
fumecheng-7267	375	18	-	-	PUNCT
fumecheng-7267	375	19	white	white	PROPN
fumecheng-7267	375	20	equation	equation	NOUN
fumecheng-7267	375	21	,	,	PUNCT
fumecheng-7267	375	22	journal	journal	NOUN
fumecheng-7267	375	23	of	of	ADP
fumecheng-7267	375	24	hydraulic	hydraulic	ADJ
fumecheng-7267	375	25	engineering	engineering	NOUN
fumecheng-7267	375	26	,	,	PUNCT
fumecheng-7267	375	27	142(2	142(2	NUM
fumecheng-7267	375	28	)	)	PUNCT
fumecheng-7267	375	29	,	,	PUNCT
fumecheng-7267	375	30	04015050	04015050	NUM
fumecheng-7267	375	31	.	.	PUNCT
fumecheng-7267	376	1	49	49	NUM
fumecheng-7267	376	2	.	.	PUNCT
fumecheng-7267	377	1	zigrang	zigrang	PROPN
fumecheng-7267	377	2	,	,	PUNCT
fumecheng-7267	377	3	d.j	d.j	PROPN
fumecheng-7267	377	4	.	.	PROPN
fumecheng-7267	377	5	,	,	PUNCT
fumecheng-7267	377	6	sylvester	sylvester	PROPN
fumecheng-7267	377	7	,	,	PUNCT
fumecheng-7267	377	8	n.d	n.d	PROPN
fumecheng-7267	377	9	.	.	PROPN
fumecheng-7267	377	10	,	,	PUNCT
fumecheng-7267	377	11	1982	1982	NUM
fumecheng-7267	377	12	,	,	PUNCT
fumecheng-7267	377	13	explicit	explicit	ADJ
fumecheng-7267	377	14	approximations	approximation	NOUN
fumecheng-7267	377	15	to	to	ADP
fumecheng-7267	377	16	the	the	DET
fumecheng-7267	377	17	solution	solution	NOUN
fumecheng-7267	377	18	of	of	ADP
fumecheng-7267	377	19	colebrook	colebrook	PROPN
fumecheng-7267	377	20	's	's	PART
fumecheng-7267	377	21	friction	friction	NOUN
fumecheng-7267	377	22	factor	factor	NOUN
fumecheng-7267	377	23	equation	equation	NOUN
fumecheng-7267	377	24	,	,	PUNCT
fumecheng-7267	377	25	aiche	aiche	PROPN
fumecheng-7267	377	26	journal	journal	PROPN
fumecheng-7267	377	27	,	,	PUNCT
fumecheng-7267	377	28	28(3	28(3	NUM
fumecheng-7267	377	29	)	)	PUNCT
fumecheng-7267	377	30	,	,	PUNCT
fumecheng-7267	377	31	pp	pp	ADP
fumecheng-7267	377	32	.	.	PUNCT
fumecheng-7267	378	1	514	514	NUM
fumecheng-7267	378	2	-	-	SYM
fumecheng-7267	378	3	515	515	NUM
fumecheng-7267	378	4	.	.	NOUN
fumecheng-7267	379	1	50	50	NUM
fumecheng-7267	379	2	.	.	PUNCT
fumecheng-7267	380	1	kesisoglou	kesisoglou	PROPN
fumecheng-7267	380	2	,	,	PUNCT
fumecheng-7267	380	3	i.	i.	PROPN
fumecheng-7267	380	4	,	,	PUNCT
fumecheng-7267	380	5	singh	singh	PROPN
fumecheng-7267	380	6	,	,	PUNCT
fumecheng-7267	380	7	g.	g.	PROPN
fumecheng-7267	380	8	,	,	PUNCT
fumecheng-7267	380	9	nikolaou	nikolaou	NOUN
fumecheng-7267	380	10	,	,	PUNCT
fumecheng-7267	380	11	m.	m.	NOUN
fumecheng-7267	380	12	,	,	PUNCT
fumecheng-7267	380	13	2021	2021	NUM
fumecheng-7267	380	14	,	,	PUNCT
fumecheng-7267	380	15	the	the	DET
fumecheng-7267	380	16	lambert	lambert	NOUN
fumecheng-7267	380	17	function	function	NOUN
fumecheng-7267	380	18	should	should	AUX
fumecheng-7267	380	19	be	be	AUX
fumecheng-7267	380	20	in	in	ADP
fumecheng-7267	380	21	the	the	DET
fumecheng-7267	380	22	engineering	engineering	NOUN
fumecheng-7267	380	23	mathematical	mathematical	ADJ
fumecheng-7267	380	24	toolbox	toolbox	NOUN
fumecheng-7267	380	25	,	,	PUNCT
fumecheng-7267	380	26	computers	computer	NOUN
fumecheng-7267	380	27	&	&	CCONJ
fumecheng-7267	380	28	chemical	chemical	PROPN
fumecheng-7267	380	29	engineering	engineering	NOUN
fumecheng-7267	380	30	,	,	PUNCT
fumecheng-7267	380	31	148	148	NUM
fumecheng-7267	380	32	,	,	PUNCT
fumecheng-7267	380	33	107259	107259	NUM
fumecheng-7267	380	34	.	.	PUNCT