id	sid	tid	token	lemma	pos
ap-8605	1	1	acta	acta	PROPN
ap-8605	1	2	polytechnica	polytechnica	PROPN
ap-8605	1	3	https://doi.org/10.14311/ap.2023.63.0103	https://doi.org/10.14311/ap.2023.63.0103	PROPN
ap-8605	1	4	acta	acta	PROPN
ap-8605	1	5	polytechnica	polytechnica	PROPN
ap-8605	1	6	63(2):103–110	63(2):103–110	PROPN
ap-8605	1	7	,	,	PUNCT
ap-8605	1	8	2023	2023	NUM
ap-8605	1	9	©	©	ADP
ap-8605	1	10	2023	2023	NUM
ap-8605	1	11	the	the	DET
ap-8605	1	12	author(s	author(s	NOUN
ap-8605	1	13	)	)	PUNCT
ap-8605	1	14	.	.	PUNCT
ap-8605	2	1	licensed	license	VERB
ap-8605	2	2	under	under	ADP
ap-8605	2	3	a	a	DET
ap-8605	2	4	cc	cc	NOUN
ap-8605	2	5	-	-	PUNCT
ap-8605	2	6	by	by	ADP
ap-8605	2	7	4.0	4.0	NUM
ap-8605	2	8	licence	licence	NOUN
ap-8605	2	9	published	publish	VERB
ap-8605	2	10	by	by	ADP
ap-8605	2	11	the	the	DET
ap-8605	2	12	czech	czech	PROPN
ap-8605	2	13	technical	technical	PROPN
ap-8605	2	14	university	university	PROPN
ap-8605	2	15	in	in	ADP
ap-8605	2	16	prague	prague	PROPN
ap-8605	2	17	derivation	derivation	NOUN
ap-8605	2	18	of	of	ADP
ap-8605	2	19	entropy	entropy	NOUN
ap-8605	2	20	production	production	NOUN
ap-8605	2	21	in	in	ADP
ap-8605	2	22	a	a	DET
ap-8605	2	23	fluid	fluid	ADJ
ap-8605	2	24	flow	flow	NOUN
ap-8605	2	25	in	in	ADP
ap-8605	2	26	a	a	DET
ap-8605	2	27	general	general	ADJ
ap-8605	2	28	curvilinear	curvilinear	NOUN
ap-8605	2	29	coordinate	coordinate	NOUN
ap-8605	2	30	system	system	NOUN
ap-8605	2	31	erik	erik	PROPN
ap-8605	2	32	flídr	flídr	PROPN
ap-8605	2	33	czech	czech	PROPN
ap-8605	2	34	technical	technical	PROPN
ap-8605	2	35	university	university	PROPN
ap-8605	2	36	in	in	ADP
ap-8605	2	37	prague	prague	PROPN
ap-8605	2	38	,	,	PUNCT
ap-8605	2	39	faculty	faculty	NOUN
ap-8605	2	40	of	of	ADP
ap-8605	2	41	mechanical	mechanical	ADJ
ap-8605	2	42	engineering	engineering	NOUN
ap-8605	2	43	,	,	PUNCT
ap-8605	2	44	technická	technická	NOUN
ap-8605	2	45	4	4	NUM
ap-8605	2	46	,	,	PUNCT
ap-8605	2	47	160	160	NUM
ap-8605	2	48	00	00	NUM
ap-8605	3	1	prague	prague	PROPN
ap-8605	3	2	6	6	NUM
ap-8605	3	3	–	–	PUNCT
ap-8605	3	4	dejvice	dejvice	NOUN
ap-8605	3	5	,	,	PUNCT
ap-8605	3	6	czech	czech	PROPN
ap-8605	3	7	republic	republic	NOUN
ap-8605	3	8	correspondence	correspondence	NOUN
ap-8605	3	9	:	:	PUNCT
ap-8605	4	1	flidreri@gmail.com	flidreri@gmail.com	X
ap-8605	4	2	abstract	abstract	ADJ
ap-8605	4	3	.	.	PUNCT
ap-8605	5	1	the	the	DET
ap-8605	5	2	paper	paper	NOUN
ap-8605	5	3	deals	deal	VERB
ap-8605	5	4	with	with	ADP
ap-8605	5	5	the	the	DET
ap-8605	5	6	derivation	derivation	NOUN
ap-8605	5	7	of	of	ADP
ap-8605	5	8	the	the	DET
ap-8605	5	9	entropy	entropy	NOUN
ap-8605	5	10	production	production	NOUN
ap-8605	5	11	in	in	ADP
ap-8605	5	12	the	the	DET
ap-8605	5	13	fluid	fluid	ADJ
ap-8605	5	14	flow	flow	NOUN
ap-8605	5	15	performed	perform	VERB
ap-8605	5	16	in	in	ADP
ap-8605	5	17	a	a	DET
ap-8605	5	18	general	general	ADJ
ap-8605	5	19	curvilinear	curvilinear	ADJ
ap-8605	5	20	coordinate	coordinate	NOUN
ap-8605	5	21	system	system	NOUN
ap-8605	5	22	.	.	PUNCT
ap-8605	6	1	the	the	DET
ap-8605	6	2	derivation	derivation	NOUN
ap-8605	6	3	of	of	ADP
ap-8605	6	4	the	the	DET
ap-8605	6	5	entropy	entropy	NOUN
ap-8605	6	6	production	production	NOUN
ap-8605	6	7	is	be	AUX
ap-8605	6	8	based	base	VERB
ap-8605	6	9	on	on	ADP
ap-8605	6	10	the	the	DET
ap-8605	6	11	thermodynamics	thermodynamic	NOUN
ap-8605	6	12	laws	law	NOUN
ap-8605	6	13	as	as	ADV
ap-8605	6	14	well	well	ADV
ap-8605	6	15	as	as	ADP
ap-8605	6	16	on	on	ADP
ap-8605	6	17	the	the	DET
ap-8605	6	18	balances	balance	NOUN
ap-8605	6	19	of	of	ADP
ap-8605	6	20	mass	mass	ADJ
ap-8605	6	21	,	,	PUNCT
ap-8605	6	22	momentum	momentum	NOUN
ap-8605	6	23	,	,	PUNCT
ap-8605	6	24	and	and	CCONJ
ap-8605	6	25	energy	energy	NOUN
ap-8605	6	26	.	.	PUNCT
ap-8605	7	1	a	a	DET
ap-8605	7	2	brief	brief	ADJ
ap-8605	7	3	description	description	NOUN
ap-8605	7	4	of	of	ADP
ap-8605	7	5	the	the	DET
ap-8605	7	6	differential	differential	ADJ
ap-8605	7	7	geometry	geometry	NOUN
ap-8605	7	8	used	use	VERB
ap-8605	7	9	in	in	ADP
ap-8605	7	10	general	general	ADJ
ap-8605	7	11	curvilinear	curvilinear	PROPN
ap-8605	7	12	coordinates	coordinate	NOUN
ap-8605	7	13	is	be	AUX
ap-8605	7	14	presented	present	VERB
ap-8605	7	15	here	here	ADV
ap-8605	7	16	as	as	ADV
ap-8605	7	17	well	well	ADV
ap-8605	7	18	to	to	PART
ap-8605	7	19	define	define	VERB
ap-8605	7	20	the	the	DET
ap-8605	7	21	used	used	ADJ
ap-8605	7	22	notation	notation	NOUN
ap-8605	7	23	.	.	PUNCT
ap-8605	8	1	the	the	DET
ap-8605	8	2	application	application	NOUN
ap-8605	8	3	of	of	ADP
ap-8605	8	4	this	this	DET
ap-8605	8	5	approach	approach	NOUN
ap-8605	8	6	is	be	AUX
ap-8605	8	7	then	then	ADV
ap-8605	8	8	shown	show	VERB
ap-8605	8	9	in	in	ADP
ap-8605	8	10	the	the	DET
ap-8605	8	11	evaluation	evaluation	NOUN
ap-8605	8	12	of	of	ADP
ap-8605	8	13	the	the	DET
ap-8605	8	14	entropy	entropy	NOUN
ap-8605	8	15	production	production	NOUN
ap-8605	8	16	along	along	ADP
ap-8605	8	17	the	the	DET
ap-8605	8	18	suction	suction	NOUN
ap-8605	8	19	side	side	NOUN
ap-8605	8	20	of	of	ADP
ap-8605	8	21	the	the	DET
ap-8605	8	22	blade	blade	NOUN
ap-8605	8	23	,	,	PUNCT
ap-8605	8	24	where	where	SCONJ
ap-8605	8	25	the	the	DET
ap-8605	8	26	calculation	calculation	NOUN
ap-8605	8	27	was	be	AUX
ap-8605	8	28	performed	perform	VERB
ap-8605	8	29	using	use	VERB
ap-8605	8	30	available	available	ADJ
ap-8605	8	31	experimental	experimental	ADJ
ap-8605	8	32	data	datum	NOUN
ap-8605	8	33	.	.	PUNCT
ap-8605	9	1	keywords	keyword	NOUN
ap-8605	9	2	:	:	PUNCT
ap-8605	9	3	entropy	entropy	PROPN
ap-8605	9	4	production	production	NOUN
ap-8605	9	5	,	,	PUNCT
ap-8605	9	6	fluid	fluid	ADJ
ap-8605	9	7	flow	flow	NOUN
ap-8605	9	8	,	,	PUNCT
ap-8605	9	9	general	general	ADJ
ap-8605	9	10	curvilinear	curvilinear	PROPN
ap-8605	9	11	coordinates	coordinate	NOUN
ap-8605	9	12	,	,	PUNCT
ap-8605	9	13	linear	linear	ADJ
ap-8605	9	14	blade	blade	NOUN
ap-8605	9	15	cascade	cascade	NOUN
ap-8605	9	16	,	,	PUNCT
ap-8605	9	17	experimental	experimental	ADJ
ap-8605	9	18	data	datum	NOUN
ap-8605	9	19	.	.	PUNCT
ap-8605	10	1	1	1	X
ap-8605	10	2	.	.	X
ap-8605	10	3	introduction	introduction	NOUN
ap-8605	10	4	a	a	DET
ap-8605	10	5	general	general	ADJ
ap-8605	10	6	curvilinear	curvilinear	ADJ
ap-8605	10	7	description	description	NOUN
ap-8605	10	8	of	of	ADP
ap-8605	10	9	a	a	DET
ap-8605	10	10	flow	flow	NOUN
ap-8605	10	11	is	be	AUX
ap-8605	10	12	useful	useful	ADJ
ap-8605	10	13	to	to	PART
ap-8605	10	14	describe	describe	VERB
ap-8605	10	15	the	the	DET
ap-8605	10	16	flow	flow	NOUN
ap-8605	10	17	in	in	ADP
ap-8605	10	18	highly	highly	ADV
ap-8605	10	19	curved	curved	ADJ
ap-8605	10	20	channels	channel	NOUN
ap-8605	10	21	,	,	PUNCT
ap-8605	10	22	e.g.	e.g.	ADV
ap-8605	10	23	turbine	turbine	NOUN
ap-8605	10	24	blade	blade	NOUN
ap-8605	10	25	passages	passage	NOUN
ap-8605	10	26	.	.	PUNCT
ap-8605	11	1	it	it	PRON
ap-8605	11	2	is	be	AUX
ap-8605	11	3	better	well	ADJ
ap-8605	11	4	for	for	ADP
ap-8605	11	5	understanding	understand	VERB
ap-8605	11	6	the	the	DET
ap-8605	11	7	processes	process	NOUN
ap-8605	11	8	that	that	PRON
ap-8605	11	9	occur	occur	VERB
ap-8605	11	10	in	in	ADP
ap-8605	11	11	the	the	DET
ap-8605	11	12	flow	flow	NOUN
ap-8605	11	13	field	field	NOUN
ap-8605	11	14	because	because	SCONJ
ap-8605	11	15	the	the	DET
ap-8605	11	16	researcher	researcher	NOUN
ap-8605	11	17	can	can	AUX
ap-8605	11	18	make	make	VERB
ap-8605	11	19	some	some	DET
ap-8605	11	20	predictions	prediction	NOUN
ap-8605	11	21	about	about	ADP
ap-8605	11	22	the	the	DET
ap-8605	11	23	flow	flow	NOUN
ap-8605	11	24	without	without	ADP
ap-8605	11	25	solving	solve	VERB
ap-8605	11	26	the	the	DET
ap-8605	11	27	equations	equation	NOUN
ap-8605	11	28	at	at	ADV
ap-8605	11	29	all	all	ADV
ap-8605	11	30	.	.	PUNCT
ap-8605	12	1	meaning	mean	VERB
ap-8605	12	2	,	,	PUNCT
ap-8605	12	3	that	that	SCONJ
ap-8605	12	4	it	it	PRON
ap-8605	12	5	can	can	AUX
ap-8605	12	6	be	be	AUX
ap-8605	12	7	deduced	deduce	VERB
ap-8605	12	8	from	from	ADP
ap-8605	12	9	the	the	DET
ap-8605	12	10	form	form	NOUN
ap-8605	12	11	of	of	ADP
ap-8605	12	12	equations	equation	NOUN
ap-8605	12	13	whose	whose	DET
ap-8605	12	14	terms	term	NOUN
ap-8605	12	15	will	will	AUX
ap-8605	12	16	affect	affect	VERB
ap-8605	12	17	the	the	DET
ap-8605	12	18	results	result	NOUN
ap-8605	12	19	mostly	mostly	ADV
ap-8605	12	20	and	and	CCONJ
ap-8605	12	21	,	,	PUNCT
ap-8605	12	22	next	next	ADV
ap-8605	12	23	,	,	PUNCT
ap-8605	12	24	if	if	SCONJ
ap-8605	12	25	the	the	DET
ap-8605	12	26	geometry	geometry	NOUN
ap-8605	12	27	of	of	ADP
ap-8605	12	28	the	the	DET
ap-8605	12	29	problem	problem	NOUN
ap-8605	12	30	under	under	ADP
ap-8605	12	31	investigation	investigation	NOUN
ap-8605	12	32	will	will	AUX
ap-8605	12	33	be	be	AUX
ap-8605	12	34	varied	varied	ADJ
ap-8605	12	35	,	,	PUNCT
ap-8605	12	36	how	how	SCONJ
ap-8605	12	37	this	this	DET
ap-8605	12	38	geometry	geometry	NOUN
ap-8605	12	39	variation	variation	NOUN
ap-8605	12	40	can	can	AUX
ap-8605	12	41	affect	affect	VERB
ap-8605	12	42	the	the	DET
ap-8605	12	43	obtained	obtain	VERB
ap-8605	12	44	data	datum	NOUN
ap-8605	12	45	.	.	PUNCT
ap-8605	13	1	the	the	DET
ap-8605	13	2	derivation	derivation	NOUN
ap-8605	13	3	of	of	ADP
ap-8605	13	4	the	the	DET
ap-8605	13	5	equations	equation	NOUN
ap-8605	13	6	of	of	ADP
ap-8605	13	7	a	a	DET
ap-8605	13	8	fluid	fluid	ADJ
ap-8605	13	9	flow	flow	NOUN
ap-8605	13	10	in	in	ADP
ap-8605	13	11	a	a	DET
ap-8605	13	12	general	general	ADJ
ap-8605	13	13	curvilinear	curvilinear	NOUN
ap-8605	13	14	coordinate	coordinate	NOUN
ap-8605	13	15	system	system	NOUN
ap-8605	13	16	was	be	AUX
ap-8605	13	17	performed	perform	VERB
ap-8605	13	18	several	several	ADJ
ap-8605	13	19	times	time	NOUN
ap-8605	13	20	.	.	PUNCT
ap-8605	14	1	for	for	ADP
ap-8605	14	2	the	the	DET
ap-8605	14	3	first	first	ADJ
ap-8605	14	4	time	time	NOUN
ap-8605	14	5	,	,	PUNCT
ap-8605	14	6	it	it	PRON
ap-8605	14	7	was	be	AUX
ap-8605	14	8	performed	perform	VERB
ap-8605	14	9	in	in	ADP
ap-8605	14	10	[	[	X
ap-8605	14	11	1	1	NUM
ap-8605	14	12	]	]	PUNCT
ap-8605	14	13	,	,	PUNCT
ap-8605	14	14	where	where	SCONJ
ap-8605	14	15	curvilinear	curvilinear	ADJ
ap-8605	14	16	components	component	NOUN
ap-8605	14	17	of	of	ADP
ap-8605	14	18	velocity	velocity	NOUN
ap-8605	14	19	vector	vector	NOUN
ap-8605	14	20	were	be	AUX
ap-8605	14	21	introduced	introduce	VERB
ap-8605	14	22	.	.	PUNCT
ap-8605	15	1	a	a	DET
ap-8605	15	2	more	more	ADV
ap-8605	15	3	detailed	detailed	ADJ
ap-8605	15	4	description	description	NOUN
ap-8605	15	5	can	can	AUX
ap-8605	15	6	be	be	AUX
ap-8605	15	7	found	find	VERB
ap-8605	15	8	in	in	ADP
ap-8605	15	9	book	book	NOUN
ap-8605	15	10	[	[	X
ap-8605	15	11	2	2	NUM
ap-8605	15	12	]	]	PUNCT
ap-8605	15	13	.	.	PUNCT
ap-8605	16	1	the	the	DET
ap-8605	16	2	derivation	derivation	NOUN
ap-8605	16	3	of	of	ADP
ap-8605	16	4	the	the	DET
ap-8605	16	5	momentum	momentum	NOUN
ap-8605	16	6	equation	equation	NOUN
ap-8605	16	7	in	in	ADP
ap-8605	16	8	general	general	ADJ
ap-8605	16	9	curvilinear	curvilinear	PROPN
ap-8605	16	10	coordinates	coordinate	NOUN
ap-8605	16	11	as	as	ADV
ap-8605	16	12	well	well	ADV
ap-8605	16	13	as	as	ADP
ap-8605	16	14	the	the	DET
ap-8605	16	15	description	description	NOUN
ap-8605	16	16	of	of	ADP
ap-8605	16	17	differential	differential	ADJ
ap-8605	16	18	geometry	geometry	NOUN
ap-8605	16	19	with	with	ADP
ap-8605	16	20	application	application	NOUN
ap-8605	16	21	to	to	ADP
ap-8605	16	22	physics	physics	NOUN
ap-8605	16	23	was	be	AUX
ap-8605	16	24	introduced	introduce	VERB
ap-8605	16	25	in	in	ADP
ap-8605	16	26	[	[	X
ap-8605	16	27	3	3	NUM
ap-8605	16	28	]	]	PUNCT
ap-8605	16	29	.	.	PUNCT
ap-8605	17	1	there	there	PRON
ap-8605	17	2	are	be	VERB
ap-8605	17	3	,	,	PUNCT
ap-8605	17	4	of	of	ADP
ap-8605	17	5	course	course	NOUN
ap-8605	17	6	,	,	PUNCT
ap-8605	17	7	papers	paper	NOUN
ap-8605	17	8	focused	focus	VERB
ap-8605	17	9	on	on	ADP
ap-8605	17	10	the	the	DET
ap-8605	17	11	application	application	NOUN
ap-8605	17	12	of	of	ADP
ap-8605	17	13	this	this	DET
ap-8605	17	14	approach	approach	NOUN
ap-8605	17	15	to	to	ADP
ap-8605	17	16	the	the	DET
ap-8605	17	17	numerical	numerical	ADJ
ap-8605	17	18	simulations	simulation	NOUN
ap-8605	17	19	,	,	PUNCT
ap-8605	17	20	see	see	VERB
ap-8605	17	21	e.g.	e.g.	ADV
ap-8605	17	22	[	[	X
ap-8605	17	23	4	4	NUM
ap-8605	17	24	]	]	PUNCT
ap-8605	17	25	,	,	PUNCT
ap-8605	17	26	or	or	CCONJ
ap-8605	17	27	[	[	X
ap-8605	17	28	5	5	NUM
ap-8605	17	29	]	]	PUNCT
ap-8605	17	30	.	.	PUNCT
ap-8605	18	1	these	these	DET
ap-8605	18	2	papers	paper	NOUN
ap-8605	18	3	,	,	PUNCT
ap-8605	18	4	however	however	ADV
ap-8605	18	5	,	,	PUNCT
ap-8605	18	6	are	be	AUX
ap-8605	18	7	considering	consider	VERB
ap-8605	18	8	only	only	ADV
ap-8605	18	9	an	an	DET
ap-8605	18	10	incompressible	incompressible	ADJ
ap-8605	18	11	fluid	fluid	ADJ
ap-8605	18	12	flow	flow	NOUN
ap-8605	18	13	.	.	PUNCT
ap-8605	19	1	the	the	DET
ap-8605	19	2	aim	aim	NOUN
ap-8605	19	3	of	of	ADP
ap-8605	19	4	this	this	DET
ap-8605	19	5	paper	paper	NOUN
ap-8605	19	6	is	be	AUX
ap-8605	19	7	to	to	PART
ap-8605	19	8	go	go	VERB
ap-8605	19	9	a	a	DET
ap-8605	19	10	little	little	ADJ
ap-8605	19	11	bit	bit	NOUN
ap-8605	19	12	further	far	ADV
ap-8605	19	13	and	and	CCONJ
ap-8605	19	14	derive	derive	VERB
ap-8605	19	15	not	not	PART
ap-8605	19	16	only	only	ADV
ap-8605	19	17	the	the	DET
ap-8605	19	18	equations	equation	NOUN
ap-8605	19	19	of	of	ADP
ap-8605	19	20	the	the	DET
ap-8605	19	21	fluid	fluid	ADJ
ap-8605	19	22	flow	flow	NOUN
ap-8605	19	23	but	but	CCONJ
ap-8605	19	24	unite	unite	VERB
ap-8605	19	25	the	the	DET
ap-8605	19	26	fluid	fluid	ADJ
ap-8605	19	27	mechanics	mechanic	NOUN
ap-8605	19	28	and	and	CCONJ
ap-8605	19	29	thermodynamics	thermodynamic	NOUN
ap-8605	19	30	to	to	PART
ap-8605	19	31	obtain	obtain	VERB
ap-8605	19	32	the	the	DET
ap-8605	19	33	entropy	entropy	NOUN
ap-8605	19	34	production	production	NOUN
ap-8605	19	35	in	in	ADP
ap-8605	19	36	the	the	DET
ap-8605	19	37	flowing	flow	VERB
ap-8605	19	38	fluid	fluid	NOUN
ap-8605	19	39	in	in	ADP
ap-8605	19	40	the	the	DET
ap-8605	19	41	general	general	ADJ
ap-8605	19	42	coordinate	coordinate	NOUN
ap-8605	19	43	system	system	NOUN
ap-8605	19	44	.	.	PUNCT
ap-8605	20	1	this	this	DET
ap-8605	20	2	result	result	NOUN
ap-8605	20	3	was	be	AUX
ap-8605	20	4	not	not	PART
ap-8605	20	5	published	publish	VERB
ap-8605	20	6	so	so	ADV
ap-8605	20	7	far	far	ADV
ap-8605	20	8	according	accord	VERB
ap-8605	20	9	to	to	ADP
ap-8605	20	10	the	the	DET
ap-8605	20	11	author	author	NOUN
ap-8605	20	12	’s	’s	PART
ap-8605	20	13	knowledge	knowledge	NOUN
ap-8605	20	14	.	.	PUNCT
ap-8605	21	1	the	the	DET
ap-8605	21	2	entropy	entropy	PROPN
ap-8605	21	3	production	production	NOUN
ap-8605	21	4	in	in	ADP
ap-8605	21	5	a	a	DET
ap-8605	21	6	flowing	flow	VERB
ap-8605	21	7	fluid	fluid	NOUN
ap-8605	21	8	was	be	AUX
ap-8605	21	9	recently	recently	ADV
ap-8605	21	10	derived	derive	VERB
ap-8605	21	11	in	in	ADP
ap-8605	21	12	[	[	X
ap-8605	21	13	6	6	NUM
ap-8605	21	14	]	]	PUNCT
ap-8605	21	15	,	,	PUNCT
ap-8605	21	16	however	however	ADV
ap-8605	21	17	,	,	PUNCT
ap-8605	21	18	this	this	DET
ap-8605	21	19	derivation	derivation	NOUN
ap-8605	21	20	was	be	AUX
ap-8605	21	21	performed	perform	VERB
ap-8605	21	22	in	in	ADP
ap-8605	21	23	a	a	DET
ap-8605	21	24	vector	vector	NOUN
ap-8605	21	25	form	form	NOUN
ap-8605	21	26	.	.	PUNCT
ap-8605	22	1	2	2	X
ap-8605	22	2	.	.	X
ap-8605	22	3	basics	basic	NOUN
ap-8605	22	4	of	of	ADP
ap-8605	22	5	differential	differential	ADJ
ap-8605	22	6	geometry	geometry	NOUN
ap-8605	22	7	the	the	DET
ap-8605	22	8	definition	definition	NOUN
ap-8605	22	9	of	of	ADP
ap-8605	22	10	the	the	DET
ap-8605	22	11	tensor1	tensor1	NOUN
ap-8605	22	12	has	have	VERB
ap-8605	22	13	to	to	PART
ap-8605	22	14	be	be	AUX
ap-8605	22	15	mentioned	mention	VERB
ap-8605	22	16	in	in	ADP
ap-8605	22	17	the	the	DET
ap-8605	22	18	following	follow	VERB
ap-8605	22	19	paragraph	paragraph	NOUN
ap-8605	22	20	.	.	PUNCT
ap-8605	23	1	the	the	DET
ap-8605	23	2	tensor	tensor	NOUN
ap-8605	23	3	is	be	AUX
ap-8605	23	4	a	a	DET
ap-8605	23	5	quantity	quantity	NOUN
ap-8605	23	6	that	that	PRON
ap-8605	23	7	exists	exist	VERB
ap-8605	23	8	independently	independently	ADV
ap-8605	23	9	whether	whether	SCONJ
ap-8605	23	10	there	there	PRON
ap-8605	23	11	is	be	VERB
ap-8605	23	12	some	some	DET
ap-8605	23	13	observer	observer	NOUN
ap-8605	23	14	present	present	ADJ
ap-8605	23	15	or	or	CCONJ
ap-8605	23	16	not	not	PART
ap-8605	23	17	.	.	PUNCT
ap-8605	24	1	tensor	tensor	NOUN
ap-8605	24	2	is	be	AUX
ap-8605	24	3	then	then	ADV
ap-8605	24	4	given	give	VERB
ap-8605	24	5	by	by	ADP
ap-8605	24	6	its	its	PRON
ap-8605	24	7	components	component	NOUN
ap-8605	24	8	multiplied	multiply	VERB
ap-8605	24	9	by	by	ADP
ap-8605	24	10	basis	basis	NOUN
ap-8605	24	11	vectors	vector	NOUN
ap-8605	24	12	.	.	PUNCT
ap-8605	25	1	the	the	DET
ap-8605	25	2	sum	sum	NOUN
ap-8605	25	3	of	of	ADP
ap-8605	25	4	these	these	DET
ap-8605	25	5	multiplied	multiply	VERB
ap-8605	25	6	components	component	NOUN
ap-8605	25	7	with	with	ADP
ap-8605	25	8	basis	basis	NOUN
ap-8605	25	9	vector	vector	NOUN
ap-8605	25	10	has	have	VERB
ap-8605	25	11	to	to	PART
ap-8605	25	12	be	be	AUX
ap-8605	25	13	invariant	invariant	ADJ
ap-8605	25	14	under	under	ADP
ap-8605	25	15	basis	basis	NOUN
ap-8605	25	16	transformation	transformation	NOUN
ap-8605	25	17	(	(	PUNCT
ap-8605	25	18	equation	equation	NOUN
ap-8605	25	19	(	(	PUNCT
ap-8605	25	20	1	1	NUM
ap-8605	25	21	)	)	PUNCT
ap-8605	25	22	)	)	PUNCT
ap-8605	25	23	,	,	PUNCT
ap-8605	25	24	i.e.	i.e.	X
ap-8605	25	25	that	that	SCONJ
ap-8605	25	26	tensors	tensor	NOUN
ap-8605	25	27	of	of	ADP
ap-8605	25	28	the	the	DET
ap-8605	25	29	first	first	ADJ
ap-8605	25	30	order	order	NOUN
ap-8605	25	31	(	(	PUNCT
ap-8605	25	32	vector	vector	NOUN
ap-8605	25	33	)	)	PUNCT
ap-8605	25	34	obey	obey	VERB
ap-8605	25	35	the	the	DET
ap-8605	25	36	transformation	transformation	NOUN
ap-8605	25	37	rule	rule	NOUN
ap-8605	25	38	(	(	PUNCT
ap-8605	25	39	equation	equation	NOUN
ap-8605	25	40	(	(	PUNCT
ap-8605	25	41	2	2	NUM
ap-8605	25	42	)	)	PUNCT
ap-8605	25	43	):	):	PUNCT
ap-8605	25	44	v	v	NOUN
ap-8605	25	45	=	=	SYM
ap-8605	25	46	vigi	vigi	NOUN
ap-8605	25	47	=	=	PUNCT
ap-8605	25	48	v̂j	v̂j	X
ap-8605	25	49	ĝj	ĝj	X
ap-8605	25	50	,	,	PUNCT
ap-8605	25	51	(	(	PUNCT
ap-8605	25	52	1	1	X
ap-8605	25	53	)	)	PUNCT
ap-8605	25	54	vi	vi	NOUN
ap-8605	26	1	=	=	NOUN
ap-8605	26	2	ai	ai	VERB
ap-8605	26	3	j	j	PROPN
ap-8605	26	4	v̂	v̂	NUM
ap-8605	26	5	j	j	PROPN
ap-8605	26	6	,	,	PUNCT
ap-8605	26	7	(	(	PUNCT
ap-8605	26	8	2	2	X
ap-8605	26	9	)	)	PUNCT
ap-8605	26	10	where	where	SCONJ
ap-8605	26	11	v	v	NOUN
ap-8605	26	12	is	be	AUX
ap-8605	26	13	the	the	DET
ap-8605	26	14	vector	vector	NOUN
ap-8605	26	15	,	,	PUNCT
ap-8605	26	16	vi	vi	PROPN
ap-8605	26	17	are	be	AUX
ap-8605	26	18	the	the	DET
ap-8605	26	19	components	component	NOUN
ap-8605	26	20	of	of	ADP
ap-8605	26	21	the	the	DET
ap-8605	26	22	vector	vector	NOUN
ap-8605	26	23	in	in	ADP
ap-8605	26	24	the	the	DET
ap-8605	26	25	new	new	ADJ
ap-8605	26	26	basis	basis	NOUN
ap-8605	26	27	,	,	PUNCT
ap-8605	26	28	gi	gi	X
ap-8605	26	29	are	be	AUX
ap-8605	26	30	the	the	DET
ap-8605	26	31	transformed	transform	VERB
ap-8605	26	32	basis	basis	NOUN
ap-8605	26	33	vectors	vector	NOUN
ap-8605	26	34	,	,	PUNCT
ap-8605	26	35	ĝj	ĝj	PROPN
ap-8605	26	36	are	be	AUX
ap-8605	26	37	the	the	DET
ap-8605	26	38	original	original	ADJ
ap-8605	26	39	basis	basis	NOUN
ap-8605	26	40	vectors	vector	NOUN
ap-8605	26	41	,	,	PUNCT
ap-8605	26	42	v̂j	v̂j	X
ap-8605	26	43	are	be	AUX
ap-8605	26	44	the	the	DET
ap-8605	26	45	components	component	NOUN
ap-8605	26	46	of	of	ADP
ap-8605	26	47	the	the	DET
ap-8605	26	48	vector	vector	NOUN
ap-8605	26	49	v	v	NOUN
ap-8605	26	50	in	in	ADP
ap-8605	26	51	the	the	DET
ap-8605	26	52	original	original	ADJ
ap-8605	26	53	basis	basis	NOUN
ap-8605	26	54	and	and	CCONJ
ap-8605	26	55	ai	ai	VERB
ap-8605	26	56	j	j	PROPN
ap-8605	26	57	is	be	AUX
ap-8605	26	58	the	the	DET
ap-8605	26	59	transformation	transformation	NOUN
ap-8605	26	60	matrix	matrix	NOUN
ap-8605	26	61	.	.	PUNCT
ap-8605	27	1	the	the	DET
ap-8605	27	2	basis	basis	NOUN
ap-8605	27	3	vectors	vector	NOUN
ap-8605	27	4	gi	gi	NOUN
ap-8605	27	5	can	can	AUX
ap-8605	27	6	be	be	AUX
ap-8605	27	7	defined	define	VERB
ap-8605	27	8	as	as	SCONJ
ap-8605	27	9	(	(	PUNCT
ap-8605	27	10	see	see	VERB
ap-8605	27	11	any	any	DET
ap-8605	27	12	textbook	textbook	NOUN
ap-8605	27	13	about	about	ADP
ap-8605	27	14	differential	differential	NOUN
ap-8605	27	15	geometry	geometry	NOUN
ap-8605	27	16	,	,	PUNCT
ap-8605	28	1	e.g.	e.g.	ADV
ap-8605	28	2	[	[	X
ap-8605	28	3	3	3	NUM
ap-8605	28	4	]	]	PUNCT
ap-8605	28	5	):	):	PUNCT
ap-8605	28	6	gi	gi	NOUN
ap-8605	28	7	=	=	PUNCT
ap-8605	28	8	∂x	∂x	PROPN
ap-8605	28	9	∂ηi	∂ηi	PROPN
ap-8605	28	10	,	,	PUNCT
ap-8605	28	11	(	(	PUNCT
ap-8605	28	12	3	3	X
ap-8605	28	13	)	)	PUNCT
ap-8605	28	14	where	where	SCONJ
ap-8605	28	15	ηi	ηi	NOUN
ap-8605	28	16	are	be	AUX
ap-8605	28	17	the	the	DET
ap-8605	28	18	coordinates	coordinate	NOUN
ap-8605	28	19	and	and	CCONJ
ap-8605	28	20	x	x	X
ap-8605	28	21	is	be	AUX
ap-8605	28	22	the	the	DET
ap-8605	28	23	position	position	NOUN
ap-8605	28	24	vector	vector	NOUN
ap-8605	28	25	.	.	PUNCT
ap-8605	29	1	similarly	similarly	ADV
ap-8605	29	2	,	,	PUNCT
ap-8605	29	3	co	co	ADJ
ap-8605	29	4	-	-	NOUN
ap-8605	29	5	basis	basis	NOUN
ap-8605	29	6	vectors	vector	NOUN
ap-8605	29	7	can	can	AUX
ap-8605	29	8	be	be	AUX
ap-8605	29	9	defined	define	VERB
ap-8605	29	10	as	as	ADP
ap-8605	29	11	:	:	PUNCT
ap-8605	29	12	gj	gj	NOUN
ap-8605	29	13	=	=	SYM
ap-8605	29	14	∂ηj	∂ηj	PROPN
ap-8605	29	15	∂x	∂x	PROPN
ap-8605	29	16	.	.	PUNCT
ap-8605	30	1	(	(	PUNCT
ap-8605	30	2	4	4	X
ap-8605	30	3	)	)	PUNCT
ap-8605	30	4	covariant	covariant	NOUN
ap-8605	30	5	,	,	PUNCT
ap-8605	30	6	contravariant	contravariant	PROPN
ap-8605	30	7	metric	metric	ADJ
ap-8605	30	8	coefficients	coefficient	NOUN
ap-8605	30	9	and	and	CCONJ
ap-8605	30	10	the	the	DET
ap-8605	30	11	kronecker	kronecker	NOUN
ap-8605	30	12	symbol	symbol	NOUN
ap-8605	30	13	can	can	AUX
ap-8605	30	14	obtained	obtain	VERB
ap-8605	30	15	as	as	ADP
ap-8605	30	16	:	:	PUNCT
ap-8605	30	17	1here	1here	NUM
ap-8605	30	18	vectors	vector	NOUN
ap-8605	30	19	and	and	CCONJ
ap-8605	30	20	scalars	scalar	NOUN
ap-8605	30	21	are	be	AUX
ap-8605	30	22	included	include	VERB
ap-8605	30	23	in	in	ADP
ap-8605	30	24	the	the	DET
ap-8605	30	25	definition	definition	NOUN
ap-8605	30	26	of	of	ADP
ap-8605	30	27	the	the	DET
ap-8605	30	28	tensors	tensor	NOUN
ap-8605	30	29	as	as	ADP
ap-8605	30	30	the	the	DET
ap-8605	30	31	tensors	tensor	NOUN
ap-8605	30	32	of	of	ADP
ap-8605	30	33	the	the	DET
ap-8605	30	34	first	first	ADJ
ap-8605	30	35	and	and	CCONJ
ap-8605	30	36	zeroth	zeroth	ADJ
ap-8605	30	37	order	order	NOUN
ap-8605	30	38	,	,	PUNCT
ap-8605	30	39	respectively	respectively	ADV
ap-8605	30	40	.	.	PUNCT
ap-8605	31	1	103	103	NUM
ap-8605	32	1	https://doi.org/10.14311/ap.2023.63.0103	https://doi.org/10.14311/ap.2023.63.0103	X
ap-8605	32	2	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-8605	32	3	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-8605	32	4	erik	erik	PROPN
ap-8605	32	5	flídr	flídr	PROPN
ap-8605	32	6	acta	acta	PROPN
ap-8605	32	7	polytechnica	polytechnica	PROPN
ap-8605	32	8	gij	gij	PROPN
ap-8605	32	9	=	=	SYM
ap-8605	32	10	gi	gi	INTJ
ap-8605	32	11	·	·	PUNCT
ap-8605	32	12	gj	gj	INTJ
ap-8605	32	13	,	,	PUNCT
ap-8605	32	14	(	(	PUNCT
ap-8605	32	15	5	5	NUM
ap-8605	32	16	)	)	PUNCT
ap-8605	32	17	gij	gij	NOUN
ap-8605	32	18	=	=	SYM
ap-8605	32	19	gi	gi	PROPN
ap-8605	32	20	·	·	PUNCT
ap-8605	32	21	gj	gj	INTJ
ap-8605	32	22	,	,	PUNCT
ap-8605	32	23	(	(	PUNCT
ap-8605	32	24	6	6	X
ap-8605	32	25	)	)	PUNCT
ap-8605	32	26	gi	gi	NOUN
ap-8605	32	27	·	·	PUNCT
ap-8605	32	28	gj	gj	NOUN
ap-8605	32	29	=	=	NOUN
ap-8605	32	30	gilg	gilg	VERB
ap-8605	32	31	lj	lj	ADV
ap-8605	33	1	=	=	VERB
ap-8605	33	2	δi	δi	PROPN
ap-8605	33	3	j	j	PROPN
ap-8605	33	4	.	.	PUNCT
ap-8605	34	1	(	(	PUNCT
ap-8605	34	2	7	7	X
ap-8605	34	3	)	)	PUNCT
ap-8605	34	4	now	now	ADV
ap-8605	34	5	,	,	PUNCT
ap-8605	34	6	derivatives	derivative	NOUN
ap-8605	34	7	of	of	ADP
ap-8605	34	8	the	the	DET
ap-8605	34	9	tensors	tensor	NOUN
ap-8605	34	10	in	in	ADP
ap-8605	34	11	general	general	ADJ
ap-8605	34	12	curvilinear	curvilinear	PROPN
ap-8605	34	13	coordinates	coordinate	NOUN
ap-8605	34	14	have	have	VERB
ap-8605	34	15	to	to	PART
ap-8605	34	16	be	be	AUX
ap-8605	34	17	determined	determine	VERB
ap-8605	34	18	.	.	PUNCT
ap-8605	35	1	the	the	DET
ap-8605	35	2	gradient	gradient	NOUN
ap-8605	35	3	of	of	ADP
ap-8605	35	4	the	the	DET
ap-8605	35	5	vector	vector	NOUN
ap-8605	35	6	function	function	NOUN
ap-8605	35	7	in	in	ADP
ap-8605	35	8	the	the	DET
ap-8605	35	9	general	general	ADJ
ap-8605	35	10	curvilinear	curvilinear	NOUN
ap-8605	35	11	coordinate	coordinate	NOUN
ap-8605	35	12	has	have	VERB
ap-8605	35	13	a	a	DET
ap-8605	35	14	form	form	NOUN
ap-8605	35	15	:	:	PUNCT
ap-8605	36	1	dv	dv	PROPN
ap-8605	36	2	dx	dx	PROPN
ap-8605	37	1	=	=	PROPN
ap-8605	38	1	∂ui	∂ui	PROPN
ap-8605	38	2	∂ηj	∂ηj	PROPN
ap-8605	38	3	gigj	gigj	NOUN
ap-8605	38	4	+	+	CCONJ
ap-8605	38	5	ui	ui	ADJ
ap-8605	38	6	∂gi	∂gi	PROPN
ap-8605	38	7	∂ηj	∂ηj	PROPN
ap-8605	38	8	gj	gj	NOUN
ap-8605	38	9	.	.	PUNCT
ap-8605	39	1	(	(	PUNCT
ap-8605	39	2	8)	8)	NUM
ap-8605	39	3	christoffel	christoffel	ADJ
ap-8605	39	4	symbols	symbol	NOUN
ap-8605	39	5	of	of	ADP
ap-8605	39	6	the	the	DET
ap-8605	39	7	second	second	ADJ
ap-8605	39	8	kind	kind	NOUN
ap-8605	39	9	can	can	AUX
ap-8605	39	10	be	be	AUX
ap-8605	39	11	defined	define	VERB
ap-8605	39	12	based	base	VERB
ap-8605	39	13	on	on	ADP
ap-8605	39	14	this	this	DET
ap-8605	39	15	relationship	relationship	NOUN
ap-8605	39	16	as	as	ADP
ap-8605	39	17	:	:	PUNCT
ap-8605	39	18	γk	γk	NOUN
ap-8605	39	19	ij	ij	NOUN
ap-8605	39	20	=	=	SYM
ap-8605	39	21	∂gi	∂gi	NOUN
ap-8605	39	22	∂ηj	∂ηj	PROPN
ap-8605	39	23	gk	gk	NOUN
ap-8605	39	24	=	=	SYM
ap-8605	39	25	1	1	NUM
ap-8605	39	26	2	2	NUM
ap-8605	39	27	g	g	NOUN
ap-8605	39	28	kl	kl	X
ap-8605	39	29	(	(	PUNCT
ap-8605	39	30	gli	gli	PROPN
ap-8605	39	31	,	,	PUNCT
ap-8605	39	32	j	j	PROPN
ap-8605	39	33	+	+	SYM
ap-8605	39	34	glj	glj	NOUN
ap-8605	39	35	,	,	PUNCT
ap-8605	39	36	i	i	PRON
ap-8605	39	37	−	−	VERB
ap-8605	39	38	gij	gij	ADJ
ap-8605	39	39	,	,	PUNCT
ap-8605	39	40	l	l	NOUN
ap-8605	39	41	)	)	PUNCT
ap-8605	39	42	.	.	PUNCT
ap-8605	40	1	(	(	PUNCT
ap-8605	40	2	9	9	X
ap-8605	40	3	)	)	PUNCT
ap-8605	40	4	substituting	substitute	VERB
ap-8605	40	5	this	this	DET
ap-8605	40	6	result	result	NOUN
ap-8605	40	7	into	into	ADP
ap-8605	40	8	equation	equation	NOUN
ap-8605	40	9	(	(	PUNCT
ap-8605	40	10	8)	8)	NUM
ap-8605	40	11	gives	give	VERB
ap-8605	40	12	:	:	PUNCT
ap-8605	40	13	dv	dv	PROPN
ap-8605	40	14	dx	dx	PROPN
ap-8605	41	1	=	=	PROPN
ap-8605	42	1	∂ui	∂ui	PROPN
ap-8605	42	2	∂ηj	∂ηj	PROPN
ap-8605	42	3	gigj	gigj	NOUN
ap-8605	42	4	+	+	CCONJ
ap-8605	42	5	uiγk	uiγk	ADJ
ap-8605	42	6	ijgkgj	ijgkgj	NOUN
ap-8605	42	7	.	.	PUNCT
ap-8605	43	1	(	(	PUNCT
ap-8605	43	2	10	10	NUM
ap-8605	43	3	)	)	PUNCT
ap-8605	43	4	finally	finally	ADV
ap-8605	43	5	,	,	PUNCT
ap-8605	43	6	the	the	DET
ap-8605	43	7	covariant	covariant	NOUN
ap-8605	43	8	and	and	CCONJ
ap-8605	43	9	contravariant	contravariant	ADJ
ap-8605	43	10	derivatives	derivative	NOUN
ap-8605	43	11	of	of	ADP
ap-8605	43	12	the	the	DET
ap-8605	43	13	vector	vector	NOUN
ap-8605	43	14	and	and	CCONJ
ap-8605	43	15	second	second	ADJ
ap-8605	43	16	order	order	NOUN
ap-8605	43	17	tensor	tensor	NOUN
ap-8605	43	18	,	,	PUNCT
ap-8605	43	19	which	which	PRON
ap-8605	43	20	will	will	AUX
ap-8605	43	21	be	be	AUX
ap-8605	43	22	frequently	frequently	ADV
ap-8605	43	23	used	use	VERB
ap-8605	43	24	in	in	ADP
ap-8605	43	25	the	the	DET
ap-8605	43	26	following	follow	VERB
ap-8605	43	27	text	text	NOUN
ap-8605	43	28	,	,	PUNCT
ap-8605	43	29	are	be	AUX
ap-8605	43	30	defined	define	VERB
ap-8605	43	31	:	:	PUNCT
ap-8605	43	32	vi	vi	ADJ
ap-8605	43	33	;	;	PUNCT
ap-8605	43	34	j	j	PROPN
ap-8605	43	35	=	=	SYM
ap-8605	43	36	∂ui	∂ui	PROPN
ap-8605	43	37	∂ηj	∂ηj	NOUN
ap-8605	43	38	+	+	CCONJ
ap-8605	43	39	ukγi	ukγi	ADJ
ap-8605	43	40	kj	kj	NOUN
ap-8605	43	41	,	,	PUNCT
ap-8605	43	42	(	(	PUNCT
ap-8605	43	43	11	11	NUM
ap-8605	43	44	)	)	PUNCT
ap-8605	43	45	vi;j	vi;j	NUM
ap-8605	43	46	=	=	PUNCT
ap-8605	44	1	∂ui	∂ui	PROPN
ap-8605	44	2	∂ηj	∂ηj	PROPN
ap-8605	44	3	−	−	PROPN
ap-8605	44	4	ukγk	ukγk	ADJ
ap-8605	44	5	ij	ij	NOUN
ap-8605	44	6	,	,	PUNCT
ap-8605	44	7	(	(	PUNCT
ap-8605	44	8	12	12	NUM
ap-8605	44	9	)	)	PUNCT
ap-8605	44	10	t	t	NOUN
ap-8605	44	11	ij	ij	NOUN
ap-8605	44	12	;	;	PUNCT
ap-8605	45	1	k	k	PROPN
ap-8605	45	2	=	=	SYM
ap-8605	45	3	t	t	PROPN
ap-8605	45	4	ij	ij	INTJ
ap-8605	45	5	,	,	PUNCT
ap-8605	45	6	k	k	PROPN
ap-8605	45	7	+	+	PROPN
ap-8605	45	8	t	t	PROPN
ap-8605	45	9	ljγi	ljγi	NOUN
ap-8605	45	10	lk	lk	PROPN
ap-8605	46	1	+	+	NUM
ap-8605	46	2	t	t	PROPN
ap-8605	46	3	ilγj	ilγj	NOUN
ap-8605	46	4	lk	lk	PROPN
ap-8605	46	5	,	,	PUNCT
ap-8605	46	6	(	(	PUNCT
ap-8605	46	7	13	13	NUM
ap-8605	46	8	)	)	PUNCT
ap-8605	46	9	tij	tij	PROPN
ap-8605	46	10	,	,	PUNCT
ap-8605	46	11	k	k	PROPN
ap-8605	46	12	=	=	SYM
ap-8605	46	13	tij	tij	PROPN
ap-8605	46	14	,	,	PUNCT
ap-8605	46	15	k	k	PROPN
ap-8605	46	16	−	−	PROPN
ap-8605	46	17	tljγl	tljγl	NOUN
ap-8605	46	18	ik	ik	PROPN
ap-8605	46	19	−	−	PROPN
ap-8605	46	20	tilγl	tilγl	PROPN
ap-8605	46	21	jk	jk	PROPN
ap-8605	46	22	,	,	PUNCT
ap-8605	46	23	(	(	PUNCT
ap-8605	46	24	14	14	NUM
ap-8605	46	25	)	)	PUNCT
ap-8605	46	26	t	t	NOUN
ap-8605	47	1	i	i	PRON
ap-8605	47	2	j;k	j;k	PROPN
ap-8605	48	1	=	=	PUNCT
ap-8605	48	2	t	t	PROPN
ap-8605	48	3	i	i	PRON
ap-8605	48	4	j	j	PROPN
ap-8605	48	5	,	,	PUNCT
ap-8605	48	6	k	k	PROPN
ap-8605	49	1	+	+	PROPN
ap-8605	49	2	t	t	PROPN
ap-8605	49	3	l	l	NOUN
ap-8605	49	4	jγi	jγi	NOUN
ap-8605	49	5	lk	lk	PROPN
ap-8605	49	6	−	−	PROPN
ap-8605	50	1	t	t	NOUN
ap-8605	51	1	i	i	PRON
ap-8605	51	2	l	l	PROPN
ap-8605	51	3	γl	γl	PROPN
ap-8605	52	1	jk	jk	PROPN
ap-8605	52	2	,	,	PUNCT
ap-8605	52	3	(	(	PUNCT
ap-8605	52	4	15	15	NUM
ap-8605	52	5	)	)	PUNCT
ap-8605	52	6	where	where	SCONJ
ap-8605	52	7	partial	partial	ADJ
ap-8605	52	8	derivatives	derivative	NOUN
ap-8605	52	9	are	be	AUX
ap-8605	52	10	noted	note	VERB
ap-8605	52	11	as	as	ADP
ap-8605	52	12	:	:	PUNCT
ap-8605	52	13	vi	vi	NUM
ap-8605	52	14	,	,	PUNCT
ap-8605	52	15	j	j	PROPN
ap-8605	52	16	=	=	SYM
ap-8605	52	17	∂ui	∂ui	PROPN
ap-8605	52	18	∂xj	∂xj	NOUN
ap-8605	52	19	.	.	PUNCT
ap-8605	53	1	(	(	PUNCT
ap-8605	53	2	16	16	NUM
ap-8605	53	3	)	)	PUNCT
ap-8605	53	4	all	all	PRON
ap-8605	53	5	of	of	ADP
ap-8605	53	6	the	the	DET
ap-8605	53	7	operations	operation	NOUN
ap-8605	53	8	,	,	PUNCT
ap-8605	53	9	such	such	ADJ
ap-8605	53	10	as	as	ADP
ap-8605	53	11	divergence	divergence	NOUN
ap-8605	53	12	,	,	PUNCT
ap-8605	53	13	gradient	gradient	NOUN
ap-8605	53	14	,	,	PUNCT
ap-8605	53	15	curl	curl	NOUN
ap-8605	53	16	etc	etc	X
ap-8605	53	17	.	.	X
ap-8605	53	18	,	,	PUNCT
ap-8605	53	19	can	can	AUX
ap-8605	53	20	be	be	AUX
ap-8605	53	21	obtained	obtain	VERB
ap-8605	53	22	from	from	ADP
ap-8605	53	23	these	these	DET
ap-8605	53	24	relationships	relationship	NOUN
ap-8605	53	25	,	,	PUNCT
ap-8605	53	26	see	see	VERB
ap-8605	53	27	again	again	ADV
ap-8605	54	1	e.g.	e.g.	ADV
ap-8605	54	2	[	[	X
ap-8605	54	3	3	3	NUM
ap-8605	54	4	]	]	PUNCT
ap-8605	54	5	.	.	PUNCT
ap-8605	55	1	3	3	X
ap-8605	55	2	.	.	X
ap-8605	55	3	laws	law	NOUN
ap-8605	55	4	of	of	ADP
ap-8605	55	5	thermodynamics	thermodynamic	NOUN
ap-8605	55	6	thermodynamics	thermodynamic	NOUN
ap-8605	55	7	is	be	AUX
ap-8605	55	8	a	a	DET
ap-8605	55	9	scientific	scientific	ADJ
ap-8605	55	10	discipline	discipline	NOUN
ap-8605	55	11	concerning	concern	VERB
ap-8605	55	12	the	the	DET
ap-8605	55	13	transformation	transformation	NOUN
ap-8605	55	14	of	of	ADP
ap-8605	55	15	thermal	thermal	ADJ
ap-8605	55	16	energy	energy	NOUN
ap-8605	55	17	into	into	ADP
ap-8605	55	18	its	its	PRON
ap-8605	55	19	other	other	ADJ
ap-8605	55	20	forms	form	NOUN
ap-8605	55	21	.	.	PUNCT
ap-8605	56	1	it	it	PRON
ap-8605	56	2	is	be	AUX
ap-8605	56	3	based	base	VERB
ap-8605	56	4	on	on	ADP
ap-8605	56	5	three	three	NUM
ap-8605	56	6	laws	law	NOUN
ap-8605	56	7	,	,	PUNCT
ap-8605	56	8	that	that	PRON
ap-8605	56	9	were	be	AUX
ap-8605	56	10	obtained	obtain	VERB
ap-8605	56	11	thanks	thank	NOUN
ap-8605	56	12	to	to	ADP
ap-8605	56	13	a	a	DET
ap-8605	56	14	combination	combination	NOUN
ap-8605	56	15	of	of	ADP
ap-8605	56	16	theoretical	theoretical	ADJ
ap-8605	56	17	and	and	CCONJ
ap-8605	56	18	experimental	experimental	ADJ
ap-8605	56	19	research	research	NOUN
ap-8605	56	20	.	.	PUNCT
ap-8605	57	1	3.1	3.1	NUM
ap-8605	57	2	.	.	PUNCT
ap-8605	58	1	the	the	DET
ap-8605	58	2	first	first	ADJ
ap-8605	58	3	law	law	NOUN
ap-8605	58	4	of	of	ADP
ap-8605	58	5	thermodynamics	thermodynamic	NOUN
ap-8605	58	6	the	the	DET
ap-8605	58	7	formulation	formulation	NOUN
ap-8605	58	8	of	of	ADP
ap-8605	58	9	the	the	DET
ap-8605	58	10	first	first	ADJ
ap-8605	58	11	law	law	NOUN
ap-8605	58	12	was	be	AUX
ap-8605	58	13	described	describe	VERB
ap-8605	58	14	in	in	ADP
ap-8605	58	15	detail	detail	NOUN
ap-8605	58	16	by	by	ADP
ap-8605	58	17	kvasnica	kvasnica	PROPN
ap-8605	59	1	[	[	X
ap-8605	59	2	7	7	NUM
ap-8605	59	3	]	]	PUNCT
ap-8605	59	4	.	.	PUNCT
ap-8605	60	1	if	if	SCONJ
ap-8605	60	2	the	the	DET
ap-8605	60	3	system	system	NOUN
ap-8605	60	4	is	be	AUX
ap-8605	60	5	free	free	ADJ
ap-8605	60	6	of	of	ADP
ap-8605	60	7	chemical	chemical	ADJ
ap-8605	60	8	reactions	reaction	NOUN
ap-8605	60	9	,	,	PUNCT
ap-8605	60	10	the	the	DET
ap-8605	60	11	first	first	ADJ
ap-8605	60	12	law	law	NOUN
ap-8605	60	13	can	can	AUX
ap-8605	60	14	be	be	AUX
ap-8605	60	15	written	write	VERB
ap-8605	60	16	in	in	ADP
ap-8605	60	17	the	the	DET
ap-8605	60	18	form	form	NOUN
ap-8605	60	19	:	:	PUNCT
ap-8605	60	20	dein	dein	NOUN
ap-8605	60	21	=	=	PUNCT
ap-8605	60	22	dq	dq	PROPN
ap-8605	60	23	+	+	CCONJ
ap-8605	60	24	dw	dw	PROPN
ap-8605	60	25	,	,	PUNCT
ap-8605	60	26	(	(	PUNCT
ap-8605	60	27	17	17	NUM
ap-8605	60	28	)	)	PUNCT
ap-8605	60	29	where	where	SCONJ
ap-8605	60	30	ein	ein	PROPN
ap-8605	60	31	is	be	AUX
ap-8605	60	32	the	the	DET
ap-8605	60	33	internal	internal	ADJ
ap-8605	60	34	energy	energy	NOUN
ap-8605	60	35	,	,	PUNCT
ap-8605	60	36	q	q	PUNCT
ap-8605	60	37	is	be	AUX
ap-8605	60	38	the	the	DET
ap-8605	60	39	heat	heat	NOUN
ap-8605	60	40	and	and	CCONJ
ap-8605	60	41	w	w	PROPN
ap-8605	60	42	is	be	AUX
ap-8605	60	43	the	the	DET
ap-8605	60	44	work	work	NOUN
ap-8605	60	45	.	.	PUNCT
ap-8605	61	1	in	in	ADP
ap-8605	61	2	other	other	ADJ
ap-8605	61	3	words	word	NOUN
ap-8605	61	4	,	,	PUNCT
ap-8605	61	5	the	the	DET
ap-8605	61	6	heat	heat	NOUN
ap-8605	61	7	given	give	VERB
ap-8605	61	8	to	to	ADP
ap-8605	61	9	the	the	DET
ap-8605	61	10	system	system	NOUN
ap-8605	61	11	can	can	AUX
ap-8605	61	12	be	be	AUX
ap-8605	61	13	transformed	transform	VERB
ap-8605	61	14	into	into	ADP
ap-8605	61	15	the	the	DET
ap-8605	61	16	system	system	NOUN
ap-8605	61	17	’s	’s	PART
ap-8605	61	18	internal	internal	ADJ
ap-8605	61	19	energy	energy	NOUN
ap-8605	61	20	and	and	CCONJ
ap-8605	61	21	work	work	NOUN
ap-8605	61	22	performed	perform	VERB
ap-8605	61	23	by	by	ADP
ap-8605	61	24	this	this	DET
ap-8605	61	25	system	system	NOUN
ap-8605	61	26	.	.	PUNCT
ap-8605	62	1	note	note	VERB
ap-8605	62	2	that	that	SCONJ
ap-8605	62	3	the	the	DET
ap-8605	62	4	number	number	NOUN
ap-8605	62	5	of	of	ADP
ap-8605	62	6	the	the	DET
ap-8605	62	7	particles	particle	NOUN
ap-8605	62	8	in	in	ADP
ap-8605	62	9	the	the	DET
ap-8605	62	10	system	system	NOUN
ap-8605	62	11	has	have	VERB
ap-8605	62	12	to	to	PART
ap-8605	62	13	be	be	AUX
ap-8605	62	14	the	the	DET
ap-8605	62	15	same	same	ADJ
ap-8605	62	16	throughout	throughout	ADP
ap-8605	62	17	the	the	DET
ap-8605	62	18	process	process	NOUN
ap-8605	62	19	.	.	PUNCT
ap-8605	63	1	it	it	PRON
ap-8605	63	2	must	must	AUX
ap-8605	63	3	also	also	ADV
ap-8605	63	4	be	be	AUX
ap-8605	63	5	noted	note	VERB
ap-8605	63	6	that	that	SCONJ
ap-8605	63	7	the	the	DET
ap-8605	63	8	heat	heat	NOUN
ap-8605	63	9	,	,	PUNCT
ap-8605	63	10	as	as	ADV
ap-8605	63	11	well	well	ADV
ap-8605	63	12	as	as	ADP
ap-8605	63	13	the	the	DET
ap-8605	63	14	work	work	NOUN
ap-8605	63	15	,	,	PUNCT
ap-8605	63	16	are	be	AUX
ap-8605	63	17	not	not	PART
ap-8605	63	18	total	total	ADJ
ap-8605	63	19	differentials	differential	NOUN
ap-8605	63	20	,	,	PUNCT
ap-8605	63	21	and	and	CCONJ
ap-8605	63	22	therefore	therefore	ADV
ap-8605	63	23	they	they	PRON
ap-8605	63	24	are	be	AUX
ap-8605	63	25	dependent	dependent	ADJ
ap-8605	63	26	on	on	ADP
ap-8605	63	27	the	the	DET
ap-8605	63	28	integral	integral	ADJ
ap-8605	63	29	path	path	NOUN
ap-8605	63	30	between	between	ADP
ap-8605	63	31	the	the	DET
ap-8605	63	32	starting	starting	NOUN
ap-8605	63	33	point	point	NOUN
ap-8605	63	34	and	and	CCONJ
ap-8605	63	35	the	the	DET
ap-8605	63	36	ending	end	VERB
ap-8605	63	37	state	state	NOUN
ap-8605	63	38	.	.	PUNCT
ap-8605	64	1	it	it	PRON
ap-8605	64	2	is	be	AUX
ap-8605	64	3	useful	useful	ADJ
ap-8605	64	4	to	to	PART
ap-8605	64	5	write	write	VERB
ap-8605	64	6	down	down	ADP
ap-8605	64	7	another	another	DET
ap-8605	64	8	formulation	formulation	NOUN
ap-8605	64	9	of	of	ADP
ap-8605	64	10	the	the	DET
ap-8605	64	11	first	first	ADJ
ap-8605	64	12	law	law	NOUN
ap-8605	64	13	,	,	PUNCT
ap-8605	64	14	where	where	SCONJ
ap-8605	64	15	enthalpy	enthalpy	NOUN
ap-8605	64	16	is	be	AUX
ap-8605	64	17	defined	define	VERB
ap-8605	64	18	as	as	ADP
ap-8605	64	19	:	:	PUNCT
ap-8605	64	20	dh	dh	NOUN
ap-8605	64	21	=	=	PUNCT
ap-8605	64	22	dein	dein	PROPN
ap-8605	64	23	+	+	CCONJ
ap-8605	64	24	pdv	pdv	PROPN
ap-8605	64	25	+	+	CCONJ
ap-8605	64	26	vdp	vdp	PROPN
ap-8605	64	27	,	,	PUNCT
ap-8605	64	28	(	(	PUNCT
ap-8605	64	29	18	18	NUM
ap-8605	64	30	)	)	PUNCT
ap-8605	64	31	where	where	SCONJ
ap-8605	64	32	p	p	NOUN
ap-8605	64	33	is	be	AUX
ap-8605	64	34	the	the	DET
ap-8605	64	35	thermodynamic	thermodynamic	ADJ
ap-8605	64	36	pressure	pressure	NOUN
ap-8605	64	37	and	and	CCONJ
ap-8605	64	38	v	v	NOUN
ap-8605	64	39	is	be	AUX
ap-8605	64	40	the	the	DET
ap-8605	64	41	volume	volume	NOUN
ap-8605	64	42	.	.	PUNCT
ap-8605	65	1	3.2	3.2	NUM
ap-8605	65	2	.	.	PUNCT
ap-8605	66	1	the	the	DET
ap-8605	66	2	second	second	ADJ
ap-8605	66	3	law	law	NOUN
ap-8605	66	4	of	of	ADP
ap-8605	66	5	thermodynamics	thermodynamic	NOUN
ap-8605	66	6	the	the	DET
ap-8605	66	7	formulation	formulation	NOUN
ap-8605	66	8	of	of	ADP
ap-8605	66	9	the	the	DET
ap-8605	66	10	second	second	ADJ
ap-8605	66	11	law	law	NOUN
ap-8605	66	12	was	be	AUX
ap-8605	66	13	motivated	motivate	VERB
ap-8605	66	14	by	by	ADP
ap-8605	66	15	the	the	DET
ap-8605	66	16	research	research	NOUN
ap-8605	66	17	of	of	ADP
ap-8605	66	18	r.	r.	PROPN
ap-8605	66	19	clausius	clausius	PROPN
ap-8605	66	20	,	,	PUNCT
ap-8605	66	21	who	who	PRON
ap-8605	66	22	followed	follow	VERB
ap-8605	66	23	the	the	DET
ap-8605	66	24	work	work	NOUN
ap-8605	66	25	of	of	ADP
ap-8605	66	26	carnot	carnot	NOUN
ap-8605	66	27	and	and	CCONJ
ap-8605	66	28	described	describe	VERB
ap-8605	66	29	the	the	DET
ap-8605	66	30	real	real	ADJ
ap-8605	66	31	processes	process	NOUN
ap-8605	66	32	in	in	ADP
ap-8605	66	33	nature	nature	NOUN
ap-8605	66	34	by	by	ADP
ap-8605	66	35	the	the	DET
ap-8605	66	36	quantity	quantity	NOUN
ap-8605	66	37	named	name	VERB
ap-8605	66	38	entropy	entropy	PROPN
ap-8605	66	39	.	.	PUNCT
ap-8605	67	1	this	this	DET
ap-8605	67	2	quantity	quantity	NOUN
ap-8605	67	3	is	be	AUX
ap-8605	67	4	defined	define	VERB
ap-8605	67	5	as	as	ADP
ap-8605	67	6	:	:	PUNCT
ap-8605	67	7	ds	ds	ADJ
ap-8605	67	8	=	=	SYM
ap-8605	67	9	dq	dq	NOUN
ap-8605	67	10	t	t	NOUN
ap-8605	67	11	,	,	PUNCT
ap-8605	67	12	(	(	PUNCT
ap-8605	67	13	19	19	NUM
ap-8605	67	14	)	)	PUNCT
ap-8605	67	15	where	where	SCONJ
ap-8605	67	16	t	t	PROPN
ap-8605	67	17	is	be	AUX
ap-8605	67	18	the	the	DET
ap-8605	67	19	thermodynamic	thermodynamic	ADJ
ap-8605	67	20	temperature	temperature	NOUN
ap-8605	67	21	.	.	PUNCT
ap-8605	68	1	this	this	DET
ap-8605	68	2	definition	definition	NOUN
ap-8605	68	3	is	be	AUX
ap-8605	68	4	valid	valid	ADJ
ap-8605	68	5	for	for	ADP
ap-8605	68	6	reversible	reversible	ADJ
ap-8605	68	7	processes	process	NOUN
ap-8605	68	8	.	.	PUNCT
ap-8605	69	1	entropy	entropy	PROPN
ap-8605	69	2	is	be	AUX
ap-8605	69	3	then	then	ADV
ap-8605	69	4	a	a	DET
ap-8605	69	5	total	total	ADJ
ap-8605	69	6	differential	differential	NOUN
ap-8605	69	7	,	,	PUNCT
ap-8605	69	8	therefore	therefore	ADV
ap-8605	69	9	,	,	PUNCT
ap-8605	69	10	for	for	ADP
ap-8605	69	11	the	the	DET
ap-8605	69	12	reversible	reversible	ADJ
ap-8605	69	13	process	process	NOUN
ap-8605	69	14	between	between	ADP
ap-8605	69	15	states	state	NOUN
ap-8605	69	16	1	1	NUM
ap-8605	69	17	and	and	CCONJ
ap-8605	69	18	2	2	NUM
ap-8605	69	19	,	,	PUNCT
ap-8605	69	20	the	the	DET
ap-8605	69	21	following	follow	VERB
ap-8605	69	22	equation	equation	NOUN
ap-8605	69	23	holds	hold	VERB
ap-8605	69	24	:	:	PUNCT
ap-8605	69	25	s2	s2	VERB
ap-8605	69	26	−	−	NOUN
ap-8605	69	27	s1	s1	NOUN
ap-8605	69	28	=	=	PUNCT
ap-8605	69	29	(	(	PUNCT
ap-8605	69	30	2)∫	2)∫	NUM
ap-8605	69	31	(	(	PUNCT
ap-8605	69	32	1	1	NUM
ap-8605	69	33	)	)	PUNCT
ap-8605	69	34	dq	dq	NOUN
ap-8605	69	35	t	t	PROPN
ap-8605	69	36	.	.	PUNCT
ap-8605	70	1	(	(	PUNCT
ap-8605	70	2	20	20	NUM
ap-8605	70	3	)	)	PUNCT
ap-8605	70	4	in	in	ADP
ap-8605	70	5	the	the	DET
ap-8605	70	6	case	case	NOUN
ap-8605	70	7	of	of	ADP
ap-8605	70	8	the	the	DET
ap-8605	70	9	reversible	reversible	ADJ
ap-8605	70	10	cycle	cycle	NOUN
ap-8605	70	11	,	,	PUNCT
ap-8605	70	12	the	the	DET
ap-8605	70	13	integral	integral	ADJ
ap-8605	70	14	on	on	ADP
ap-8605	70	15	the	the	DET
ap-8605	70	16	r.h.s	r.h.s	NOUN
ap-8605	70	17	.	.	PUNCT
ap-8605	71	1	of	of	ADP
ap-8605	71	2	this	this	DET
ap-8605	71	3	equation	equation	NOUN
ap-8605	71	4	is	be	AUX
ap-8605	71	5	equal	equal	ADJ
ap-8605	71	6	to	to	ADP
ap-8605	71	7	zero	zero	NUM
ap-8605	71	8	.	.	PUNCT
ap-8605	72	1	note	note	VERB
ap-8605	72	2	that	that	SCONJ
ap-8605	72	3	at	at	ADP
ap-8605	72	4	this	this	DET
ap-8605	72	5	moment	moment	NOUN
ap-8605	72	6	,	,	PUNCT
ap-8605	72	7	the	the	DET
ap-8605	72	8	integral	integral	ADJ
ap-8605	72	9	constant	constant	NOUN
ap-8605	72	10	has	have	VERB
ap-8605	72	11	to	to	PART
ap-8605	72	12	be	be	AUX
ap-8605	72	13	determined	determine	VERB
ap-8605	72	14	.	.	PUNCT
ap-8605	73	1	this	this	PRON
ap-8605	73	2	can	can	AUX
ap-8605	73	3	be	be	AUX
ap-8605	73	4	done	do	VERB
ap-8605	73	5	thanks	thank	NOUN
ap-8605	73	6	to	to	ADP
ap-8605	73	7	the	the	DET
ap-8605	73	8	nernst	nernst	PROPN
ap-8605	73	9	theorem	theorem	PROPN
ap-8605	73	10	:	:	PUNCT
ap-8605	73	11	lim	lim	PROPN
ap-8605	73	12	t	t	PROPN
ap-8605	73	13	−→0	−→0	PROPN
ap-8605	73	14	∆s	∆s	PROPN
ap-8605	73	15	=	=	SYM
ap-8605	73	16	0	0	PROPN
ap-8605	73	17	.	.	PUNCT
ap-8605	74	1	(	(	PUNCT
ap-8605	74	2	21	21	NUM
ap-8605	74	3	)	)	PUNCT
ap-8605	74	4	the	the	DET
ap-8605	74	5	real	real	ADJ
ap-8605	74	6	processes	process	NOUN
ap-8605	74	7	are	be	AUX
ap-8605	74	8	,	,	PUNCT
ap-8605	74	9	however	however	ADV
ap-8605	74	10	irreversible	irreversible	ADJ
ap-8605	74	11	and	and	CCONJ
ap-8605	74	12	therefore	therefore	ADV
ap-8605	74	13	the	the	DET
ap-8605	74	14	equations	equation	NOUN
ap-8605	74	15	(	(	PUNCT
ap-8605	74	16	19	19	NUM
ap-8605	74	17	)	)	PUNCT
ap-8605	74	18	and	and	CCONJ
ap-8605	74	19	(	(	PUNCT
ap-8605	74	20	20	20	NUM
ap-8605	74	21	)	)	PUNCT
ap-8605	74	22	are	be	AUX
ap-8605	74	23	actually	actually	ADV
ap-8605	74	24	inequalities	inequality	NOUN
ap-8605	74	25	:	:	PUNCT
ap-8605	74	26	ds	ds	ADJ
ap-8605	74	27	≥	≥	NOUN
ap-8605	74	28	dq	dq	NUM
ap-8605	74	29	t	t	PROPN
ap-8605	74	30	.	.	PUNCT
ap-8605	75	1	(	(	PUNCT
ap-8605	75	2	22	22	NUM
ap-8605	75	3	)	)	PUNCT
ap-8605	75	4	now	now	ADV
ap-8605	75	5	,	,	PUNCT
ap-8605	75	6	entropy	entropy	NOUN
ap-8605	75	7	increase	increase	NOUN
ap-8605	75	8	can	can	AUX
ap-8605	75	9	be	be	AUX
ap-8605	75	10	easily	easily	ADV
ap-8605	75	11	obtained	obtain	VERB
ap-8605	75	12	(	(	PUNCT
ap-8605	75	13	e.g.	e.g.	ADV
ap-8605	75	14	bejan	bejan	NOUN
ap-8605	75	15	[	[	X
ap-8605	75	16	8	8	NUM
ap-8605	75	17	]	]	SYM
ap-8605	75	18	)	)	PUNCT
ap-8605	76	1	sgen	sgen	NOUN
ap-8605	76	2	=	=	NOUN
ap-8605	76	3	s2	s2	PROPN
ap-8605	76	4	−	−	PROPN
ap-8605	76	5	s1	s1	PROPN
ap-8605	76	6	−	−	PROPN
ap-8605	76	7	(	(	PUNCT
ap-8605	76	8	2)∫	2)∫	NUM
ap-8605	76	9	(	(	PUNCT
ap-8605	76	10	1	1	NUM
ap-8605	76	11	)	)	PUNCT
ap-8605	76	12	dq	dq	NOUN
ap-8605	76	13	t	t	PROPN
ap-8605	76	14	.	.	PUNCT
ap-8605	77	1	(	(	PUNCT
ap-8605	77	2	23	23	NUM
ap-8605	77	3	)	)	PUNCT
ap-8605	77	4	104	104	NUM
ap-8605	77	5	vol	vol	NOUN
ap-8605	77	6	.	.	PUNCT
ap-8605	78	1	63	63	NUM
ap-8605	78	2	no	no	NOUN
ap-8605	78	3	.	.	PUNCT
ap-8605	79	1	2/2023	2/2023	NUM
ap-8605	79	2	derivation	derivation	NOUN
ap-8605	79	3	of	of	ADP
ap-8605	79	4	entropy	entropy	NOUN
ap-8605	79	5	production	production	NOUN
ap-8605	79	6	in	in	ADP
ap-8605	79	7	a	a	DET
ap-8605	79	8	fluid	fluid	ADJ
ap-8605	79	9	flow	flow	NOUN
ap-8605	79	10	4	4	NUM
ap-8605	79	11	.	.	PUNCT
ap-8605	79	12	balances	balance	VERB
ap-8605	79	13	laws	law	NOUN
ap-8605	79	14	if	if	SCONJ
ap-8605	79	15	some	some	DET
ap-8605	79	16	quantity	quantity	NOUN
ap-8605	79	17	has	have	VERB
ap-8605	79	18	to	to	PART
ap-8605	79	19	be	be	AUX
ap-8605	79	20	conserved	conserve	VERB
ap-8605	79	21	in	in	ADP
ap-8605	79	22	time	time	NOUN
ap-8605	79	23	,	,	PUNCT
ap-8605	79	24	then	then	ADV
ap-8605	79	25	its	its	PRON
ap-8605	79	26	time	time	NOUN
ap-8605	79	27	derivative	derivative	NOUN
ap-8605	79	28	has	have	VERB
ap-8605	79	29	to	to	PART
ap-8605	79	30	be	be	AUX
ap-8605	79	31	equal	equal	ADJ
ap-8605	79	32	to	to	ADP
ap-8605	79	33	zero2	zero2	NOUN
ap-8605	79	34	,	,	PUNCT
ap-8605	79	35	see	see	VERB
ap-8605	79	36	e.g.	e.g.	ADV
ap-8605	79	37	maršík	maršík	NOUN
ap-8605	79	38	[	[	X
ap-8605	79	39	9	9	NUM
ap-8605	79	40	]	]	PUNCT
ap-8605	79	41	:	:	PUNCT
ap-8605	79	42	dψ	dψ	INTJ
ap-8605	79	43	dt	dt	NOUN
ap-8605	80	1	=	=	PUNCT
ap-8605	80	2	j	j	PROPN
ap-8605	80	3	(	(	PUNCT
ap-8605	80	4	ψ	ψ	NOUN
ap-8605	80	5	)	)	PUNCT
ap-8605	80	6	+	+	CCONJ
ap-8605	80	7	p	p	X
ap-8605	80	8	(	(	PUNCT
ap-8605	80	9	ψ	ψ	NOUN
ap-8605	80	10	)	)	PUNCT
ap-8605	80	11	=	=	SYM
ap-8605	80	12	0	0	NUM
ap-8605	80	13	,	,	PUNCT
ap-8605	80	14	(	(	PUNCT
ap-8605	80	15	24	24	NUM
ap-8605	80	16	)	)	PUNCT
ap-8605	80	17	where	where	SCONJ
ap-8605	80	18	j	j	PROPN
ap-8605	80	19	(	(	PUNCT
ap-8605	80	20	ψ	ψ	NOUN
ap-8605	80	21	)	)	PUNCT
ap-8605	80	22	is	be	AUX
ap-8605	80	23	the	the	DET
ap-8605	80	24	flux	flux	NOUN
ap-8605	80	25	of	of	ADP
ap-8605	80	26	quantity	quantity	NOUN
ap-8605	80	27	ψ	ψ	NOUN
ap-8605	80	28	through	through	ADP
ap-8605	80	29	a	a	DET
ap-8605	80	30	boundary	boundary	NOUN
ap-8605	80	31	of	of	ADP
ap-8605	80	32	the	the	DET
ap-8605	80	33	control	control	NOUN
ap-8605	80	34	volume	volume	NOUN
ap-8605	80	35	and	and	CCONJ
ap-8605	80	36	p	p	NOUN
ap-8605	80	37	(	(	PUNCT
ap-8605	80	38	ψ	ψ	NOUN
ap-8605	80	39	)	)	PUNCT
ap-8605	80	40	is	be	AUX
ap-8605	80	41	its	its	PRON
ap-8605	80	42	production	production	NOUN
ap-8605	80	43	within	within	ADP
ap-8605	80	44	the	the	DET
ap-8605	80	45	control	control	NOUN
ap-8605	80	46	volume	volume	NOUN
ap-8605	80	47	.	.	PUNCT
ap-8605	81	1	4.1	4.1	NUM
ap-8605	81	2	.	.	PUNCT
ap-8605	81	3	continuity	continuity	NOUN
ap-8605	81	4	equation	equation	NOUN
ap-8605	81	5	creation	creation	NOUN
ap-8605	81	6	or	or	CCONJ
ap-8605	81	7	destruction	destruction	NOUN
ap-8605	81	8	of	of	ADP
ap-8605	81	9	mass	mass	NOUN
ap-8605	81	10	can	can	AUX
ap-8605	81	11	not	not	PART
ap-8605	81	12	occur	occur	VERB
ap-8605	81	13	in	in	ADP
ap-8605	81	14	the	the	DET
ap-8605	81	15	control	control	NOUN
ap-8605	81	16	volume	volume	NOUN
ap-8605	81	17	,	,	PUNCT
ap-8605	81	18	this	this	PRON
ap-8605	81	19	means	mean	VERB
ap-8605	81	20	that	that	SCONJ
ap-8605	81	21	the	the	DET
ap-8605	81	22	production	production	NOUN
ap-8605	81	23	term	term	NOUN
ap-8605	81	24	in	in	ADP
ap-8605	81	25	equation	equation	NOUN
ap-8605	81	26	(	(	PUNCT
ap-8605	81	27	24	24	NUM
ap-8605	81	28	)	)	PUNCT
ap-8605	81	29	has	have	VERB
ap-8605	81	30	to	to	PART
ap-8605	81	31	be	be	AUX
ap-8605	81	32	equal	equal	ADJ
ap-8605	81	33	to	to	ADP
ap-8605	81	34	zero	zero	NUM
ap-8605	81	35	,	,	PUNCT
ap-8605	81	36	therefore	therefore	ADV
ap-8605	81	37	:	:	PUNCT
ap-8605	81	38	d	d	X
ap-8605	81	39	dt	dt	X
ap-8605	81	40	∫	∫	PROPN
ap-8605	82	1	dm	dm	PROPN
ap-8605	82	2	=	=	SYM
ap-8605	82	3	d	d	NOUN
ap-8605	82	4	dt	dt	X
ap-8605	82	5	∫	∫	PROPN
ap-8605	82	6	v	v	X
ap-8605	82	7	ϱdv	ϱdv	NOUN
ap-8605	82	8	=	=	SYM
ap-8605	82	9	0	0	NUM
ap-8605	82	10	,	,	PUNCT
ap-8605	82	11	(	(	PUNCT
ap-8605	82	12	25	25	NUM
ap-8605	82	13	)	)	PUNCT
ap-8605	82	14	where	where	SCONJ
ap-8605	82	15	ϱ	ϱ	PROPN
ap-8605	82	16	is	be	AUX
ap-8605	82	17	the	the	DET
ap-8605	82	18	fluid	fluid	ADJ
ap-8605	82	19	density	density	NOUN
ap-8605	82	20	and	and	CCONJ
ap-8605	82	21	v	v	NOUN
ap-8605	82	22	is	be	AUX
ap-8605	82	23	the	the	DET
ap-8605	82	24	control	control	NOUN
ap-8605	82	25	volume	volume	NOUN
ap-8605	82	26	.	.	PUNCT
ap-8605	83	1	changing	change	VERB
ap-8605	83	2	the	the	DET
ap-8605	83	3	sequence	sequence	NOUN
ap-8605	83	4	of	of	ADP
ap-8605	83	5	the	the	DET
ap-8605	83	6	derivatives	derivative	NOUN
ap-8605	83	7	and	and	CCONJ
ap-8605	83	8	integration	integration	NOUN
ap-8605	83	9	(	(	PUNCT
ap-8605	83	10	thanks	thank	NOUN
ap-8605	83	11	to	to	ADP
ap-8605	83	12	the	the	DET
ap-8605	83	13	leibniz	leibniz	PROPN
ap-8605	83	14	rule	rule	NOUN
ap-8605	83	15	for	for	ADP
ap-8605	83	16	integration	integration	NOUN
ap-8605	83	17	)	)	PUNCT
ap-8605	83	18	,	,	PUNCT
ap-8605	83	19	the	the	DET
ap-8605	83	20	following	follow	VERB
ap-8605	83	21	equation	equation	NOUN
ap-8605	83	22	is	be	AUX
ap-8605	83	23	obtained:∫	obtained:∫	NUM
ap-8605	83	24	v	v	ADJ
ap-8605	83	25	dϱ	dϱ	NOUN
ap-8605	83	26	dt	dt	X
ap-8605	83	27	dv	dv	PROPN
ap-8605	83	28	=	=	PROPN
ap-8605	83	29	0	0	PROPN
ap-8605	83	30	.	.	PUNCT
ap-8605	84	1	(	(	PUNCT
ap-8605	84	2	26	26	NUM
ap-8605	84	3	)	)	PUNCT
ap-8605	84	4	this	this	DET
ap-8605	84	5	relationship	relationship	NOUN
ap-8605	84	6	has	have	VERB
ap-8605	84	7	to	to	PART
ap-8605	84	8	hold	hold	VERB
ap-8605	84	9	in	in	ADP
ap-8605	84	10	any	any	DET
ap-8605	84	11	control	control	NOUN
ap-8605	84	12	volume	volume	NOUN
ap-8605	84	13	dv	dv	PROPN
ap-8605	84	14	̸=	̸=	PROPN
ap-8605	84	15	0	0	NUM
ap-8605	84	16	,	,	PUNCT
ap-8605	84	17	therefore	therefore	ADV
ap-8605	84	18	:	:	PUNCT
ap-8605	84	19	dϱ	dϱ	NOUN
ap-8605	84	20	dt	dt	NOUN
ap-8605	84	21	=	=	PUNCT
ap-8605	84	22	∂tϱ	∂tϱ	NOUN
ap-8605	84	23	+	+	ADV
ap-8605	84	24	uiϱi	uiϱi	ADJ
ap-8605	84	25	;	;	PUNCT
ap-8605	84	26	+	+	CCONJ
ap-8605	84	27	ϱui	ϱui	NOUN
ap-8605	84	28	;	;	PUNCT
ap-8605	84	29	i	i	PROPN
ap-8605	84	30	=	=	NOUN
ap-8605	84	31	0	0	NUM
ap-8605	84	32	,	,	PUNCT
ap-8605	84	33	(	(	PUNCT
ap-8605	84	34	27	27	NUM
ap-8605	84	35	)	)	PUNCT
ap-8605	84	36	where	where	SCONJ
ap-8605	84	37	ui	ui	PROPN
ap-8605	84	38	are	be	AUX
ap-8605	84	39	contravariant	contravariant	ADJ
ap-8605	84	40	components	component	NOUN
ap-8605	84	41	of	of	ADP
ap-8605	84	42	the	the	DET
ap-8605	84	43	velocity	velocity	NOUN
ap-8605	84	44	vector	vector	NOUN
ap-8605	84	45	.	.	PUNCT
ap-8605	85	1	4.2	4.2	NUM
ap-8605	85	2	.	.	PUNCT
ap-8605	86	1	momentum	momentum	NOUN
ap-8605	86	2	conservation	conservation	NOUN
ap-8605	86	3	law	law	NOUN
ap-8605	86	4	the	the	DET
ap-8605	86	5	momentum	momentum	NOUN
ap-8605	86	6	conservation	conservation	NOUN
ap-8605	86	7	law	law	NOUN
ap-8605	86	8	describes	describe	VERB
ap-8605	86	9	in	in	ADP
ap-8605	86	10	newtonian	newtonian	ADJ
ap-8605	86	11	mechanics	mechanic	NOUN
ap-8605	86	12	that	that	PRON
ap-8605	86	13	the	the	DET
ap-8605	86	14	time	time	NOUN
ap-8605	86	15	derivative	derivative	NOUN
ap-8605	86	16	of	of	ADP
ap-8605	86	17	the	the	DET
ap-8605	86	18	momentum	momentum	NOUN
ap-8605	86	19	has	have	VERB
ap-8605	86	20	to	to	PART
ap-8605	86	21	be	be	AUX
ap-8605	86	22	equal	equal	ADJ
ap-8605	86	23	to	to	ADP
ap-8605	86	24	all	all	PRON
ap-8605	86	25	of	of	ADP
ap-8605	86	26	the	the	DET
ap-8605	86	27	forces	force	NOUN
ap-8605	86	28	acting	act	VERB
ap-8605	86	29	on	on	ADP
ap-8605	86	30	the	the	DET
ap-8605	86	31	control	control	NOUN
ap-8605	86	32	volume	volume	NOUN
ap-8605	86	33	:	:	PUNCT
ap-8605	86	34	dmi	dmi	PROPN
ap-8605	87	1	dt	dt	PROPN
ap-8605	88	1	=	=	PUNCT
ap-8605	88	2	f	f	PROPN
ap-8605	89	1	i	i	PRON
ap-8605	89	2	+	+	CCONJ
ap-8605	89	3	si	si	INTJ
ap-8605	89	4	,	,	PUNCT
ap-8605	89	5	(	(	PUNCT
ap-8605	89	6	28	28	NUM
ap-8605	89	7	)	)	PUNCT
ap-8605	89	8	where	where	SCONJ
ap-8605	89	9	f	f	PROPN
ap-8605	89	10	i	i	PRON
ap-8605	89	11	are	be	AUX
ap-8605	89	12	components	component	NOUN
ap-8605	89	13	of	of	ADP
ap-8605	89	14	the	the	DET
ap-8605	89	15	volume	volume	NOUN
ap-8605	89	16	forces	force	NOUN
ap-8605	89	17	and	and	CCONJ
ap-8605	89	18	si	si	X
ap-8605	89	19	are	be	AUX
ap-8605	89	20	components	component	NOUN
ap-8605	89	21	of	of	ADP
ap-8605	89	22	the	the	DET
ap-8605	89	23	surface	surface	NOUN
ap-8605	89	24	forces	force	NOUN
ap-8605	89	25	,	,	PUNCT
ap-8605	89	26	respectively	respectively	ADV
ap-8605	89	27	,	,	PUNCT
ap-8605	89	28	that	that	PRON
ap-8605	89	29	are	be	AUX
ap-8605	89	30	defined	define	VERB
ap-8605	89	31	as	as	ADP
ap-8605	89	32	:	:	PUNCT
ap-8605	89	33	2note	2note	NUM
ap-8605	89	34	about	about	ADP
ap-8605	89	35	the	the	DET
ap-8605	89	36	notations	notation	NOUN
ap-8605	89	37	of	of	ADP
ap-8605	89	38	derivatives	derivative	NOUN
ap-8605	89	39	:	:	PUNCT
ap-8605	89	40	in	in	ADP
ap-8605	89	41	literature	literature	NOUN
ap-8605	89	42	,	,	PUNCT
ap-8605	89	43	there	there	PRON
ap-8605	89	44	usually	usually	ADV
ap-8605	89	45	is	be	AUX
ap-8605	89	46	a	a	DET
ap-8605	89	47	difference	difference	NOUN
ap-8605	89	48	in	in	ADP
ap-8605	89	49	the	the	DET
ap-8605	89	50	notation	notation	NOUN
ap-8605	89	51	of	of	ADP
ap-8605	89	52	derivative	derivative	NOUN
ap-8605	89	53	.	.	PUNCT
ap-8605	90	1	in	in	ADP
ap-8605	90	2	lagrangian	lagrangian	ADJ
ap-8605	90	3	description	description	NOUN
ap-8605	90	4	material	material	NOUN
ap-8605	90	5	derivative	derivative	NOUN
ap-8605	90	6	of	of	ADP
ap-8605	90	7	quantity	quantity	NOUN
ap-8605	90	8	,	,	PUNCT
ap-8605	90	9	ψ	ψ	NOUN
ap-8605	90	10	is	be	AUX
ap-8605	90	11	dψ	dψ	INTJ
ap-8605	90	12	/	/	SYM
ap-8605	90	13	dt	dt	NOUN
ap-8605	90	14	=	=	SYM
ap-8605	90	15	∂ψ/∂t	∂ψ/∂t	PROPN
ap-8605	90	16	,	,	PUNCT
ap-8605	90	17	in	in	ADP
ap-8605	90	18	euler	euler	NOUN
ap-8605	90	19	description	description	NOUN
ap-8605	90	20	,	,	PUNCT
ap-8605	90	21	the	the	DET
ap-8605	90	22	material	material	NOUN
ap-8605	90	23	derivative	derivative	NOUN
ap-8605	90	24	is	be	AUX
ap-8605	90	25	given	give	VERB
ap-8605	90	26	as	as	ADP
ap-8605	90	27	dψ	dψ	NOUN
ap-8605	90	28	/	/	SYM
ap-8605	90	29	dt	dt	NOUN
ap-8605	91	1	=	=	SYM
ap-8605	91	2	∂ψ/∂t+	∂ψ/∂t+	PROPN
ap-8605	91	3	uj∂ψ/∂xj	uj∂ψ/∂xj	PROPN
ap-8605	91	4	.	.	PUNCT
ap-8605	92	1	here	here	ADV
ap-8605	92	2	,	,	PUNCT
ap-8605	92	3	the	the	DET
ap-8605	92	4	material	material	NOUN
ap-8605	92	5	derivative	derivative	NOUN
ap-8605	92	6	in	in	ADP
ap-8605	92	7	the	the	DET
ap-8605	92	8	sense	sense	NOUN
ap-8605	92	9	of	of	ADP
ap-8605	92	10	euler	euler	NOUN
ap-8605	92	11	description	description	NOUN
ap-8605	92	12	will	will	AUX
ap-8605	92	13	be	be	AUX
ap-8605	92	14	noted	note	VERB
ap-8605	92	15	as	as	ADP
ap-8605	92	16	dψ	dψ	NOUN
ap-8605	92	17	/	/	SYM
ap-8605	92	18	dt	dt	NOUN
ap-8605	92	19	to	to	PART
ap-8605	92	20	emphasise	emphasise	VERB
ap-8605	92	21	the	the	DET
ap-8605	92	22	fact	fact	NOUN
ap-8605	92	23	that	that	SCONJ
ap-8605	92	24	the	the	DET
ap-8605	92	25	derivations	derivation	NOUN
ap-8605	92	26	are	be	AUX
ap-8605	92	27	performed	perform	VERB
ap-8605	92	28	in	in	ADP
ap-8605	92	29	general	general	ADJ
ap-8605	92	30	curvilinear	curvilinear	PROPN
ap-8605	92	31	coordinates	coordinate	NOUN
ap-8605	92	32	,	,	PUNCT
ap-8605	92	33	and	and	CCONJ
ap-8605	92	34	therefore	therefore	ADV
ap-8605	92	35	the	the	DET
ap-8605	92	36	convective	convective	ADJ
ap-8605	92	37	term	term	NOUN
ap-8605	92	38	in	in	ADP
ap-8605	92	39	the	the	DET
ap-8605	92	40	material	material	NOUN
ap-8605	92	41	derivative	derivative	NOUN
ap-8605	92	42	is	be	AUX
ap-8605	92	43	covariant	covariant	ADJ
ap-8605	92	44	derivative	derivative	NOUN
ap-8605	92	45	,	,	PUNCT
ap-8605	92	46	that	that	PRON
ap-8605	92	47	contains	contain	VERB
ap-8605	92	48	christoffel	christoffel	ADJ
ap-8605	92	49	symbols	symbol	NOUN
ap-8605	92	50	of	of	ADP
ap-8605	92	51	the	the	DET
ap-8605	92	52	second	second	ADJ
ap-8605	92	53	kind	kind	NOUN
ap-8605	92	54	.	.	PUNCT
ap-8605	93	1	mi	mi	PROPN
ap-8605	94	1	=	=	NOUN
ap-8605	94	2	∫	∫	PROPN
ap-8605	94	3	v	v	ADP
ap-8605	94	4	ϱuidv	ϱuidv	NOUN
ap-8605	94	5	,	,	PUNCT
ap-8605	94	6	(	(	PUNCT
ap-8605	94	7	29	29	NUM
ap-8605	94	8	)	)	PUNCT
ap-8605	94	9	f	f	NOUN
ap-8605	95	1	i	i	PRON
ap-8605	95	2	=	=	NOUN
ap-8605	95	3	∫	∫	PROPN
ap-8605	95	4	v	v	X
ap-8605	95	5	ϱaidv	ϱaidv	NOUN
ap-8605	95	6	,	,	PUNCT
ap-8605	95	7	(	(	PUNCT
ap-8605	95	8	30	30	NUM
ap-8605	95	9	)	)	PUNCT
ap-8605	95	10	si	si	NOUN
ap-8605	95	11	=	=	PUNCT
ap-8605	95	12	∮	∮	NUM
ap-8605	95	13	a	a	DET
ap-8605	95	14	σijdaj	σijdaj	NOUN
ap-8605	95	15	,	,	PUNCT
ap-8605	95	16	(	(	PUNCT
ap-8605	95	17	31	31	NUM
ap-8605	95	18	)	)	PUNCT
ap-8605	95	19	where	where	SCONJ
ap-8605	95	20	ai	ai	VERB
ap-8605	95	21	are	be	AUX
ap-8605	95	22	the	the	DET
ap-8605	95	23	components	component	NOUN
ap-8605	95	24	of	of	ADP
ap-8605	95	25	the	the	DET
ap-8605	95	26	acceleration	acceleration	NOUN
ap-8605	95	27	vector	vector	NOUN
ap-8605	95	28	and	and	CCONJ
ap-8605	95	29	σij	σij	NOUN
ap-8605	95	30	are	be	AUX
ap-8605	95	31	the	the	DET
ap-8605	95	32	components	component	NOUN
ap-8605	95	33	of	of	ADP
ap-8605	95	34	the	the	DET
ap-8605	95	35	stress	stress	NOUN
ap-8605	95	36	tensor	tensor	NOUN
ap-8605	95	37	.	.	PUNCT
ap-8605	96	1	if	if	SCONJ
ap-8605	96	2	the	the	DET
ap-8605	96	3	control	control	NOUN
ap-8605	96	4	volume	volume	NOUN
ap-8605	96	5	bonded	bond	VERB
ap-8605	96	6	by	by	ADP
ap-8605	96	7	the	the	DET
ap-8605	96	8	surface	surface	NOUN
ap-8605	96	9	a	a	PRON
ap-8605	96	10	is	be	AUX
ap-8605	96	11	free	free	ADJ
ap-8605	96	12	of	of	ADP
ap-8605	96	13	discontinuity	discontinuity	NOUN
ap-8605	96	14	or	or	CCONJ
ap-8605	96	15	singular	singular	ADJ
ap-8605	96	16	points	point	NOUN
ap-8605	96	17	,	,	PUNCT
ap-8605	96	18	then	then	ADV
ap-8605	96	19	integral	integral	ADJ
ap-8605	96	20	(	(	PUNCT
ap-8605	96	21	28	28	NUM
ap-8605	96	22	)	)	PUNCT
ap-8605	96	23	can	can	AUX
ap-8605	96	24	be	be	AUX
ap-8605	96	25	transformed	transform	VERB
ap-8605	96	26	by	by	ADP
ap-8605	96	27	the	the	DET
ap-8605	96	28	gauss	gauss	PROPN
ap-8605	96	29	divergence	divergence	NOUN
ap-8605	96	30	theorem	theorem	ADJ
ap-8605	96	31	into	into	ADP
ap-8605	96	32	:	:	PUNCT
ap-8605	96	33	∮	∮	NUM
ap-8605	96	34	a	a	DET
ap-8605	96	35	σijdaj	σijdaj	NOUN
ap-8605	96	36	=	=	SYM
ap-8605	96	37	∫	∫	PROPN
ap-8605	96	38	v	v	NUM
ap-8605	96	39	σij	σij	NOUN
ap-8605	96	40	;	;	PUNCT
ap-8605	96	41	j	j	PROPN
ap-8605	96	42	dv	dv	PROPN
ap-8605	96	43	.	.	PUNCT
ap-8605	97	1	(	(	PUNCT
ap-8605	97	2	32	32	NUM
ap-8605	97	3	)	)	PUNCT
ap-8605	97	4	substituting	substitute	VERB
ap-8605	97	5	equations	equation	NOUN
ap-8605	97	6	(	(	PUNCT
ap-8605	97	7	29	29	NUM
ap-8605	97	8	)	)	PUNCT
ap-8605	97	9	–	–	PUNCT
ap-8605	97	10	(	(	PUNCT
ap-8605	97	11	32	32	NUM
ap-8605	97	12	)	)	PUNCT
ap-8605	97	13	into	into	ADP
ap-8605	97	14	equation	equation	NOUN
ap-8605	97	15	(	(	PUNCT
ap-8605	97	16	28	28	NUM
ap-8605	97	17	)	)	PUNCT
ap-8605	97	18	,	,	PUNCT
ap-8605	97	19	the	the	DET
ap-8605	97	20	balance	balance	NOUN
ap-8605	97	21	of	of	ADP
ap-8605	97	22	momentum	momentum	NOUN
ap-8605	97	23	is	be	AUX
ap-8605	97	24	given	give	VERB
ap-8605	97	25	by	by	ADP
ap-8605	97	26	:	:	PUNCT
ap-8605	97	27	d	d	X
ap-8605	97	28	dt	dt	X
ap-8605	97	29	∫	∫	PROPN
ap-8605	97	30	v	v	INTJ
ap-8605	97	31	ϱuidv	ϱuidv	NOUN
ap-8605	97	32	=	=	PUNCT
ap-8605	98	1	∫	∫	PROPN
ap-8605	99	1	v	v	X
ap-8605	99	2	ϱaidv	ϱaidv	NOUN
ap-8605	100	1	+	+	CCONJ
ap-8605	100	2	∫	∫	PROPN
ap-8605	101	1	v	v	NUM
ap-8605	101	2	σij	σij	NOUN
ap-8605	101	3	;	;	PUNCT
ap-8605	102	1	j	j	PROPN
ap-8605	102	2	dv	dv	PROPN
ap-8605	102	3	.	.	PUNCT
ap-8605	103	1	(	(	PUNCT
ap-8605	103	2	33	33	NUM
ap-8605	103	3	)	)	PUNCT
ap-8605	103	4	another	another	DET
ap-8605	103	5	change	change	NOUN
ap-8605	103	6	in	in	ADP
ap-8605	103	7	the	the	DET
ap-8605	103	8	sequence	sequence	NOUN
ap-8605	103	9	of	of	ADP
ap-8605	103	10	derivation	derivation	NOUN
ap-8605	103	11	and	and	CCONJ
ap-8605	103	12	integration	integration	NOUN
ap-8605	103	13	transforms	transform	VERB
ap-8605	103	14	this	this	DET
ap-8605	103	15	relationship	relationship	NOUN
ap-8605	103	16	into	into	ADP
ap-8605	103	17	the	the	DET
ap-8605	103	18	form:∫	form:∫	NOUN
ap-8605	103	19	v	v	NOUN
ap-8605	103	20	[	[	PUNCT
ap-8605	103	21	ϱai	ϱai	PROPN
ap-8605	103	22	+	+	CCONJ
ap-8605	103	23	σij	σij	NOUN
ap-8605	103	24	;	;	PUNCT
ap-8605	103	25	j	j	PROPN
ap-8605	103	26	−	−	PROPN
ap-8605	103	27	d	d	PROPN
ap-8605	103	28	(	(	PUNCT
ap-8605	103	29	ϱui	ϱui	PROPN
ap-8605	103	30	)	)	PUNCT
ap-8605	103	31	dt	dt	X
ap-8605	103	32	]	]	PUNCT
ap-8605	104	1	dv	dv	PROPN
ap-8605	104	2	.	.	PUNCT
ap-8605	105	1	(	(	PUNCT
ap-8605	105	2	34	34	NUM
ap-8605	105	3	)	)	PUNCT
ap-8605	105	4	this	this	PRON
ap-8605	105	5	again	again	ADV
ap-8605	105	6	has	have	VERB
ap-8605	105	7	to	to	PART
ap-8605	105	8	be	be	AUX
ap-8605	105	9	true	true	ADJ
ap-8605	105	10	in	in	ADP
ap-8605	105	11	any	any	DET
ap-8605	105	12	control	control	NOUN
ap-8605	105	13	volume	volume	NOUN
ap-8605	105	14	dv	dv	PROPN
ap-8605	105	15	̸=	̸=	PROPN
ap-8605	105	16	0	0	NUM
ap-8605	105	17	,	,	PUNCT
ap-8605	105	18	therefore	therefore	ADV
ap-8605	105	19	:	:	PUNCT
ap-8605	105	20	d	d	X
ap-8605	105	21	(	(	PUNCT
ap-8605	105	22	ϱui	ϱui	PROPN
ap-8605	105	23	)	)	PUNCT
ap-8605	105	24	dt	dt	NOUN
ap-8605	106	1	=	=	SYM
ap-8605	106	2	ϱ	ϱ	PROPN
ap-8605	106	3	(	(	PUNCT
ap-8605	106	4	∂tu	∂tu	ADV
ap-8605	106	5	i	i	PRON
ap-8605	106	6	+	+	CCONJ
ap-8605	106	7	ujui	ujui	ADJ
ap-8605	106	8	;	;	PUNCT
ap-8605	106	9	j	j	X
ap-8605	106	10	)	)	PUNCT
ap-8605	107	1	=	=	PRON
ap-8605	107	2	ϱai	ϱai	PROPN
ap-8605	107	3	+	+	CCONJ
ap-8605	107	4	σij	σij	NOUN
ap-8605	107	5	;	;	PUNCT
ap-8605	107	6	j	j	PROPN
ap-8605	107	7	,	,	PUNCT
ap-8605	107	8	(	(	PUNCT
ap-8605	107	9	35	35	NUM
ap-8605	107	10	)	)	PUNCT
ap-8605	107	11	no	no	DET
ap-8605	107	12	special	special	ADJ
ap-8605	107	13	assumptions	assumption	NOUN
ap-8605	107	14	about	about	ADP
ap-8605	107	15	fluid	fluid	ADJ
ap-8605	107	16	flow	flow	NOUN
ap-8605	107	17	were	be	AUX
ap-8605	107	18	made	make	VERB
ap-8605	107	19	to	to	ADP
ap-8605	107	20	this	this	DET
ap-8605	107	21	point	point	NOUN
ap-8605	107	22	.	.	PUNCT
ap-8605	108	1	the	the	DET
ap-8605	108	2	stress	stress	NOUN
ap-8605	108	3	tensor	tensor	NOUN
ap-8605	108	4	can	can	AUX
ap-8605	108	5	be	be	AUX
ap-8605	108	6	decomposed	decompose	VERB
ap-8605	108	7	into	into	ADP
ap-8605	108	8	two	two	NUM
ap-8605	108	9	parts	part	NOUN
ap-8605	108	10	:	:	PUNCT
ap-8605	108	11	σij	σij	NOUN
ap-8605	108	12	=	=	SYM
ap-8605	108	13	−gijp+	−gijp+	NOUN
ap-8605	108	14	τ	τ	X
ap-8605	108	15	ij	ij	INTJ
ap-8605	108	16	,	,	PUNCT
ap-8605	108	17	(	(	PUNCT
ap-8605	108	18	36	36	NUM
ap-8605	108	19	)	)	PUNCT
ap-8605	108	20	where	where	SCONJ
ap-8605	108	21	p	p	NOUN
ap-8605	108	22	is	be	AUX
ap-8605	108	23	the	the	DET
ap-8605	108	24	thermodynamic	thermodynamic	ADJ
ap-8605	108	25	pressure	pressure	NOUN
ap-8605	108	26	,	,	PUNCT
ap-8605	108	27	gij	gij	PROPN
ap-8605	108	28	is	be	AUX
ap-8605	108	29	the	the	DET
ap-8605	108	30	inverse	inverse	NOUN
ap-8605	108	31	of	of	ADP
ap-8605	108	32	the	the	DET
ap-8605	108	33	metric	metric	ADJ
ap-8605	108	34	tensor	tensor	NOUN
ap-8605	108	35	,	,	PUNCT
ap-8605	108	36	and	and	CCONJ
ap-8605	108	37	τ	τ	PROPN
ap-8605	108	38	ij	ij	NOUN
ap-8605	108	39	are	be	AUX
ap-8605	108	40	the	the	DET
ap-8605	108	41	components	component	NOUN
ap-8605	108	42	of	of	ADP
ap-8605	108	43	the	the	DET
ap-8605	108	44	viscous	viscous	ADJ
ap-8605	108	45	tensor	tensor	NOUN
ap-8605	108	46	.	.	PUNCT
ap-8605	109	1	the	the	DET
ap-8605	109	2	negative	negative	ADJ
ap-8605	109	3	sign	sign	NOUN
ap-8605	109	4	in	in	ADP
ap-8605	109	5	the	the	DET
ap-8605	109	6	thermodynamic	thermodynamic	ADJ
ap-8605	109	7	pressure	pressure	NOUN
ap-8605	109	8	means	mean	VERB
ap-8605	109	9	that	that	SCONJ
ap-8605	109	10	the	the	DET
ap-8605	109	11	force	force	NOUN
ap-8605	109	12	caused	cause	VERB
ap-8605	109	13	by	by	ADP
ap-8605	109	14	this	this	DET
ap-8605	109	15	pressure	pressure	NOUN
ap-8605	109	16	acts	act	VERB
ap-8605	109	17	in	in	ADP
ap-8605	109	18	the	the	DET
ap-8605	109	19	opposite	opposite	ADJ
ap-8605	109	20	direction	direction	NOUN
ap-8605	109	21	of	of	ADP
ap-8605	109	22	the	the	DET
ap-8605	109	23	outer	outer	ADJ
ap-8605	109	24	normal	normal	ADJ
ap-8605	109	25	.	.	PUNCT
ap-8605	110	1	if	if	SCONJ
ap-8605	110	2	the	the	DET
ap-8605	110	3	fluid	fluid	NOUN
ap-8605	110	4	is	be	AUX
ap-8605	110	5	at	at	ADP
ap-8605	110	6	rest	rest	NOUN
ap-8605	110	7	,	,	PUNCT
ap-8605	110	8	a	a	DET
ap-8605	110	9	viscous	viscous	ADJ
ap-8605	110	10	tensor	tensor	NOUN
ap-8605	110	11	is	be	AUX
ap-8605	110	12	zero	zero	NUM
ap-8605	110	13	and	and	CCONJ
ap-8605	110	14	the	the	DET
ap-8605	110	15	thermodynamics	thermodynamic	NOUN
ap-8605	110	16	pressure	pressure	NOUN
ap-8605	110	17	is	be	AUX
ap-8605	110	18	equal	equal	ADJ
ap-8605	110	19	to	to	ADP
ap-8605	110	20	the	the	DET
ap-8605	110	21	hydrostatic	hydrostatic	ADJ
ap-8605	110	22	pressure	pressure	NOUN
ap-8605	110	23	.	.	PUNCT
ap-8605	111	1	at	at	ADP
ap-8605	111	2	last	last	ADJ
ap-8605	111	3	,	,	PUNCT
ap-8605	111	4	the	the	DET
ap-8605	111	5	momentum	momentum	NOUN
ap-8605	111	6	balance	balance	NOUN
ap-8605	111	7	can	can	AUX
ap-8605	111	8	be	be	AUX
ap-8605	111	9	written	write	VERB
ap-8605	111	10	in	in	ADP
ap-8605	111	11	the	the	DET
ap-8605	111	12	form	form	NOUN
ap-8605	111	13	of	of	ADP
ap-8605	111	14	:	:	PUNCT
ap-8605	111	15	ϱ	ϱ	PROPN
ap-8605	111	16	(	(	PUNCT
ap-8605	111	17	∂tu	∂tu	ADV
ap-8605	111	18	i	i	PRON
ap-8605	111	19	+	+	CCONJ
ap-8605	111	20	ujui	ujui	ADJ
ap-8605	111	21	;	;	PUNCT
ap-8605	111	22	j	j	X
ap-8605	111	23	)	)	PUNCT
ap-8605	112	1	=	=	AUX
ap-8605	112	2	ϱai	ϱai	ADJ
ap-8605	113	1	−	−	PROPN
ap-8605	113	2	gijp;j	gijp;j	PROPN
ap-8605	114	1	+	+	CCONJ
ap-8605	114	2	τ	τ	X
ap-8605	114	3	ij	ij	INTJ
ap-8605	114	4	;	;	PUNCT
ap-8605	114	5	j	j	PROPN
ap-8605	114	6	.	.	PUNCT
ap-8605	115	1	(	(	PUNCT
ap-8605	115	2	37	37	NUM
ap-8605	115	3	)	)	PUNCT
ap-8605	115	4	4.3	4.3	NUM
ap-8605	115	5	.	.	PUNCT
ap-8605	116	1	energy	energy	NOUN
ap-8605	116	2	conservation	conservation	NOUN
ap-8605	116	3	law	law	NOUN
ap-8605	116	4	energy	energy	NOUN
ap-8605	116	5	can	can	AUX
ap-8605	116	6	not	not	PART
ap-8605	116	7	be	be	AUX
ap-8605	116	8	created	create	VERB
ap-8605	116	9	nor	nor	CCONJ
ap-8605	116	10	destroyed	destroy	VERB
ap-8605	116	11	by	by	ADP
ap-8605	116	12	any	any	DET
ap-8605	116	13	known	know	VERB
ap-8605	116	14	mechanism	mechanism	NOUN
ap-8605	116	15	,	,	PUNCT
ap-8605	116	16	the	the	DET
ap-8605	116	17	law	law	NOUN
ap-8605	116	18	of	of	ADP
ap-8605	116	19	balance	balance	NOUN
ap-8605	116	20	of	of	ADP
ap-8605	116	21	energy	energy	NOUN
ap-8605	116	22	tells	tell	VERB
ap-8605	116	23	us	we	PRON
ap-8605	116	24	,	,	PUNCT
ap-8605	116	25	that	that	SCONJ
ap-8605	116	26	the	the	DET
ap-8605	116	27	energy	energy	NOUN
ap-8605	116	28	is	be	AUX
ap-8605	116	29	transforming	transform	VERB
ap-8605	116	30	between	between	ADP
ap-8605	116	31	its	its	PRON
ap-8605	116	32	different	different	ADJ
ap-8605	116	33	forms	form	NOUN
ap-8605	116	34	.	.	PUNCT
ap-8605	117	1	the	the	DET
ap-8605	117	2	change	change	NOUN
ap-8605	117	3	of	of	ADP
ap-8605	117	4	total	total	ADJ
ap-8605	117	5	energy	energy	NOUN
ap-8605	117	6	of	of	ADP
ap-8605	117	7	the	the	DET
ap-8605	117	8	flowing	flow	VERB
ap-8605	117	9	fluid	fluid	NOUN
ap-8605	117	10	is	be	AUX
ap-8605	117	11	given	give	VERB
ap-8605	117	12	by	by	ADP
ap-8605	117	13	:	:	PUNCT
ap-8605	117	14	105	105	NUM
ap-8605	117	15	erik	erik	PROPN
ap-8605	117	16	flídr	flídr	PROPN
ap-8605	117	17	acta	acta	PROPN
ap-8605	117	18	polytechnica	polytechnica	PROPN
ap-8605	118	1	d	d	X
ap-8605	118	2	dt	dt	X
ap-8605	118	3	∫	∫	PROPN
ap-8605	118	4	v	v	NUM
ap-8605	118	5	ϱetotdv	ϱetotdv	PROPN
ap-8605	119	1	=	=	PUNCT
ap-8605	120	1	d	d	NOUN
ap-8605	120	2	dt	dt	X
ap-8605	120	3	∫	∫	PROPN
ap-8605	120	4	v	v	X
ap-8605	120	5	ϱ	ϱ	PROPN
ap-8605	120	6	(	(	PUNCT
ap-8605	120	7	ein	ein	NOUN
ap-8605	120	8	+	+	CCONJ
ap-8605	120	9	ekin)dv	ekin)dv	NOUN
ap-8605	120	10	=	=	SYM
ap-8605	120	11	(	(	PUNCT
ap-8605	120	12	38	38	NUM
ap-8605	120	13	)	)	PUNCT
ap-8605	120	14	=	=	PUNCT
ap-8605	121	1	−	−	PROPN
ap-8605	121	2	∮	∮	VERB
ap-8605	121	3	a	a	DET
ap-8605	121	4	gjlqldaj	gjlqldaj	NOUN
ap-8605	121	5	+	+	CCONJ
ap-8605	121	6	∮	∮	NUM
ap-8605	121	7	a	a	DET
ap-8605	121	8	gilu	gilu	NOUN
ap-8605	121	9	lσijdaj	lσijdaj	NOUN
ap-8605	121	10	+	+	CCONJ
ap-8605	121	11	∫	∫	PROPN
ap-8605	121	12	v	v	NUM
ap-8605	121	13	ϱgiju	ϱgiju	ADJ
ap-8605	121	14	iajdv	iajdv	NOUN
ap-8605	121	15	,	,	PUNCT
ap-8605	121	16	where	where	SCONJ
ap-8605	121	17	total	total	ADJ
ap-8605	121	18	energy	energy	NOUN
ap-8605	121	19	etot	etot	NOUN
ap-8605	121	20	is	be	AUX
ap-8605	121	21	a	a	DET
ap-8605	121	22	sum	sum	NOUN
ap-8605	121	23	of	of	ADP
ap-8605	121	24	internal	internal	ADJ
ap-8605	121	25	energy	energy	NOUN
ap-8605	121	26	ein	ein	NOUN
ap-8605	121	27	and	and	CCONJ
ap-8605	121	28	kinetic	kinetic	ADJ
ap-8605	121	29	energy	energy	NOUN
ap-8605	121	30	ekin	ekin	NOUN
ap-8605	121	31	.	.	PUNCT
ap-8605	122	1	next	next	ADV
ap-8605	122	2	,	,	PUNCT
ap-8605	122	3	ql	ql	X
ap-8605	122	4	is	be	AUX
ap-8605	122	5	the	the	DET
ap-8605	122	6	covector	covector	NOUN
ap-8605	122	7	of	of	ADP
ap-8605	122	8	the	the	DET
ap-8605	122	9	heat	heat	NOUN
ap-8605	122	10	flux	flux	NOUN
ap-8605	122	11	and	and	CCONJ
ap-8605	122	12	gil	gil	PROPN
ap-8605	122	13	is	be	AUX
ap-8605	122	14	the	the	DET
ap-8605	122	15	metric	metric	ADJ
ap-8605	122	16	tensor	tensor	NOUN
ap-8605	122	17	.	.	PUNCT
ap-8605	123	1	on	on	ADP
ap-8605	123	2	the	the	DET
ap-8605	123	3	l.h.s	l.h.s	NOUN
ap-8605	123	4	.	.	PUNCT
ap-8605	124	1	of	of	ADP
ap-8605	124	2	the	the	DET
ap-8605	124	3	equation	equation	NOUN
ap-8605	124	4	(	(	PUNCT
ap-8605	124	5	38	38	NUM
ap-8605	124	6	)	)	PUNCT
ap-8605	124	7	,	,	PUNCT
ap-8605	124	8	the	the	DET
ap-8605	124	9	sequence	sequence	NOUN
ap-8605	124	10	of	of	ADP
ap-8605	124	11	the	the	DET
ap-8605	124	12	derivation	derivation	NOUN
ap-8605	124	13	and	and	CCONJ
ap-8605	124	14	integration	integration	NOUN
ap-8605	124	15	will	will	AUX
ap-8605	124	16	be	be	AUX
ap-8605	124	17	switched	switch	VERB
ap-8605	124	18	and	and	CCONJ
ap-8605	124	19	on	on	ADP
ap-8605	124	20	the	the	DET
ap-8605	124	21	r.h.s	r.h.s	NOUN
ap-8605	124	22	.	.	PUNCT
ap-8605	125	1	of	of	ADP
ap-8605	125	2	the	the	DET
ap-8605	125	3	equation	equation	NOUN
ap-8605	125	4	(	(	PUNCT
ap-8605	125	5	38	38	NUM
ap-8605	125	6	)	)	PUNCT
ap-8605	125	7	,	,	PUNCT
ap-8605	125	8	the	the	DET
ap-8605	125	9	gauss	gauss	PROPN
ap-8605	125	10	divergence	divergence	NOUN
ap-8605	125	11	theorem	theorem	NOUN
ap-8605	125	12	will	will	AUX
ap-8605	125	13	be	be	AUX
ap-8605	125	14	used	use	VERB
ap-8605	125	15	to	to	PART
ap-8605	125	16	convert	convert	VERB
ap-8605	125	17	the	the	DET
ap-8605	125	18	surface	surface	NOUN
ap-8605	125	19	integrals	integral	NOUN
ap-8605	125	20	into	into	ADP
ap-8605	125	21	volume	volume	NOUN
ap-8605	125	22	integrals	integral	NOUN
ap-8605	125	23	,	,	PUNCT
ap-8605	125	24	resulting	result	VERB
ap-8605	125	25	into	into	ADP
ap-8605	125	26	:	:	PUNCT
ap-8605	125	27	∫	∫	PROPN
ap-8605	125	28	v	v	NUM
ap-8605	125	29	d	d	X
ap-8605	125	30	dt	dt	X
ap-8605	126	1	[	[	X
ap-8605	126	2	ϱ	ϱ	X
ap-8605	126	3	(	(	PUNCT
ap-8605	126	4	ein	ein	NOUN
ap-8605	126	5	+	+	CCONJ
ap-8605	126	6	ekin)]dv	ekin)]dv	PROPN
ap-8605	126	7	=	=	PUNCT
ap-8605	126	8	(	(	PUNCT
ap-8605	126	9	39	39	NUM
ap-8605	126	10	)	)	PUNCT
ap-8605	126	11	=	=	SYM
ap-8605	127	1	∫	∫	PROPN
ap-8605	127	2	v	v	X
ap-8605	127	3	[	[	PUNCT
ap-8605	127	4	−	−	PROPN
ap-8605	127	5	(	(	PUNCT
ap-8605	127	6	gilql	gilql	PROPN
ap-8605	127	7	)	)	PUNCT
ap-8605	127	8	;	;	PUNCT
ap-8605	128	1	i	i	PRON
ap-8605	128	2	+	+	CCONJ
ap-8605	128	3	(	(	PUNCT
ap-8605	128	4	gjlu	gjlu	ADJ
ap-8605	128	5	lσij	lσij	PROPN
ap-8605	128	6	)	)	PUNCT
ap-8605	128	7	;	;	PUNCT
ap-8605	128	8	i	i	PRON
ap-8605	128	9	+	+	CCONJ
ap-8605	128	10	ϱgiju	ϱgiju	ADJ
ap-8605	128	11	iaj	iaj	ADJ
ap-8605	128	12	]	]	PUNCT
ap-8605	128	13	dv	dv	PROPN
ap-8605	128	14	.	.	PUNCT
ap-8605	129	1	again	again	ADV
ap-8605	129	2	,	,	PUNCT
ap-8605	129	3	this	this	PRON
ap-8605	129	4	has	have	VERB
ap-8605	129	5	to	to	PART
ap-8605	129	6	hold	hold	VERB
ap-8605	129	7	in	in	ADP
ap-8605	129	8	any	any	DET
ap-8605	129	9	control	control	NOUN
ap-8605	129	10	volume	volume	NOUN
ap-8605	129	11	,	,	PUNCT
ap-8605	129	12	therefore	therefore	ADV
ap-8605	129	13	:	:	PUNCT
ap-8605	129	14	d	d	X
ap-8605	129	15	dt	dt	X
ap-8605	130	1	[	[	X
ap-8605	130	2	ϱ	ϱ	X
ap-8605	130	3	(	(	PUNCT
ap-8605	130	4	ein	ein	NOUN
ap-8605	130	5	+	+	CCONJ
ap-8605	130	6	ekin	ekin	NOUN
ap-8605	130	7	)	)	PUNCT
ap-8605	130	8	]	]	PUNCT
ap-8605	131	1	=	=	PUNCT
ap-8605	131	2	−	−	PROPN
ap-8605	131	3	(	(	PUNCT
ap-8605	131	4	gilql	gilql	PROPN
ap-8605	131	5	)	)	PUNCT
ap-8605	131	6	;	;	PUNCT
ap-8605	132	1	i	i	PRON
ap-8605	132	2	+	+	CCONJ
ap-8605	132	3	(	(	PUNCT
ap-8605	132	4	gjlu	gjlu	ADJ
ap-8605	132	5	lσij	lσij	PROPN
ap-8605	132	6	)	)	PUNCT
ap-8605	132	7	;	;	PUNCT
ap-8605	132	8	i	i	PRON
ap-8605	132	9	+	+	CCONJ
ap-8605	132	10	ϱgiju	ϱgiju	ADV
ap-8605	132	11	iaj	iaj	ADJ
ap-8605	132	12	.	.	PUNCT
ap-8605	133	1	(	(	PUNCT
ap-8605	133	2	40	40	NUM
ap-8605	133	3	)	)	PUNCT
ap-8605	133	4	4.4	4.4	NUM
ap-8605	133	5	.	.	PUNCT
ap-8605	134	1	entropy	entropy	PROPN
ap-8605	134	2	balance	balance	NOUN
ap-8605	134	3	entropy	entropy	NOUN
ap-8605	134	4	balance	balance	NOUN
ap-8605	134	5	can	can	AUX
ap-8605	134	6	be	be	AUX
ap-8605	134	7	written	write	VERB
ap-8605	134	8	in	in	ADP
ap-8605	134	9	the	the	DET
ap-8605	134	10	form	form	NOUN
ap-8605	134	11	of	of	ADP
ap-8605	134	12	the	the	DET
ap-8605	134	13	balance	balance	NOUN
ap-8605	134	14	equation	equation	NOUN
ap-8605	134	15	(	(	PUNCT
ap-8605	134	16	24	24	NUM
ap-8605	134	17	)	)	PUNCT
ap-8605	134	18	as	as	ADP
ap-8605	134	19	:	:	PUNCT
ap-8605	134	20	ds	ds	ADJ
ap-8605	134	21	dt	dt	NOUN
ap-8605	134	22	=	=	SYM
ap-8605	134	23	j	j	PROPN
ap-8605	134	24	(	(	PUNCT
ap-8605	134	25	s	s	NOUN
ap-8605	134	26	)	)	PUNCT
ap-8605	134	27	+	+	CCONJ
ap-8605	134	28	p(s	p(s	NUM
ap-8605	134	29	)	)	PUNCT
ap-8605	134	30	=	=	SYM
ap-8605	134	31	0	0	NUM
ap-8605	134	32	,	,	PUNCT
ap-8605	134	33	(	(	PUNCT
ap-8605	134	34	41	41	NUM
ap-8605	134	35	)	)	PUNCT
ap-8605	134	36	from	from	ADP
ap-8605	134	37	where	where	SCONJ
ap-8605	134	38	entropy	entropy	NOUN
ap-8605	134	39	production	production	NOUN
ap-8605	134	40	can	can	AUX
ap-8605	134	41	be	be	AUX
ap-8605	134	42	obtained	obtain	VERB
ap-8605	134	43	as	as	ADP
ap-8605	134	44	:	:	PUNCT
ap-8605	134	45	p(s	p(s	NUM
ap-8605	134	46	)	)	PUNCT
ap-8605	135	1	=	=	PUNCT
ap-8605	135	2	ds	ds	ADJ
ap-8605	136	1	dt	dt	X
ap-8605	136	2	−	−	PROPN
ap-8605	136	3	j	j	PROPN
ap-8605	136	4	(	(	PUNCT
ap-8605	136	5	s	s	PROPN
ap-8605	136	6	)	)	PUNCT
ap-8605	136	7	≥	≥	NOUN
ap-8605	136	8	0	0	NUM
ap-8605	136	9	.	.	PUNCT
ap-8605	137	1	(	(	PUNCT
ap-8605	137	2	42	42	NUM
ap-8605	137	3	)	)	PUNCT
ap-8605	137	4	entropy	entropy	NOUN
ap-8605	137	5	contained	contain	VERB
ap-8605	137	6	in	in	ADP
ap-8605	137	7	the	the	DET
ap-8605	137	8	control	control	NOUN
ap-8605	137	9	volume	volume	NOUN
ap-8605	137	10	can	can	AUX
ap-8605	137	11	be	be	AUX
ap-8605	137	12	calculated	calculate	VERB
ap-8605	137	13	as	as	ADP
ap-8605	137	14	:	:	PUNCT
ap-8605	137	15	s	s	PART
ap-8605	137	16	=	=	PUNCT
ap-8605	137	17	∫	∫	PROPN
ap-8605	137	18	v	v	INTJ
ap-8605	137	19	ϱsdv	ϱsdv	NOUN
ap-8605	137	20	,	,	PUNCT
ap-8605	137	21	(	(	PUNCT
ap-8605	137	22	43	43	NUM
ap-8605	137	23	)	)	PUNCT
ap-8605	137	24	where	where	SCONJ
ap-8605	137	25	s	s	NOUN
ap-8605	137	26	is	be	AUX
ap-8605	137	27	the	the	DET
ap-8605	137	28	specific	specific	ADJ
ap-8605	137	29	entropy	entropy	NOUN
ap-8605	137	30	.	.	PUNCT
ap-8605	138	1	using	use	VERB
ap-8605	138	2	clausius	clausius	NOUN
ap-8605	138	3	-	-	PUNCT
ap-8605	138	4	duhem	duhem	NOUN
ap-8605	138	5	inequality	inequality	NOUN
ap-8605	138	6	and	and	CCONJ
ap-8605	138	7	by	by	ADP
ap-8605	138	8	performing	perform	VERB
ap-8605	138	9	the	the	DET
ap-8605	138	10	time	time	NOUN
ap-8605	138	11	derivative	derivative	NOUN
ap-8605	138	12	of	of	ADP
ap-8605	138	13	equation	equation	NOUN
ap-8605	138	14	(	(	PUNCT
ap-8605	138	15	43	43	NUM
ap-8605	138	16	)	)	PUNCT
ap-8605	138	17	,	,	PUNCT
ap-8605	138	18	the	the	DET
ap-8605	138	19	integral	integral	ADJ
ap-8605	138	20	value	value	NOUN
ap-8605	138	21	of	of	ADP
ap-8605	138	22	the	the	DET
ap-8605	138	23	entropy	entropy	NOUN
ap-8605	138	24	production	production	NOUN
ap-8605	138	25	in	in	ADP
ap-8605	138	26	the	the	DET
ap-8605	138	27	control	control	NOUN
ap-8605	138	28	volume	volume	NOUN
ap-8605	138	29	can	can	AUX
ap-8605	138	30	be	be	AUX
ap-8605	138	31	obtained	obtain	VERB
ap-8605	138	32	as	as	ADP
ap-8605	138	33	:	:	PUNCT
ap-8605	138	34	p	p	X
ap-8605	138	35	=	=	PUNCT
ap-8605	138	36	∫	∫	PROPN
ap-8605	138	37	v	v	X
ap-8605	138	38	pdv	pdv	NOUN
ap-8605	138	39	=	=	SYM
ap-8605	138	40	∫	∫	PROPN
ap-8605	138	41	v	v	INTJ
ap-8605	138	42	ϱ	ϱ	X
ap-8605	138	43	ds	ds	PROPN
ap-8605	138	44	dt	dt	PROPN
ap-8605	138	45	dv	dv	PROPN
ap-8605	138	46	+	+	CCONJ
ap-8605	138	47	∮	∮	NUM
ap-8605	138	48	a	a	DET
ap-8605	138	49	gijqj	gijqj	NOUN
ap-8605	138	50	t	t	NOUN
ap-8605	138	51	dai	dai	PROPN
ap-8605	139	1	=	=	PUNCT
ap-8605	140	1	=	=	SYM
ap-8605	140	2	∫	∫	PROPN
ap-8605	140	3	v	v	X
ap-8605	140	4	[	[	PUNCT
ap-8605	140	5	ϱ	ϱ	X
ap-8605	140	6	ds	ds	X
ap-8605	140	7	dt	dt	NOUN
ap-8605	140	8	+	+	CCONJ
ap-8605	140	9	gijqj;i	gijqj;i	PROPN
ap-8605	140	10	t	t	X
ap-8605	140	11	]	]	PUNCT
ap-8605	140	12	dv	dv	PROPN
ap-8605	140	13	,	,	PUNCT
ap-8605	140	14	(	(	PUNCT
ap-8605	140	15	44	44	NUM
ap-8605	140	16	)	)	PUNCT
ap-8605	140	17	where	where	SCONJ
ap-8605	140	18	the	the	DET
ap-8605	140	19	flux	flux	NOUN
ap-8605	140	20	through	through	ADP
ap-8605	140	21	the	the	DET
ap-8605	140	22	boundary	boundary	NOUN
ap-8605	140	23	is	be	AUX
ap-8605	140	24	given	give	VERB
ap-8605	140	25	by	by	ADP
ap-8605	140	26	covector	covector	NOUN
ap-8605	140	27	of	of	ADP
ap-8605	140	28	the	the	DET
ap-8605	140	29	flux	flux	NOUN
ap-8605	140	30	of	of	ADP
ap-8605	140	31	heat	heat	PROPN
ap-8605	140	32	qj	qj	PROPN
ap-8605	140	33	.	.	PUNCT
ap-8605	141	1	equation	equation	NOUN
ap-8605	141	2	(	(	PUNCT
ap-8605	141	3	44	44	NUM
ap-8605	141	4	)	)	PUNCT
ap-8605	141	5	has	have	VERB
ap-8605	141	6	to	to	PART
ap-8605	141	7	be	be	AUX
ap-8605	141	8	true	true	ADJ
ap-8605	141	9	in	in	ADP
ap-8605	141	10	any	any	DET
ap-8605	141	11	control	control	NOUN
ap-8605	141	12	volume	volume	NOUN
ap-8605	141	13	,	,	PUNCT
ap-8605	141	14	therefore	therefore	ADV
ap-8605	141	15	:	:	PUNCT
ap-8605	141	16	p	p	X
ap-8605	141	17	=	=	PUNCT
ap-8605	141	18	ϱ	ϱ	X
ap-8605	141	19	ds	ds	X
ap-8605	141	20	dt	dt	X
ap-8605	141	21	+	+	CCONJ
ap-8605	141	22	gijqj	gijqj	PROPN
ap-8605	141	23	,	,	PUNCT
ap-8605	141	24	i	i	PRON
ap-8605	141	25	t	t	X
ap-8605	141	26	,	,	PUNCT
ap-8605	141	27	(	(	PUNCT
ap-8605	141	28	45	45	NUM
ap-8605	141	29	)	)	PUNCT
ap-8605	141	30	where	where	SCONJ
ap-8605	141	31	the	the	DET
ap-8605	141	32	continuity	continuity	NOUN
ap-8605	141	33	equation	equation	NOUN
ap-8605	141	34	was	be	AUX
ap-8605	141	35	taken	take	VERB
ap-8605	141	36	into	into	ADP
ap-8605	141	37	account	account	NOUN
ap-8605	141	38	.	.	PUNCT
ap-8605	142	1	5	5	X
ap-8605	142	2	.	.	X
ap-8605	142	3	entropy	entropy	PROPN
ap-8605	142	4	production	production	NOUN
ap-8605	142	5	in	in	ADP
ap-8605	142	6	flowing	flow	VERB
ap-8605	142	7	fluid	fluid	ADJ
ap-8605	142	8	relationships	relationship	NOUN
ap-8605	142	9	from	from	ADP
ap-8605	142	10	section	section	NOUN
ap-8605	142	11	3	3	NUM
ap-8605	142	12	are	be	AUX
ap-8605	142	13	used	use	VERB
ap-8605	142	14	for	for	ADP
ap-8605	142	15	the	the	DET
ap-8605	142	16	determination	determination	NOUN
ap-8605	142	17	of	of	ADP
ap-8605	142	18	the	the	DET
ap-8605	142	19	entropy	entropy	NOUN
ap-8605	142	20	production	production	NOUN
ap-8605	142	21	in	in	ADP
ap-8605	142	22	the	the	DET
ap-8605	142	23	flowing	flow	VERB
ap-8605	142	24	fluid	fluid	NOUN
ap-8605	142	25	.	.	PUNCT
ap-8605	143	1	by	by	ADP
ap-8605	143	2	applying	apply	VERB
ap-8605	143	3	the	the	DET
ap-8605	143	4	time	time	NOUN
ap-8605	143	5	derivative	derivative	ADJ
ap-8605	143	6	on	on	ADP
ap-8605	143	7	equations	equation	NOUN
ap-8605	143	8	(	(	PUNCT
ap-8605	143	9	17)–(19	17)–(19	NUM
ap-8605	143	10	)	)	PUNCT
ap-8605	143	11	,	,	PUNCT
ap-8605	143	12	the	the	DET
ap-8605	143	13	following	follow	VERB
ap-8605	143	14	relationships	relationship	NOUN
ap-8605	143	15	are	be	AUX
ap-8605	143	16	obtained	obtain	VERB
ap-8605	143	17	:	:	PUNCT
ap-8605	144	1	dein	dein	ADJ
ap-8605	144	2	dt	dt	NOUN
ap-8605	144	3	=	=	SYM
ap-8605	144	4	dq	dq	PROPN
ap-8605	144	5	dt	dt	NOUN
ap-8605	144	6	−	−	PROPN
ap-8605	144	7	p	p	PROPN
ap-8605	144	8	ϱ2	ϱ2	PROPN
ap-8605	144	9	dϱ	dϱ	NOUN
ap-8605	144	10	dt	dt	X
ap-8605	144	11	,	,	PUNCT
ap-8605	144	12	(	(	PUNCT
ap-8605	144	13	46	46	NUM
ap-8605	144	14	)	)	PUNCT
ap-8605	144	15	dh	dh	NOUN
ap-8605	145	1	dt	dt	NOUN
ap-8605	145	2	=	=	SYM
ap-8605	146	1	dein	dein	ADJ
ap-8605	146	2	dt	dt	X
ap-8605	147	1	+	+	CCONJ
ap-8605	147	2	1	1	NUM
ap-8605	147	3	ϱ	ϱ	ADP
ap-8605	147	4	dp	dp	NOUN
ap-8605	147	5	dt	dt	NOUN
ap-8605	147	6	−	−	PROPN
ap-8605	147	7	p	p	PROPN
ap-8605	147	8	ϱ2	ϱ2	PROPN
ap-8605	147	9	dϱ	dϱ	NOUN
ap-8605	147	10	dt	dt	X
ap-8605	147	11	,	,	PUNCT
ap-8605	147	12	(	(	PUNCT
ap-8605	147	13	47	47	NUM
ap-8605	147	14	)	)	PUNCT
ap-8605	147	15	ds	ds	ADJ
ap-8605	147	16	dt	dt	NOUN
ap-8605	147	17	=	=	SYM
ap-8605	148	1	1	1	NUM
ap-8605	148	2	t	t	NOUN
ap-8605	148	3	dq	dq	NOUN
ap-8605	148	4	dt	dt	X
ap-8605	148	5	(	(	PUNCT
ap-8605	148	6	48	48	NUM
ap-8605	148	7	)	)	PUNCT
ap-8605	148	8	where	where	SCONJ
ap-8605	148	9	,	,	PUNCT
ap-8605	148	10	for	for	ADP
ap-8605	148	11	the	the	DET
ap-8605	148	12	work	work	NOUN
ap-8605	148	13	,	,	PUNCT
ap-8605	148	14	the	the	DET
ap-8605	148	15	following	follow	VERB
ap-8605	148	16	relationship	relationship	NOUN
ap-8605	148	17	holds	hold	VERB
ap-8605	148	18	:	:	PUNCT
ap-8605	148	19	dw	dw	PROPN
ap-8605	148	20	=	=	PROPN
ap-8605	148	21	pd	pd	PROPN
ap-8605	148	22	(	(	PUNCT
ap-8605	148	23	1	1	NUM
ap-8605	148	24	ϱ	ϱ	NOUN
ap-8605	148	25	)	)	PUNCT
ap-8605	148	26	.	.	PUNCT
ap-8605	149	1	(	(	PUNCT
ap-8605	149	2	49	49	NUM
ap-8605	149	3	)	)	PUNCT
ap-8605	149	4	time	time	NOUN
ap-8605	149	5	change	change	NOUN
ap-8605	149	6	of	of	ADP
ap-8605	149	7	entropy	entropy	NOUN
ap-8605	149	8	can	can	AUX
ap-8605	149	9	be	be	AUX
ap-8605	149	10	obtained	obtain	VERB
ap-8605	149	11	after	after	ADP
ap-8605	149	12	some	some	DET
ap-8605	149	13	elementary	elementary	ADJ
ap-8605	149	14	manipulations	manipulation	NOUN
ap-8605	149	15	as	as	ADP
ap-8605	149	16	:	:	PUNCT
ap-8605	149	17	ϱt	ϱt	X
ap-8605	149	18	ds	ds	ADJ
ap-8605	149	19	dt	dt	NOUN
ap-8605	149	20	=	=	PUNCT
ap-8605	149	21	ϱ	ϱ	PROPN
ap-8605	149	22	dh	dh	NOUN
ap-8605	149	23	dt	dt	X
ap-8605	149	24	−	−	PROPN
ap-8605	149	25	dp	dp	NOUN
ap-8605	149	26	dt	dt	X
ap-8605	149	27	.	.	PUNCT
ap-8605	150	1	(	(	PUNCT
ap-8605	150	2	50	50	NUM
ap-8605	150	3	)	)	PUNCT
ap-8605	150	4	the	the	DET
ap-8605	150	5	kinetic	kinetic	ADJ
ap-8605	150	6	energy	energy	NOUN
ap-8605	150	7	of	of	ADP
ap-8605	150	8	the	the	DET
ap-8605	150	9	flowing	flow	VERB
ap-8605	150	10	fluid	fluid	NOUN
ap-8605	150	11	can	can	AUX
ap-8605	150	12	be	be	AUX
ap-8605	150	13	obtained	obtain	VERB
ap-8605	150	14	by	by	ADP
ap-8605	150	15	taking	take	VERB
ap-8605	150	16	the	the	DET
ap-8605	150	17	dot	dot	NOUN
ap-8605	150	18	product	product	NOUN
ap-8605	150	19	between	between	ADP
ap-8605	150	20	the	the	DET
ap-8605	150	21	momentum	momentum	NOUN
ap-8605	150	22	equation	equation	NOUN
ap-8605	150	23	and	and	CCONJ
ap-8605	150	24	velocity	velocity	NOUN
ap-8605	150	25	in	in	ADP
ap-8605	150	26	the	the	DET
ap-8605	150	27	form	form	NOUN
ap-8605	150	28	:	:	PUNCT
ap-8605	150	29	ϱgilu	ϱgilu	NOUN
ap-8605	150	30	l	l	NOUN
ap-8605	150	31	dui	dui	PROPN
ap-8605	150	32	dt	dt	PROPN
ap-8605	151	1	=	=	PUNCT
ap-8605	151	2	ϱ	ϱ	ADP
ap-8605	151	3	dekin	dekin	X
ap-8605	151	4	dt	dt	X
ap-8605	152	1	=	=	SYM
ap-8605	152	2	gilu	gilu	PROPN
ap-8605	152	3	lσij	lσij	NOUN
ap-8605	152	4	;	;	PUNCT
ap-8605	152	5	j	j	PROPN
ap-8605	152	6	+	+	NUM
ap-8605	152	7	ϱgilu	ϱgilu	PROPN
ap-8605	152	8	lai	lai	NOUN
ap-8605	152	9	.	.	PUNCT
ap-8605	153	1	(	(	PUNCT
ap-8605	153	2	51	51	NUM
ap-8605	153	3	)	)	PUNCT
ap-8605	153	4	extracting	extract	VERB
ap-8605	153	5	equation	equation	NOUN
ap-8605	153	6	(	(	PUNCT
ap-8605	153	7	51	51	NUM
ap-8605	153	8	)	)	PUNCT
ap-8605	153	9	from	from	ADP
ap-8605	153	10	equation	equation	NOUN
ap-8605	153	11	(	(	PUNCT
ap-8605	153	12	40	40	NUM
ap-8605	153	13	)	)	PUNCT
ap-8605	153	14	,	,	PUNCT
ap-8605	153	15	the	the	DET
ap-8605	153	16	internal	internal	ADJ
ap-8605	153	17	energy	energy	NOUN
ap-8605	153	18	is	be	AUX
ap-8605	153	19	obtained	obtain	VERB
ap-8605	153	20	:	:	PUNCT
ap-8605	153	21	ϱ	ϱ	VERB
ap-8605	153	22	dein	dein	NOUN
ap-8605	153	23	dt	dt	NOUN
ap-8605	153	24	=	=	SYM
ap-8605	154	1	−	−	PROPN
ap-8605	154	2	(	(	PUNCT
ap-8605	154	3	gijqj	gijqj	PROPN
ap-8605	154	4	)	)	PUNCT
ap-8605	154	5	;	;	PUNCT
ap-8605	155	1	i	i	PRON
ap-8605	155	2	+	+	CCONJ
ap-8605	155	3	(	(	PUNCT
ap-8605	155	4	gjlu	gjlu	ADJ
ap-8605	155	5	lσij	lσij	PROPN
ap-8605	155	6	)	)	PUNCT
ap-8605	155	7	;	;	PUNCT
ap-8605	155	8	i	i	PRON
ap-8605	155	9	−	−	PROPN
ap-8605	155	10	gjlu	gjlu	ADJ
ap-8605	155	11	lσij	lσij	NOUN
ap-8605	155	12	;	;	PUNCT
ap-8605	155	13	i	i	PRON
ap-8605	155	14	=	=	NOUN
ap-8605	155	15	=	=	PUNCT
ap-8605	155	16	gjlu	gjlu	PROPN
ap-8605	155	17	l	l	NOUN
ap-8605	155	18	;	;	PUNCT
ap-8605	155	19	iσ	iσ	VERB
ap-8605	155	20	ij	ij	INTJ
ap-8605	155	21	−	−	PROPN
ap-8605	156	1	(	(	PUNCT
ap-8605	156	2	gijqj	gijqj	PROPN
ap-8605	156	3	)	)	PUNCT
ap-8605	156	4	;	;	PUNCT
ap-8605	157	1	i	i	PRON
ap-8605	157	2	.	.	PUNCT
ap-8605	158	1	(	(	PUNCT
ap-8605	158	2	52	52	NUM
ap-8605	158	3	)	)	PUNCT
ap-8605	158	4	substituting	substitute	VERB
ap-8605	158	5	equation	equation	NOUN
ap-8605	158	6	(	(	PUNCT
ap-8605	158	7	52	52	NUM
ap-8605	158	8	)	)	PUNCT
ap-8605	158	9	into	into	ADP
ap-8605	158	10	equation	equation	NOUN
ap-8605	158	11	(	(	PUNCT
ap-8605	158	12	47	47	NUM
ap-8605	158	13	)	)	PUNCT
ap-8605	158	14	and	and	CCONJ
ap-8605	158	15	subsequently	subsequently	ADV
ap-8605	158	16	substituting	substitute	VERB
ap-8605	158	17	this	this	PRON
ap-8605	158	18	into	into	ADP
ap-8605	158	19	equation	equation	NOUN
ap-8605	158	20	(	(	PUNCT
ap-8605	158	21	50	50	NUM
ap-8605	158	22	)	)	PUNCT
ap-8605	158	23	,	,	PUNCT
ap-8605	158	24	the	the	DET
ap-8605	158	25	following	follow	VERB
ap-8605	158	26	relation	relation	NOUN
ap-8605	158	27	for	for	ADP
ap-8605	158	28	the	the	DET
ap-8605	158	29	time	time	NOUN
ap-8605	158	30	change	change	NOUN
ap-8605	158	31	of	of	ADP
ap-8605	158	32	entropy	entropy	NOUN
ap-8605	158	33	is	be	AUX
ap-8605	158	34	obtained	obtain	VERB
ap-8605	158	35	:	:	PUNCT
ap-8605	159	1	ϱt	ϱt	NOUN
ap-8605	159	2	ds	ds	ADJ
ap-8605	159	3	dt	dt	NOUN
ap-8605	159	4	=	=	PUNCT
ap-8605	159	5	gjlu	gjlu	PROPN
ap-8605	159	6	l	l	NOUN
ap-8605	159	7	;	;	PUNCT
ap-8605	159	8	iσ	iσ	VERB
ap-8605	159	9	ij	ij	INTJ
ap-8605	159	10	−	−	PROPN
ap-8605	159	11	(	(	PUNCT
ap-8605	159	12	gijqj	gijqj	PROPN
ap-8605	159	13	)	)	PUNCT
ap-8605	159	14	;	;	PUNCT
ap-8605	160	1	i	i	PRON
ap-8605	160	2	.	.	PUNCT
ap-8605	161	1	(	(	PUNCT
ap-8605	161	2	53	53	NUM
ap-8605	161	3	)	)	PUNCT
ap-8605	161	4	the	the	DET
ap-8605	161	5	continuity	continuity	NOUN
ap-8605	161	6	equation	equation	NOUN
ap-8605	161	7	was	be	AUX
ap-8605	161	8	used	use	VERB
ap-8605	161	9	as	as	ADV
ap-8605	161	10	well	well	ADV
ap-8605	161	11	during	during	ADP
ap-8605	161	12	the	the	DET
ap-8605	161	13	manipulations	manipulation	NOUN
ap-8605	161	14	.	.	PUNCT
ap-8605	162	1	comparing	compare	VERB
ap-8605	162	2	the	the	DET
ap-8605	162	3	relationships	relationship	NOUN
ap-8605	162	4	equation	equation	NOUN
ap-8605	162	5	(	(	PUNCT
ap-8605	162	6	45	45	NUM
ap-8605	162	7	)	)	PUNCT
ap-8605	162	8	and	and	CCONJ
ap-8605	162	9	equation	equation	NOUN
ap-8605	162	10	(	(	PUNCT
ap-8605	162	11	53	53	NUM
ap-8605	162	12	)	)	PUNCT
ap-8605	162	13	,	,	PUNCT
ap-8605	162	14	the	the	DET
ap-8605	162	15	local	local	ADJ
ap-8605	162	16	entropy	entropy	NOUN
ap-8605	162	17	production	production	NOUN
ap-8605	162	18	can	can	AUX
ap-8605	162	19	be	be	AUX
ap-8605	162	20	obtained	obtain	VERB
ap-8605	162	21	as	as	ADP
ap-8605	162	22	:	:	PUNCT
ap-8605	162	23	p	p	X
ap-8605	162	24	=	=	PUNCT
ap-8605	162	25	gjlu	gjlu	NOUN
ap-8605	162	26	l	l	NOUN
ap-8605	162	27	;	;	PUNCT
ap-8605	162	28	iσ	iσ	VERB
ap-8605	162	29	ij	ij	NOUN
ap-8605	162	30	.	.	PUNCT
ap-8605	163	1	(	(	PUNCT
ap-8605	163	2	54	54	NUM
ap-8605	163	3	)	)	PUNCT
ap-8605	163	4	this	this	PRON
ap-8605	163	5	means	mean	VERB
ap-8605	163	6	,	,	PUNCT
ap-8605	163	7	that	that	PRON
ap-8605	163	8	irreversible	irreversible	ADJ
ap-8605	163	9	processes	process	NOUN
ap-8605	163	10	in	in	ADP
ap-8605	163	11	the	the	DET
ap-8605	163	12	fluid	fluid	ADJ
ap-8605	163	13	flow	flow	NOUN
ap-8605	163	14	are	be	AUX
ap-8605	163	15	connected	connect	VERB
ap-8605	163	16	with	with	ADP
ap-8605	163	17	the	the	DET
ap-8605	163	18	stress	stress	NOUN
ap-8605	163	19	tensor	tensor	NOUN
ap-8605	163	20	.	.	PUNCT
ap-8605	164	1	106	106	NUM
ap-8605	164	2	vol	vol	NOUN
ap-8605	164	3	.	.	PUNCT
ap-8605	165	1	63	63	NUM
ap-8605	165	2	no	no	NOUN
ap-8605	165	3	.	.	PUNCT
ap-8605	166	1	2/2023	2/2023	NUM
ap-8605	166	2	derivation	derivation	NOUN
ap-8605	166	3	of	of	ADP
ap-8605	166	4	entropy	entropy	NOUN
ap-8605	166	5	production	production	NOUN
ap-8605	166	6	in	in	ADP
ap-8605	166	7	a	a	DET
ap-8605	166	8	fluid	fluid	ADJ
ap-8605	166	9	flow	flow	NOUN
ap-8605	166	10	6	6	NUM
ap-8605	166	11	.	.	PUNCT
ap-8605	167	1	newtonian	newtonian	ADJ
ap-8605	167	2	fluid	fluid	NOUN
ap-8605	167	3	no	no	DET
ap-8605	167	4	special	special	ADJ
ap-8605	167	5	assumption	assumption	NOUN
ap-8605	167	6	was	be	AUX
ap-8605	167	7	made	make	VERB
ap-8605	167	8	to	to	ADP
ap-8605	167	9	this	this	DET
ap-8605	167	10	point	point	NOUN
ap-8605	167	11	about	about	ADP
ap-8605	167	12	the	the	DET
ap-8605	167	13	stress	stress	NOUN
ap-8605	167	14	tensor	tensor	NOUN
ap-8605	167	15	σij	σij	NOUN
ap-8605	167	16	except	except	SCONJ
ap-8605	167	17	that	that	SCONJ
ap-8605	167	18	if	if	SCONJ
ap-8605	167	19	the	the	DET
ap-8605	167	20	fluid	fluid	NOUN
ap-8605	167	21	is	be	AUX
ap-8605	167	22	at	at	ADP
ap-8605	167	23	rest	rest	NOUN
ap-8605	167	24	,	,	PUNCT
ap-8605	167	25	the	the	DET
ap-8605	167	26	stress	stress	NOUN
ap-8605	167	27	tensor	tensor	NOUN
ap-8605	167	28	is	be	AUX
ap-8605	167	29	equal	equal	ADJ
ap-8605	167	30	to	to	ADP
ap-8605	167	31	the	the	DET
ap-8605	167	32	thermodynamic	thermodynamic	ADJ
ap-8605	167	33	pressure	pressure	NOUN
ap-8605	167	34	and	and	CCONJ
ap-8605	167	35	if	if	SCONJ
ap-8605	167	36	this	this	DET
ap-8605	167	37	fluid	fluid	NOUN
ap-8605	167	38	is	be	AUX
ap-8605	167	39	in	in	ADP
ap-8605	167	40	the	the	DET
ap-8605	167	41	external	external	ADJ
ap-8605	167	42	force	force	NOUN
ap-8605	167	43	field	field	NOUN
ap-8605	167	44	that	that	PRON
ap-8605	167	45	is	be	AUX
ap-8605	167	46	acting	act	VERB
ap-8605	167	47	on	on	ADP
ap-8605	167	48	that	that	DET
ap-8605	167	49	fluid	fluid	NOUN
ap-8605	167	50	,	,	PUNCT
ap-8605	167	51	the	the	DET
ap-8605	167	52	thermodynamic	thermodynamic	ADJ
ap-8605	167	53	pressure	pressure	NOUN
ap-8605	167	54	has	have	VERB
ap-8605	167	55	to	to	PART
ap-8605	167	56	be	be	AUX
ap-8605	167	57	equal	equal	ADJ
ap-8605	167	58	to	to	ADP
ap-8605	167	59	the	the	DET
ap-8605	167	60	hydrostatic	hydrostatic	ADJ
ap-8605	167	61	pressure	pressure	NOUN
ap-8605	167	62	.	.	PUNCT
ap-8605	168	1	this	this	PRON
ap-8605	168	2	transforms	transform	VERB
ap-8605	168	3	the	the	DET
ap-8605	168	4	problem	problem	NOUN
ap-8605	168	5	of	of	ADP
ap-8605	168	6	establishing	establish	VERB
ap-8605	168	7	the	the	DET
ap-8605	168	8	stress	stress	NOUN
ap-8605	168	9	tensor	tensor	NOUN
ap-8605	168	10	to	to	ADP
ap-8605	168	11	the	the	DET
ap-8605	168	12	problem	problem	NOUN
ap-8605	168	13	of	of	ADP
ap-8605	168	14	determination	determination	NOUN
ap-8605	168	15	of	of	ADP
ap-8605	168	16	the	the	DET
ap-8605	168	17	viscous	viscous	ADJ
ap-8605	168	18	tensor	tensor	NOUN
ap-8605	168	19	τ	τ	PROPN
ap-8605	168	20	ij	ij	INTJ
ap-8605	168	21	.	.	PUNCT
ap-8605	169	1	let	let	VERB
ap-8605	169	2	’s	’s	NOUN
ap-8605	169	3	suppose	suppose	VERB
ap-8605	169	4	,	,	PUNCT
ap-8605	169	5	that	that	SCONJ
ap-8605	169	6	this	this	DET
ap-8605	169	7	viscous	viscous	ADJ
ap-8605	169	8	tensor	tensor	NOUN
ap-8605	169	9	is	be	AUX
ap-8605	169	10	a	a	DET
ap-8605	169	11	linear	linear	ADJ
ap-8605	169	12	combination	combination	NOUN
ap-8605	169	13	of	of	ADP
ap-8605	169	14	the	the	DET
ap-8605	169	15	strain	strain	NOUN
ap-8605	169	16	rate	rate	NOUN
ap-8605	169	17	tensor	tensor	NOUN
ap-8605	169	18	elm	elm	NOUN
ap-8605	170	1	=	=	SYM
ap-8605	170	2	gklem	gklem	NOUN
ap-8605	170	3	k	k	NOUN
ap-8605	170	4	,	,	PUNCT
ap-8605	170	5	where	where	SCONJ
ap-8605	170	6	the	the	DET
ap-8605	170	7	mixed	mixed	ADJ
ap-8605	170	8	type	type	NOUN
ap-8605	170	9	of	of	ADP
ap-8605	170	10	tensor	tensor	NOUN
ap-8605	170	11	is	be	AUX
ap-8605	170	12	given	give	VERB
ap-8605	170	13	by	by	ADP
ap-8605	170	14	his	his	PRON
ap-8605	170	15	definition	definition	NOUN
ap-8605	170	16	through	through	ADP
ap-8605	170	17	the	the	DET
ap-8605	170	18	covariant	covariant	ADJ
ap-8605	170	19	derivatives	derivative	NOUN
ap-8605	170	20	of	of	ADP
ap-8605	170	21	the	the	DET
ap-8605	170	22	velocity	velocity	NOUN
ap-8605	170	23	field	field	NOUN
ap-8605	170	24	,	,	PUNCT
ap-8605	170	25	then	then	ADV
ap-8605	170	26	in	in	ADP
ap-8605	170	27	general	general	ADJ
ap-8605	170	28	,	,	PUNCT
ap-8605	170	29	the	the	DET
ap-8605	170	30	relationship	relationship	NOUN
ap-8605	170	31	between	between	ADP
ap-8605	170	32	these	these	DET
ap-8605	170	33	two	two	NUM
ap-8605	170	34	tensors	tensor	NOUN
ap-8605	170	35	can	can	AUX
ap-8605	170	36	be	be	AUX
ap-8605	170	37	written	write	VERB
ap-8605	170	38	as	as	ADP
ap-8605	170	39	:	:	PUNCT
ap-8605	170	40	τ	τ	PROPN
ap-8605	170	41	ij	ij	INTJ
ap-8605	171	1	=	=	X
ap-8605	171	2	agijgkle	agijgkle	X
ap-8605	171	3	kl	kl	NOUN
ap-8605	172	1	+	+	CCONJ
ap-8605	172	2	b	b	PROPN
ap-8605	172	3	(	(	PUNCT
ap-8605	172	4	gi	gi	INTJ
ap-8605	172	5	kg	kg	INTJ
ap-8605	172	6	j	j	PROPN
ap-8605	172	7	l	l	PROPN
ap-8605	173	1	+	+	CCONJ
ap-8605	173	2	gi	gi	VERB
ap-8605	173	3	lg	lg	PROPN
ap-8605	173	4	j	j	PROPN
ap-8605	173	5	k	k	PROPN
ap-8605	173	6	)	)	PUNCT
ap-8605	174	1	ekl+	ekl+	PROPN
ap-8605	175	1	+	+	NUM
ap-8605	175	2	c	c	X
ap-8605	175	3	(	(	PUNCT
ap-8605	175	4	gi	gi	INTJ
ap-8605	175	5	kg	kg	INTJ
ap-8605	175	6	j	j	PROPN
ap-8605	175	7	l	l	PROPN
ap-8605	176	1	+	+	CCONJ
ap-8605	176	2	gi	gi	AUX
ap-8605	176	3	lg	lg	PROPN
ap-8605	176	4	j	j	PROPN
ap-8605	176	5	k	k	PROPN
ap-8605	176	6	)	)	PUNCT
ap-8605	176	7	ek	ek	VERB
ap-8605	176	8	me	i	PRON
ap-8605	176	9	ml	ml	INTJ
ap-8605	176	10	,	,	PUNCT
ap-8605	176	11	(	(	PUNCT
ap-8605	176	12	55	55	NUM
ap-8605	176	13	)	)	PUNCT
ap-8605	176	14	where	where	SCONJ
ap-8605	176	15	the	the	DET
ap-8605	176	16	non	non	ADJ
ap-8605	176	17	-	-	ADJ
ap-8605	176	18	linear	linear	ADJ
ap-8605	176	19	third	third	ADJ
ap-8605	176	20	term	term	NOUN
ap-8605	176	21	on	on	ADP
ap-8605	176	22	the	the	DET
ap-8605	176	23	r.h.s	r.h.s	NOUN
ap-8605	176	24	.	.	PUNCT
ap-8605	177	1	of	of	ADP
ap-8605	177	2	this	this	DET
ap-8605	177	3	equation	equation	NOUN
ap-8605	177	4	will	will	AUX
ap-8605	177	5	be	be	AUX
ap-8605	177	6	neglected	neglect	VERB
ap-8605	177	7	in	in	ADP
ap-8605	177	8	the	the	DET
ap-8605	177	9	following	follow	VERB
ap-8605	177	10	text	text	NOUN
ap-8605	177	11	,	,	PUNCT
ap-8605	177	12	therefore	therefore	ADV
ap-8605	177	13	:	:	PUNCT
ap-8605	177	14	τ	τ	PROPN
ap-8605	177	15	ij	ij	INTJ
ap-8605	178	1	=	=	X
ap-8605	178	2	agijgkle	agijgkle	X
ap-8605	178	3	kl	kl	NOUN
ap-8605	179	1	+	+	CCONJ
ap-8605	179	2	b	b	PROPN
ap-8605	179	3	(	(	PUNCT
ap-8605	179	4	gi	gi	INTJ
ap-8605	179	5	kg	kg	INTJ
ap-8605	179	6	j	j	PROPN
ap-8605	179	7	l	l	PROPN
ap-8605	180	1	+	+	CCONJ
ap-8605	180	2	gi	gi	VERB
ap-8605	180	3	lg	lg	PROPN
ap-8605	180	4	j	j	PROPN
ap-8605	180	5	k	k	PROPN
ap-8605	180	6	)	)	PUNCT
ap-8605	180	7	ekl	ekl	PROPN
ap-8605	180	8	.	.	PUNCT
ap-8605	181	1	(	(	PUNCT
ap-8605	181	2	56	56	NUM
ap-8605	181	3	)	)	PUNCT
ap-8605	181	4	this	this	DET
ap-8605	181	5	relationship	relationship	NOUN
ap-8605	181	6	,	,	PUNCT
ap-8605	181	7	however	however	ADV
ap-8605	181	8	,	,	PUNCT
ap-8605	181	9	tells	tell	VERB
ap-8605	181	10	nothing	nothing	PRON
ap-8605	181	11	about	about	ADP
ap-8605	181	12	the	the	DET
ap-8605	181	13	properties	property	NOUN
ap-8605	181	14	of	of	ADP
ap-8605	181	15	the	the	DET
ap-8605	181	16	tensor	tensor	NOUN
ap-8605	181	17	τ	τ	PROPN
ap-8605	181	18	ij	ij	INTJ
ap-8605	181	19	,	,	PUNCT
ap-8605	181	20	meaning	mean	VERB
ap-8605	181	21	mainly	mainly	ADV
ap-8605	181	22	about	about	ADP
ap-8605	181	23	its	its	PRON
ap-8605	181	24	symmetry	symmetry	NOUN
ap-8605	181	25	.	.	PUNCT
ap-8605	182	1	the	the	DET
ap-8605	182	2	coefficients	coefficient	NOUN
ap-8605	182	3	are	be	AUX
ap-8605	182	4	then	then	ADV
ap-8605	182	5	functions	function	NOUN
ap-8605	182	6	of	of	ADP
ap-8605	182	7	the	the	DET
ap-8605	182	8	invariants	invariant	NOUN
ap-8605	182	9	of	of	ADP
ap-8605	182	10	the	the	DET
ap-8605	182	11	tensor	tensor	NOUN
ap-8605	182	12	of	of	ADP
ap-8605	182	13	deformation	deformation	NOUN
ap-8605	182	14	,	,	PUNCT
ap-8605	182	15	see	see	VERB
ap-8605	182	16	e.g.	e.g.	ADV
ap-8605	182	17	[	[	X
ap-8605	182	18	2	2	NUM
ap-8605	182	19	]	]	PUNCT
ap-8605	182	20	.	.	PUNCT
ap-8605	183	1	if	if	SCONJ
ap-8605	183	2	the	the	DET
ap-8605	183	3	fluid	fluid	NOUN
ap-8605	183	4	is	be	AUX
ap-8605	183	5	homogeneous	homogeneous	ADJ
ap-8605	183	6	and	and	CCONJ
ap-8605	183	7	isotropic	isotropic	NOUN
ap-8605	183	8	,	,	PUNCT
ap-8605	183	9	and	and	CCONJ
ap-8605	183	10	if	if	SCONJ
ap-8605	183	11	the	the	DET
ap-8605	183	12	viscous	viscous	ADJ
ap-8605	183	13	tensor	tensor	NOUN
ap-8605	183	14	is	be	AUX
ap-8605	183	15	a	a	DET
ap-8605	183	16	continuous	continuous	ADJ
ap-8605	183	17	function	function	NOUN
ap-8605	183	18	of	of	ADP
ap-8605	183	19	the	the	DET
ap-8605	183	20	stress	stress	NOUN
ap-8605	183	21	tensor	tensor	NOUN
ap-8605	183	22	,	,	PUNCT
ap-8605	183	23	then	then	ADV
ap-8605	183	24	:	:	PUNCT
ap-8605	183	25	τ	τ	PROPN
ap-8605	183	26	ij	ij	INTJ
ap-8605	183	27	=	=	PROPN
ap-8605	183	28	agij	agij	PROPN
ap-8605	183	29	+	+	CCONJ
ap-8605	183	30	λgijek	λgijek	NOUN
ap-8605	183	31	k	k	NOUN
ap-8605	183	32	+	+	NOUN
ap-8605	183	33	2µeij	2µeij	NUM
ap-8605	183	34	.	.	PUNCT
ap-8605	184	1	(	(	PUNCT
ap-8605	184	2	57	57	NUM
ap-8605	184	3	)	)	PUNCT
ap-8605	184	4	this	this	DET
ap-8605	184	5	tensor	tensor	NOUN
ap-8605	184	6	has	have	VERB
ap-8605	184	7	to	to	PART
ap-8605	184	8	be	be	AUX
ap-8605	184	9	symmetric	symmetric	ADJ
ap-8605	184	10	due	due	ADP
ap-8605	184	11	to	to	ADP
ap-8605	184	12	the	the	DET
ap-8605	184	13	law	law	NOUN
ap-8605	184	14	of	of	ADP
ap-8605	184	15	conservation	conservation	NOUN
ap-8605	184	16	of	of	ADP
ap-8605	184	17	moment	moment	NOUN
ap-8605	184	18	of	of	ADP
ap-8605	184	19	momentum	momentum	NOUN
ap-8605	184	20	.	.	PUNCT
ap-8605	185	1	now	now	ADV
ap-8605	185	2	strain	strain	NOUN
ap-8605	185	3	rate	rate	NOUN
ap-8605	185	4	can	can	AUX
ap-8605	185	5	be	be	AUX
ap-8605	185	6	substituted	substitute	VERB
ap-8605	185	7	into	into	ADP
ap-8605	185	8	the	the	DET
ap-8605	185	9	equation	equation	NOUN
ap-8605	185	10	(	(	PUNCT
ap-8605	185	11	57	57	NUM
ap-8605	185	12	):	):	PUNCT
ap-8605	185	13	ek	ek	PROPN
ap-8605	185	14	k	k	PROPN
ap-8605	185	15	=	=	PUNCT
ap-8605	185	16	uk	uk	PROPN
ap-8605	185	17	;	;	PUNCT
ap-8605	185	18	k	k	PROPN
ap-8605	185	19	,	,	PUNCT
ap-8605	185	20	(	(	PUNCT
ap-8605	185	21	58	58	NUM
ap-8605	185	22	)	)	PUNCT
ap-8605	185	23	eij	eij	PROPN
ap-8605	185	24	=	=	NOUN
ap-8605	185	25	1	1	NUM
ap-8605	185	26	2	2	NUM
ap-8605	185	27	(	(	PUNCT
ap-8605	185	28	gjkui	gjkui	NOUN
ap-8605	185	29	;	;	PUNCT
ap-8605	185	30	k	k	PROPN
ap-8605	185	31	+	+	CCONJ
ap-8605	185	32	giluj	giluj	NOUN
ap-8605	185	33	;	;	PUNCT
ap-8605	185	34	l	l	NOUN
ap-8605	185	35	)	)	PUNCT
ap-8605	185	36	.	.	PUNCT
ap-8605	186	1	(	(	PUNCT
ap-8605	186	2	59	59	NUM
ap-8605	186	3	)	)	PUNCT
ap-8605	186	4	the	the	DET
ap-8605	186	5	stress	stress	NOUN
ap-8605	186	6	tensor	tensor	NOUN
ap-8605	186	7	can	can	AUX
ap-8605	186	8	be	be	AUX
ap-8605	186	9	written	write	VERB
ap-8605	186	10	in	in	ADP
ap-8605	186	11	the	the	DET
ap-8605	186	12	form	form	NOUN
ap-8605	186	13	:	:	PUNCT
ap-8605	186	14	σij	σij	NOUN
ap-8605	186	15	=	=	SYM
ap-8605	187	1	−gijp+	−gijp+	NOUN
ap-8605	187	2	λgijuk	λgijuk	ADJ
ap-8605	187	3	;	;	PUNCT
ap-8605	188	1	k	k	X
ap-8605	188	2	+	+	X
ap-8605	188	3	µgjkui	µgjkui	ADJ
ap-8605	188	4	;	;	PUNCT
ap-8605	188	5	k	k	PROPN
ap-8605	188	6	+	+	NUM
ap-8605	188	7	µgiluj	µgiluj	NOUN
ap-8605	188	8	;	;	PUNCT
ap-8605	188	9	l	l	NOUN
ap-8605	188	10	,	,	PUNCT
ap-8605	188	11	(	(	PUNCT
ap-8605	188	12	60	60	NUM
ap-8605	188	13	)	)	PUNCT
ap-8605	188	14	where	where	SCONJ
ap-8605	188	15	λ	λ	PROPN
ap-8605	188	16	is	be	AUX
ap-8605	188	17	the	the	DET
ap-8605	188	18	second	second	ADJ
ap-8605	188	19	viscosity	viscosity	NOUN
ap-8605	188	20	and	and	CCONJ
ap-8605	188	21	µ	µ	NOUN
ap-8605	188	22	is	be	AUX
ap-8605	188	23	the	the	DET
ap-8605	188	24	dynamic	dynamic	ADJ
ap-8605	188	25	viscosity	viscosity	NOUN
ap-8605	188	26	.	.	PUNCT
ap-8605	189	1	substituting	substitute	VERB
ap-8605	189	2	equation	equation	NOUN
ap-8605	189	3	(	(	PUNCT
ap-8605	189	4	60	60	NUM
ap-8605	189	5	)	)	PUNCT
ap-8605	189	6	into	into	ADP
ap-8605	189	7	(	(	PUNCT
ap-8605	189	8	37	37	NUM
ap-8605	189	9	)	)	PUNCT
ap-8605	189	10	,	,	PUNCT
ap-8605	189	11	navierstokes	navierstoke	NOUN
ap-8605	189	12	equation	equation	NOUN
ap-8605	189	13	is	be	AUX
ap-8605	189	14	obtained	obtain	VERB
ap-8605	189	15	:	:	PUNCT
ap-8605	189	16	ϱ	ϱ	PROPN
ap-8605	189	17	(	(	PUNCT
ap-8605	189	18	∂tu	∂tu	ADV
ap-8605	189	19	i	i	PRON
ap-8605	189	20	+	+	CCONJ
ap-8605	189	21	ujui	ujui	ADJ
ap-8605	189	22	;	;	PUNCT
ap-8605	189	23	j	j	X
ap-8605	189	24	)	)	PUNCT
ap-8605	190	1	=	=	PUNCT
ap-8605	191	1	−gijp;j+	−gijp;j+	PROPN
ap-8605	191	2	+	+	CCONJ
ap-8605	191	3	(	(	PUNCT
ap-8605	191	4	λgijuk	λgijuk	ADJ
ap-8605	191	5	;	;	PUNCT
ap-8605	191	6	k	k	X
ap-8605	191	7	+	+	X
ap-8605	191	8	µgjkui	µgjkui	ADJ
ap-8605	191	9	;	;	PUNCT
ap-8605	191	10	k	k	PROPN
ap-8605	191	11	+	+	NUM
ap-8605	191	12	µgiluj	µgiluj	NOUN
ap-8605	191	13	;	;	PUNCT
ap-8605	191	14	l	l	NOUN
ap-8605	191	15	)	)	PUNCT
ap-8605	191	16	;	;	PUNCT
ap-8605	191	17	j	j	PROPN
ap-8605	191	18	+	+	CCONJ
ap-8605	191	19	ϱai	ϱai	ADJ
ap-8605	191	20	.	.	PUNCT
ap-8605	192	1	(	(	PUNCT
ap-8605	192	2	61	61	NUM
ap-8605	192	3	)	)	PUNCT
ap-8605	192	4	coefficients	coefficient	NOUN
ap-8605	192	5	of	of	ADP
ap-8605	192	6	viscosity	viscosity	NOUN
ap-8605	192	7	are	be	AUX
ap-8605	192	8	,	,	PUNCT
ap-8605	192	9	in	in	ADP
ap-8605	192	10	general	general	ADJ
ap-8605	192	11	,	,	PUNCT
ap-8605	192	12	functions	function	NOUN
ap-8605	192	13	of	of	ADP
ap-8605	192	14	temperature	temperature	NOUN
ap-8605	192	15	and	and	CCONJ
ap-8605	192	16	pressure	pressure	NOUN
ap-8605	192	17	,	,	PUNCT
ap-8605	192	18	however	however	ADV
ap-8605	192	19	,	,	PUNCT
ap-8605	192	20	in	in	ADP
ap-8605	192	21	most	most	ADJ
ap-8605	192	22	of	of	ADP
ap-8605	192	23	the	the	DET
ap-8605	192	24	cases	case	NOUN
ap-8605	192	25	,	,	PUNCT
ap-8605	192	26	their	their	PRON
ap-8605	192	27	variations	variation	NOUN
ap-8605	192	28	in	in	ADP
ap-8605	192	29	the	the	DET
ap-8605	192	30	flowing	flow	VERB
ap-8605	192	31	fluid	fluid	NOUN
ap-8605	192	32	are	be	AUX
ap-8605	192	33	minimal	minimal	ADJ
ap-8605	192	34	(	(	PUNCT
ap-8605	192	35	see	see	VERB
ap-8605	192	36	e.g.	e.g.	ADV
ap-8605	192	37	[	[	X
ap-8605	192	38	10	10	NUM
ap-8605	192	39	]	]	NUM
ap-8605	192	40	)	)	PUNCT
ap-8605	192	41	,	,	PUNCT
ap-8605	192	42	therefore	therefore	ADV
ap-8605	192	43	,	,	PUNCT
ap-8605	192	44	they	they	PRON
ap-8605	192	45	can	can	AUX
ap-8605	192	46	be	be	AUX
ap-8605	192	47	considered	consider	VERB
ap-8605	192	48	constant	constant	ADJ
ap-8605	192	49	.	.	PUNCT
ap-8605	193	1	finally	finally	ADV
ap-8605	193	2	,	,	PUNCT
ap-8605	193	3	the	the	DET
ap-8605	193	4	navier	navier	NOUN
ap-8605	193	5	-	-	PUNCT
ap-8605	193	6	stokes	stoke	NOUN
ap-8605	193	7	equation	equation	NOUN
ap-8605	193	8	is	be	AUX
ap-8605	193	9	obtained	obtain	VERB
ap-8605	193	10	in	in	ADP
ap-8605	193	11	a	a	DET
ap-8605	193	12	general	general	ADJ
ap-8605	193	13	curvilinear	curvilinear	NOUN
ap-8605	193	14	coordinate	coordinate	NOUN
ap-8605	193	15	system	system	NOUN
ap-8605	193	16	in	in	ADP
ap-8605	193	17	the	the	DET
ap-8605	193	18	form	form	NOUN
ap-8605	193	19	:	:	PUNCT
ap-8605	193	20	ϱ	ϱ	PROPN
ap-8605	193	21	(	(	PUNCT
ap-8605	193	22	∂tu	∂tu	ADV
ap-8605	193	23	i	i	PROPN
ap-8605	193	24	+	+	NOUN
ap-8605	193	25	ujui	ujui	ADJ
ap-8605	193	26	;	;	PUNCT
ap-8605	193	27	j	j	X
ap-8605	193	28	)	)	PUNCT
ap-8605	194	1	=	=	PUNCT
ap-8605	194	2	−gijp;j+	−gijp;j+	PROPN
ap-8605	194	3	+	+	X
ap-8605	194	4	(	(	PUNCT
ap-8605	194	5	λ+	λ+	NOUN
ap-8605	194	6	µ	µ	X
ap-8605	194	7	)	)	PUNCT
ap-8605	194	8	gijuk	gijuk	NOUN
ap-8605	194	9	;	;	PUNCT
ap-8605	194	10	kj	kj	PROPN
ap-8605	194	11	+	+	CCONJ
ap-8605	194	12	µgjkui	µgjkui	ADJ
ap-8605	194	13	;	;	PUNCT
ap-8605	194	14	kj	kj	PROPN
ap-8605	194	15	+	+	CCONJ
ap-8605	194	16	ϱai	ϱai	ADJ
ap-8605	194	17	.	.	PUNCT
ap-8605	195	1	(	(	PUNCT
ap-8605	195	2	62	62	NUM
ap-8605	195	3	)	)	PUNCT
ap-8605	195	4	6.1	6.1	NUM
ap-8605	195	5	.	.	PUNCT
ap-8605	195	6	entropy	entropy	PROPN
ap-8605	195	7	production	production	NOUN
ap-8605	195	8	in	in	ADP
ap-8605	195	9	newtonian	newtonian	ADJ
ap-8605	195	10	fluid	fluid	ADJ
ap-8605	195	11	entropy	entropy	NOUN
ap-8605	195	12	production	production	NOUN
ap-8605	195	13	in	in	ADP
ap-8605	195	14	newtonian	newtonian	ADJ
ap-8605	195	15	fluid	fluid	NOUN
ap-8605	195	16	can	can	AUX
ap-8605	195	17	be	be	AUX
ap-8605	195	18	easily	easily	ADV
ap-8605	195	19	obtained	obtain	VERB
ap-8605	195	20	by	by	ADP
ap-8605	195	21	substituting	substitute	VERB
ap-8605	195	22	the	the	DET
ap-8605	195	23	stress	stress	NOUN
ap-8605	195	24	tensor	tensor	NOUN
ap-8605	195	25	into	into	ADP
ap-8605	195	26	the	the	DET
ap-8605	195	27	equation	equation	NOUN
ap-8605	195	28	(	(	PUNCT
ap-8605	195	29	54	54	NUM
ap-8605	195	30	)	)	PUNCT
ap-8605	195	31	.	.	PUNCT
ap-8605	196	1	prior	prior	ADV
ap-8605	196	2	this	this	DET
ap-8605	196	3	step	step	NOUN
ap-8605	196	4	,	,	PUNCT
ap-8605	196	5	however	however	ADV
ap-8605	196	6	,	,	PUNCT
ap-8605	196	7	the	the	DET
ap-8605	196	8	vector	vector	NOUN
ap-8605	196	9	of	of	ADP
ap-8605	196	10	the	the	DET
ap-8605	196	11	heat	heat	NOUN
ap-8605	196	12	flux	flux	NOUN
ap-8605	196	13	will	will	AUX
ap-8605	196	14	be	be	AUX
ap-8605	196	15	obtained	obtain	VERB
ap-8605	196	16	from	from	ADP
ap-8605	196	17	the	the	DET
ap-8605	196	18	constitutive	constitutive	ADJ
ap-8605	196	19	relation	relation	NOUN
ap-8605	196	20	:	:	PUNCT
ap-8605	196	21	qi	qi	PROPN
ap-8605	196	22	=	=	PROPN
ap-8605	196	23	kgijt;j	kgijt;j	NOUN
ap-8605	196	24	.	.	PUNCT
ap-8605	197	1	(	(	PUNCT
ap-8605	197	2	63	63	NUM
ap-8605	197	3	)	)	PUNCT
ap-8605	197	4	substituting	substitute	VERB
ap-8605	197	5	equations	equation	NOUN
ap-8605	197	6	(	(	PUNCT
ap-8605	197	7	63	63	NUM
ap-8605	197	8	)	)	PUNCT
ap-8605	197	9	and	and	CCONJ
ap-8605	197	10	(	(	PUNCT
ap-8605	197	11	60	60	NUM
ap-8605	197	12	)	)	PUNCT
ap-8605	197	13	into	into	ADP
ap-8605	197	14	(	(	PUNCT
ap-8605	197	15	54	54	NUM
ap-8605	197	16	)	)	PUNCT
ap-8605	197	17	gives	give	VERB
ap-8605	197	18	:	:	PUNCT
ap-8605	197	19	ϱt	ϱt	NOUN
ap-8605	197	20	ds	ds	ADJ
ap-8605	197	21	dt	dt	NOUN
ap-8605	197	22	=	=	PUNCT
ap-8605	197	23	−kgijt;ji	−kgijt;ji	PUNCT
ap-8605	197	24	+	+	NUM
ap-8605	197	25	gilu	gilu	NOUN
ap-8605	197	26	l	l	NOUN
ap-8605	197	27	;	;	PUNCT
ap-8605	198	1	j	j	PROPN
ap-8605	198	2	(	(	PUNCT
ap-8605	198	3	−gijp;j	−gijp;j	ADV
ap-8605	198	4	+	+	CCONJ
ap-8605	198	5	λgijuk	λgijuk	ADJ
ap-8605	198	6	;	;	PUNCT
ap-8605	198	7	k	k	PROPN
ap-8605	199	1	+	+	PROPN
ap-8605	199	2	+	+	NUM
ap-8605	199	3	µ	µ	X
ap-8605	199	4	[	[	PUNCT
ap-8605	199	5	gjlui	gjlui	NOUN
ap-8605	199	6	;	;	PUNCT
ap-8605	199	7	l	l	NOUN
ap-8605	200	1	+	+	CCONJ
ap-8605	200	2	gimuj	gimuj	NOUN
ap-8605	200	3	;	;	PUNCT
ap-8605	200	4	m	m	VERB
ap-8605	200	5	]	]	PUNCT
ap-8605	200	6	)	)	PUNCT
ap-8605	200	7	.	.	PUNCT
ap-8605	201	1	(	(	PUNCT
ap-8605	201	2	64	64	NUM
ap-8605	201	3	)	)	PUNCT
ap-8605	201	4	using	use	VERB
ap-8605	201	5	relationship	relationship	NOUN
ap-8605	201	6	(	(	PUNCT
ap-8605	201	7	7	7	NUM
ap-8605	201	8	)	)	PUNCT
ap-8605	201	9	and	and	CCONJ
ap-8605	201	10	after	after	ADP
ap-8605	201	11	some	some	DET
ap-8605	201	12	manipulations	manipulation	NOUN
ap-8605	201	13	,	,	PUNCT
ap-8605	201	14	time	time	NOUN
ap-8605	201	15	change	change	NOUN
ap-8605	201	16	of	of	ADP
ap-8605	201	17	entropy	entropy	NOUN
ap-8605	201	18	can	can	AUX
ap-8605	201	19	be	be	AUX
ap-8605	201	20	determined	determine	VERB
ap-8605	201	21	as	as	ADP
ap-8605	201	22	:	:	PUNCT
ap-8605	201	23	ϱt	ϱt	X
ap-8605	201	24	ds	ds	ADJ
ap-8605	201	25	dt	dt	X
ap-8605	201	26	=	=	PUNCT
ap-8605	201	27	−kgijt;ji	−kgijt;ji	NOUN
ap-8605	201	28	−	−	NOUN
ap-8605	201	29	pui	pui	NOUN
ap-8605	201	30	;	;	PUNCT
ap-8605	201	31	i	i	PROPN
ap-8605	201	32	+	+	NUM
ap-8605	201	33	λui	λui	NOUN
ap-8605	201	34	;	;	PUNCT
ap-8605	201	35	iu	iu	ADP
ap-8605	201	36	j	j	PROPN
ap-8605	201	37	;	;	PUNCT
ap-8605	201	38	j	j	PROPN
ap-8605	202	1	+	+	CCONJ
ap-8605	202	2	2µui	2µui	NUM
ap-8605	202	3	;	;	PUNCT
ap-8605	202	4	ju	ju	PROPN
ap-8605	202	5	j	j	PROPN
ap-8605	202	6	;	;	PUNCT
ap-8605	202	7	i	i	PRON
ap-8605	202	8	.	.	PUNCT
ap-8605	203	1	(	(	PUNCT
ap-8605	203	2	65	65	NUM
ap-8605	203	3	)	)	PUNCT
ap-8605	203	4	by	by	ADP
ap-8605	203	5	a	a	DET
ap-8605	203	6	comparison	comparison	NOUN
ap-8605	203	7	of	of	ADP
ap-8605	203	8	equations	equation	NOUN
ap-8605	203	9	(	(	PUNCT
ap-8605	203	10	65	65	NUM
ap-8605	203	11	)	)	PUNCT
ap-8605	203	12	and	and	CCONJ
ap-8605	203	13	(	(	PUNCT
ap-8605	203	14	45	45	NUM
ap-8605	203	15	)	)	PUNCT
ap-8605	203	16	,	,	PUNCT
ap-8605	203	17	local	local	ADJ
ap-8605	203	18	entropy	entropy	NOUN
ap-8605	203	19	production	production	NOUN
ap-8605	203	20	can	can	AUX
ap-8605	203	21	be	be	AUX
ap-8605	203	22	obtained	obtain	VERB
ap-8605	203	23	as	as	ADP
ap-8605	203	24	:	:	PUNCT
ap-8605	203	25	p	p	X
ap-8605	203	26	=	=	NOUN
ap-8605	203	27	−pui	−pui	NOUN
ap-8605	203	28	;	;	PUNCT
ap-8605	204	1	i	i	PRON
ap-8605	204	2	+	+	PUNCT
ap-8605	204	3	λ	λ	X
ap-8605	204	4	(	(	PUNCT
ap-8605	204	5	ui	ui	NOUN
ap-8605	204	6	;	;	PUNCT
ap-8605	204	7	i	i	PRON
ap-8605	204	8	)	)	PUNCT
ap-8605	204	9	2	2	NUM
ap-8605	205	1	+	+	CCONJ
ap-8605	205	2	2µui	2µui	NUM
ap-8605	205	3	;	;	PUNCT
ap-8605	205	4	ju	ju	PROPN
ap-8605	205	5	j	j	PROPN
ap-8605	205	6	;	;	PUNCT
ap-8605	205	7	i	i	PRON
ap-8605	205	8	.	.	PUNCT
ap-8605	206	1	(	(	PUNCT
ap-8605	206	2	66	66	NUM
ap-8605	206	3	)	)	PUNCT
ap-8605	206	4	it	it	PRON
ap-8605	206	5	can	can	AUX
ap-8605	206	6	be	be	AUX
ap-8605	206	7	seen	see	VERB
ap-8605	206	8	that	that	SCONJ
ap-8605	206	9	the	the	DET
ap-8605	206	10	entropy	entropy	NOUN
ap-8605	206	11	production	production	NOUN
ap-8605	206	12	in	in	ADP
ap-8605	206	13	the	the	DET
ap-8605	206	14	flowing	flow	VERB
ap-8605	206	15	fluid	fluid	NOUN
ap-8605	206	16	will	will	AUX
ap-8605	206	17	be	be	AUX
ap-8605	206	18	dependent	dependent	ADJ
ap-8605	206	19	only	only	ADV
ap-8605	206	20	on	on	ADP
ap-8605	206	21	the	the	DET
ap-8605	206	22	stress	stress	NOUN
ap-8605	206	23	tensor	tensor	NOUN
ap-8605	206	24	.	.	PUNCT
ap-8605	207	1	moreover	moreover	ADV
ap-8605	207	2	,	,	PUNCT
ap-8605	207	3	if	if	SCONJ
ap-8605	207	4	the	the	DET
ap-8605	207	5	fluid	fluid	NOUN
ap-8605	207	6	will	will	AUX
ap-8605	207	7	be	be	AUX
ap-8605	207	8	incompressible	incompressible	ADJ
ap-8605	207	9	,	,	PUNCT
ap-8605	207	10	the	the	DET
ap-8605	207	11	entropy	entropy	NOUN
ap-8605	207	12	production	production	NOUN
ap-8605	207	13	will	will	AUX
ap-8605	207	14	depend	depend	VERB
ap-8605	207	15	only	only	ADV
ap-8605	207	16	on	on	ADP
ap-8605	207	17	the	the	DET
ap-8605	207	18	last	last	ADJ
ap-8605	207	19	term	term	NOUN
ap-8605	207	20	on	on	ADP
ap-8605	207	21	the	the	DET
ap-8605	207	22	r.h.s	r.h.s	NOUN
ap-8605	207	23	.	.	PUNCT
ap-8605	207	24	of	of	ADP
ap-8605	207	25	the	the	DET
ap-8605	207	26	equation	equation	NOUN
ap-8605	207	27	(	(	PUNCT
ap-8605	207	28	66	66	NUM
ap-8605	207	29	)	)	PUNCT
ap-8605	207	30	,	,	PUNCT
ap-8605	207	31	as	as	SCONJ
ap-8605	207	32	the	the	DET
ap-8605	207	33	other	other	ADJ
ap-8605	207	34	terms	term	NOUN
ap-8605	207	35	will	will	AUX
ap-8605	207	36	be	be	AUX
ap-8605	207	37	zero	zero	NUM
ap-8605	207	38	due	due	ADP
ap-8605	207	39	to	to	ADP
ap-8605	207	40	the	the	DET
ap-8605	207	41	continuity	continuity	NOUN
ap-8605	207	42	equation	equation	NOUN
ap-8605	207	43	,	,	PUNCT
ap-8605	207	44	where	where	SCONJ
ap-8605	207	45	the	the	DET
ap-8605	207	46	divergence	divergence	NOUN
ap-8605	207	47	of	of	ADP
ap-8605	207	48	the	the	DET
ap-8605	207	49	velocity	velocity	NOUN
ap-8605	207	50	vector	vector	NOUN
ap-8605	207	51	will	will	AUX
ap-8605	207	52	be	be	AUX
ap-8605	207	53	zero	zero	NUM
ap-8605	207	54	.	.	PUNCT
ap-8605	208	1	7	7	X
ap-8605	208	2	.	.	X
ap-8605	208	3	application	application	NOUN
ap-8605	208	4	to	to	PART
ap-8605	208	5	linear	linear	VERB
ap-8605	208	6	blade	blade	NOUN
ap-8605	208	7	cascade	cascade	NOUN
ap-8605	208	8	application	application	NOUN
ap-8605	208	9	of	of	ADP
ap-8605	208	10	the	the	DET
ap-8605	208	11	curvilinear	curvilinear	PROPN
ap-8605	208	12	coordinates	coordinate	NOUN
ap-8605	208	13	for	for	ADP
ap-8605	208	14	calculation	calculation	NOUN
ap-8605	208	15	of	of	ADP
ap-8605	208	16	the	the	DET
ap-8605	208	17	entropy	entropy	NOUN
ap-8605	208	18	production	production	NOUN
ap-8605	208	19	is	be	AUX
ap-8605	208	20	demonstrated	demonstrate	VERB
ap-8605	208	21	on	on	ADP
ap-8605	208	22	a	a	DET
ap-8605	208	23	linear	linear	ADJ
ap-8605	208	24	blade	blade	NOUN
ap-8605	208	25	cascade	cascade	NOUN
ap-8605	208	26	,	,	PUNCT
ap-8605	208	27	which	which	PRON
ap-8605	208	28	was	be	AUX
ap-8605	208	29	experimentally	experimentally	ADV
ap-8605	208	30	investigated	investigate	VERB
ap-8605	208	31	by	by	ADP
ap-8605	208	32	perdichizzi	perdichizzi	NOUN
ap-8605	208	33	&	&	CCONJ
ap-8605	208	34	dossena	dossena	PROPN
ap-8605	208	35	[	[	X
ap-8605	208	36	11	11	NUM
ap-8605	208	37	]	]	PUNCT
ap-8605	208	38	.	.	PUNCT
ap-8605	209	1	in	in	ADP
ap-8605	209	2	this	this	DET
ap-8605	209	3	case	case	NOUN
ap-8605	209	4	,	,	PUNCT
ap-8605	209	5	the	the	DET
ap-8605	209	6	two	two	NUM
ap-8605	209	7	-	-	PUNCT
ap-8605	209	8	dimensional	dimensional	ADJ
ap-8605	209	9	flow	flow	NOUN
ap-8605	209	10	is	be	AUX
ap-8605	209	11	considered	consider	VERB
ap-8605	209	12	to	to	PART
ap-8605	209	13	demonstrate	demonstrate	VERB
ap-8605	209	14	the	the	DET
ap-8605	209	15	usability	usability	NOUN
ap-8605	209	16	of	of	ADP
ap-8605	209	17	curvilinear	curvilinear	PROPN
ap-8605	209	18	coordinates	coordinate	NOUN
ap-8605	209	19	.	.	PUNCT
ap-8605	210	1	the	the	DET
ap-8605	210	2	blade	blade	NOUN
ap-8605	210	3	under	under	ADP
ap-8605	210	4	investigation	investigation	NOUN
ap-8605	210	5	is	be	AUX
ap-8605	210	6	depicted	depict	VERB
ap-8605	210	7	in	in	ADP
ap-8605	210	8	figure	figure	NOUN
ap-8605	210	9	1	1	NUM
ap-8605	210	10	,	,	PUNCT
ap-8605	210	11	where	where	SCONJ
ap-8605	210	12	the	the	DET
ap-8605	210	13	suction	suction	NOUN
ap-8605	210	14	side	side	NOUN
ap-8605	210	15	is	be	AUX
ap-8605	210	16	approximated	approximate	VERB
ap-8605	210	17	by	by	ADP
ap-8605	210	18	the	the	DET
ap-8605	210	19	fourth	fourth	ADJ
ap-8605	210	20	-	-	PUNCT
ap-8605	210	21	order	order	NOUN
ap-8605	210	22	polynomial	polynomial	ADJ
ap-8605	210	23	function	function	NOUN
ap-8605	210	24	.	.	PUNCT
ap-8605	211	1	the	the	DET
ap-8605	211	2	positions	position	NOUN
ap-8605	211	3	of	of	ADP
ap-8605	211	4	the	the	DET
ap-8605	211	5	pressure	pressure	NOUN
ap-8605	211	6	taps	tap	NOUN
ap-8605	211	7	are	be	AUX
ap-8605	211	8	highlighted	highlight	VERB
ap-8605	211	9	by	by	ADP
ap-8605	211	10	red	red	ADJ
ap-8605	211	11	points	point	NOUN
ap-8605	211	12	.	.	PUNCT
ap-8605	212	1	107	107	NUM
ap-8605	212	2	erik	erik	PROPN
ap-8605	212	3	flídr	flídr	PROPN
ap-8605	212	4	acta	acta	PROPN
ap-8605	212	5	polytechnica	polytechnica	PROPN
ap-8605	212	6	0	0	NUM
ap-8605	212	7	10	10	NUM
ap-8605	212	8	20	20	NUM
ap-8605	212	9	30	30	NUM
ap-8605	212	10	x	x	SYM
ap-8605	212	11	(	(	PUNCT
ap-8605	212	12	mm	mm	NOUN
ap-8605	212	13	)	)	PUNCT
ap-8605	212	14	−40	−40	NOUN
ap-8605	213	1	−30	−30	PROPN
ap-8605	213	2	−20	−20	PROPN
ap-8605	214	1	−10	−10	X
ap-8605	214	2	0	0	PUNCT
ap-8605	215	1	y	y	PROPN
ap-8605	215	2	(	(	PUNCT
ap-8605	215	3	m	m	PROPN
ap-8605	215	4	m	m	VERB
ap-8605	215	5	)	)	PUNCT
ap-8605	215	6	y	y	PROPN
ap-8605	215	7	=	=	PROPN
ap-8605	215	8	a0	a0	PROPN
ap-8605	215	9	+	+	CCONJ
ap-8605	215	10	a1x	a1x	NOUN
ap-8605	215	11	+	+	CCONJ
ap-8605	215	12	a2x	a2x	PROPN
ap-8605	215	13	2	2	NUM
ap-8605	215	14	+	+	NUM
ap-8605	215	15	+	+	ADJ
ap-8605	215	16	a3x	a3x	ADJ
ap-8605	215	17	3	3	NUM
ap-8605	215	18	+	+	CCONJ
ap-8605	215	19	a4x	a4x	ADJ
ap-8605	215	20	4	4	NUM
ap-8605	215	21	polynomial	polynomial	ADJ
ap-8605	215	22	approximation	approximation	NOUN
ap-8605	215	23	of	of	ADP
ap-8605	215	24	the	the	DET
ap-8605	215	25	blade	blade	NOUN
ap-8605	215	26	suction	suction	NOUN
ap-8605	215	27	surface	surface	NOUN
ap-8605	215	28	suction	suction	NOUN
ap-8605	215	29	surface	surface	NOUN
ap-8605	215	30	pressure	pressure	NOUN
ap-8605	215	31	surface	surface	NOUN
ap-8605	215	32	pressure	pressure	NOUN
ap-8605	215	33	taps	tap	NOUN
ap-8605	215	34	positions	position	NOUN
ap-8605	215	35	figure	figure	VERB
ap-8605	215	36	1	1	NUM
ap-8605	215	37	.	.	PUNCT
ap-8605	215	38	blade	blade	NOUN
ap-8605	215	39	under	under	ADP
ap-8605	215	40	investigation	investigation	NOUN
ap-8605	215	41	.	.	PUNCT
ap-8605	216	1	the	the	DET
ap-8605	216	2	coefficients	coefficient	NOUN
ap-8605	216	3	in	in	ADP
ap-8605	216	4	the	the	DET
ap-8605	216	5	polynomial	polynomial	ADJ
ap-8605	216	6	function	function	NOUN
ap-8605	216	7	have	have	VERB
ap-8605	216	8	values	value	NOUN
ap-8605	216	9	a0	a0	NOUN
ap-8605	216	10	=	=	SYM
ap-8605	216	11	1.64	1.64	NUM
ap-8605	216	12	,	,	PUNCT
ap-8605	216	13	a1	a1	NOUN
ap-8605	216	14	=	=	SYM
ap-8605	216	15	1.16	1.16	NUM
ap-8605	216	16	,	,	PUNCT
ap-8605	216	17	a2	a2	PROPN
ap-8605	216	18	=	=	NUM
ap-8605	216	19	7.14	7.14	NUM
ap-8605	216	20	×	×	NOUN
ap-8605	216	21	10−2	10−2	NUM
ap-8605	216	22	,	,	PUNCT
ap-8605	216	23	a3	a3	NOUN
ap-8605	216	24	=	=	NOUN
ap-8605	216	25	1.56	1.56	NUM
ap-8605	216	26	×	×	NOUN
ap-8605	216	27	10−3	10−3	NUM
ap-8605	216	28	and	and	CCONJ
ap-8605	216	29	a4	a4	NOUN
ap-8605	216	30	=	=	SYM
ap-8605	216	31	4.55×10−5	4.55×10−5	NUM
ap-8605	216	32	.	.	PUNCT
ap-8605	217	1	the	the	DET
ap-8605	217	2	curvilinear	curvilinear	ADJ
ap-8605	217	3	coordinate	coordinate	NOUN
ap-8605	217	4	system	system	NOUN
ap-8605	217	5	of	of	ADP
ap-8605	217	6	the	the	DET
ap-8605	217	7	blade	blade	NOUN
ap-8605	217	8	can	can	AUX
ap-8605	217	9	be	be	AUX
ap-8605	217	10	introduced	introduce	VERB
ap-8605	217	11	if	if	SCONJ
ap-8605	217	12	the	the	DET
ap-8605	217	13	blade	blade	NOUN
ap-8605	217	14	geometry	geometry	NOUN
ap-8605	217	15	is	be	AUX
ap-8605	217	16	known	know	VERB
ap-8605	217	17	.	.	PUNCT
ap-8605	218	1	this	this	DET
ap-8605	218	2	system	system	NOUN
ap-8605	218	3	is	be	AUX
ap-8605	218	4	shown	show	VERB
ap-8605	218	5	in	in	ADP
ap-8605	218	6	figure	figure	NOUN
ap-8605	218	7	2	2	NUM
ap-8605	218	8	.	.	PUNCT
ap-8605	218	9	figure	figure	NOUN
ap-8605	218	10	2	2	NUM
ap-8605	218	11	.	.	PUNCT
ap-8605	218	12	blade	blade	NOUN
ap-8605	218	13	curvilinear	curvilinear	PROPN
ap-8605	218	14	coordinates	coordinate	NOUN
ap-8605	218	15	.	.	PUNCT
ap-8605	219	1	the	the	DET
ap-8605	219	2	relations	relation	NOUN
ap-8605	219	3	between	between	ADP
ap-8605	219	4	the	the	DET
ap-8605	219	5	cartesian	cartesian	ADJ
ap-8605	219	6	and	and	CCONJ
ap-8605	219	7	curvilinear	curvilinear	PROPN
ap-8605	219	8	coordinates	coordinate	NOUN
ap-8605	219	9	are	be	AUX
ap-8605	219	10	given	give	VERB
ap-8605	219	11	by	by	ADP
ap-8605	219	12	:	:	PUNCT
ap-8605	219	13	x1	x1	PROPN
ap-8605	219	14	=	=	SYM
ap-8605	219	15	ζ1	ζ1	PROPN
ap-8605	219	16	,	,	PUNCT
ap-8605	219	17	(	(	PUNCT
ap-8605	219	18	67	67	NUM
ap-8605	219	19	)	)	PUNCT
ap-8605	219	20	x2	x2	NOUN
ap-8605	220	1	=	=	PUNCT
ap-8605	220	2	ζ2	ζ2	NOUN
ap-8605	220	3	+	+	CCONJ
ap-8605	220	4	4∑	4∑	NOUN
ap-8605	220	5	i=1	i=1	PRON
ap-8605	220	6	ai	ai	VERB
ap-8605	220	7	(	(	PUNCT
ap-8605	220	8	ζ1)i	ζ1)i	ADJ
ap-8605	220	9	,	,	PUNCT
ap-8605	220	10	(	(	PUNCT
ap-8605	220	11	68	68	NUM
ap-8605	220	12	)	)	PUNCT
ap-8605	220	13	ζ1	ζ1	NOUN
ap-8605	220	14	=	=	SYM
ap-8605	220	15	x1	x1	PROPN
ap-8605	220	16	,	,	PUNCT
ap-8605	220	17	(	(	PUNCT
ap-8605	220	18	69	69	NUM
ap-8605	221	1	)	)	PUNCT
ap-8605	221	2	ζ2	ζ2	NOUN
ap-8605	221	3	=	=	SYM
ap-8605	221	4	x2	x2	NOUN
ap-8605	222	1	−	−	PROPN
ap-8605	222	2	4∑	4∑	NOUN
ap-8605	222	3	i=1	i=1	PROPN
ap-8605	222	4	ai	ai	VERB
ap-8605	222	5	(	(	PUNCT
ap-8605	222	6	x1)i	x1)i	PROPN
ap-8605	222	7	.	.	PUNCT
ap-8605	223	1	(	(	PUNCT
ap-8605	223	2	70	70	NUM
ap-8605	223	3	)	)	PUNCT
ap-8605	223	4	by	by	ADP
ap-8605	223	5	introducing	introduce	VERB
ap-8605	223	6	substitution	substitution	NOUN
ap-8605	223	7	:	:	PUNCT
ap-8605	224	1	σ	σ	PROPN
ap-8605	224	2	=	=	SYM
ap-8605	224	3	4∑	4∑	PRON
ap-8605	224	4	i=1	i=1	PRON
ap-8605	224	5	ai	ai	VERB
ap-8605	224	6	(	(	PUNCT
ap-8605	224	7	x1)i	x1)i	ADJ
ap-8605	224	8	,	,	PUNCT
ap-8605	224	9	(	(	PUNCT
ap-8605	224	10	71	71	NUM
ap-8605	224	11	)	)	PUNCT
ap-8605	224	12	the	the	DET
ap-8605	224	13	metric	metric	ADJ
ap-8605	224	14	tensor	tensor	NOUN
ap-8605	224	15	as	as	ADV
ap-8605	224	16	well	well	ADV
ap-8605	224	17	as	as	ADP
ap-8605	224	18	its	its	PRON
ap-8605	224	19	inverse	inverse	NOUN
ap-8605	224	20	can	can	AUX
ap-8605	224	21	be	be	AUX
ap-8605	224	22	calculated	calculate	VERB
ap-8605	224	23	as	as	ADP
ap-8605	224	24	:	:	PUNCT
ap-8605	224	25	gij	gij	ADJ
ap-8605	224	26	=	=	SYM
ap-8605	224	27	(	(	PUNCT
ap-8605	224	28	1	1	NUM
ap-8605	224	29	−σ	−σ	NOUN
ap-8605	224	30	−σ	−σ	NOUN
ap-8605	224	31	1	1	NUM
ap-8605	224	32	+	+	NUM
ap-8605	224	33	σ2	σ2	NOUN
ap-8605	224	34	)	)	PUNCT
ap-8605	224	35	,	,	PUNCT
ap-8605	224	36	(	(	PUNCT
ap-8605	224	37	72	72	X
ap-8605	224	38	)	)	PUNCT
ap-8605	224	39	gij	gij	NOUN
ap-8605	224	40	=	=	PUNCT
ap-8605	225	1	(	(	PUNCT
ap-8605	225	2	1	1	NUM
ap-8605	225	3	+	+	NUM
ap-8605	225	4	σ2	σ2	PROPN
ap-8605	225	5	σ	σ	PROPN
ap-8605	225	6	σ	σ	PROPN
ap-8605	225	7	1	1	NUM
ap-8605	225	8	)	)	PUNCT
ap-8605	225	9	.	.	PUNCT
ap-8605	226	1	(	(	PUNCT
ap-8605	226	2	73	73	NUM
ap-8605	226	3	)	)	PUNCT
ap-8605	226	4	christoffel	christoffel	ADJ
ap-8605	226	5	symbols	symbol	NOUN
ap-8605	226	6	of	of	ADP
ap-8605	226	7	the	the	DET
ap-8605	226	8	second	second	ADJ
ap-8605	226	9	kind	kind	NOUN
ap-8605	226	10	can	can	AUX
ap-8605	226	11	be	be	AUX
ap-8605	226	12	then	then	ADV
ap-8605	226	13	calculated	calculate	VERB
ap-8605	226	14	using	use	VERB
ap-8605	226	15	equation	equation	NOUN
ap-8605	226	16	(	(	PUNCT
ap-8605	226	17	8)	8)	NUM
ap-8605	226	18	.	.	PUNCT
ap-8605	227	1	at	at	ADP
ap-8605	227	2	first	first	ADV
ap-8605	227	3	,	,	PUNCT
ap-8605	227	4	the	the	DET
ap-8605	227	5	derivatives	derivative	NOUN
ap-8605	227	6	of	of	ADP
ap-8605	227	7	the	the	DET
ap-8605	227	8	metric	metric	ADJ
ap-8605	227	9	components	component	NOUN
ap-8605	227	10	,	,	PUNCT
ap-8605	227	11	with	with	ADP
ap-8605	227	12	respect	respect	NOUN
ap-8605	227	13	to	to	ADP
ap-8605	227	14	the	the	DET
ap-8605	227	15	coordinate	coordinate	NOUN
ap-8605	227	16	xi	xi	PROPN
ap-8605	227	17	,	,	PUNCT
ap-8605	227	18	are	be	AUX
ap-8605	227	19	calculated	calculate	VERB
ap-8605	227	20	as	as	ADP
ap-8605	227	21	:	:	PUNCT
ap-8605	227	22	∂x1g11	∂x1g11	PROPN
ap-8605	227	23	=	=	PROPN
ap-8605	227	24	2σβ	2σβ	NOUN
ap-8605	227	25	,	,	PUNCT
ap-8605	227	26	(	(	PUNCT
ap-8605	227	27	74	74	NUM
ap-8605	227	28	)	)	PUNCT
ap-8605	227	29	∂x1g12	∂x1g12	PROPN
ap-8605	227	30	=	=	SYM
ap-8605	227	31	∂x1g21	∂x1g21	PROPN
ap-8605	227	32	=	=	PUNCT
ap-8605	227	33	β	β	X
ap-8605	227	34	,	,	PUNCT
ap-8605	227	35	(	(	PUNCT
ap-8605	227	36	75	75	NUM
ap-8605	227	37	)	)	PUNCT
ap-8605	227	38	∂x1g22	∂x1g22	NOUN
ap-8605	227	39	=	=	SYM
ap-8605	227	40	0	0	NUM
ap-8605	227	41	,	,	PUNCT
ap-8605	227	42	(	(	PUNCT
ap-8605	227	43	76	76	NUM
ap-8605	227	44	)	)	PUNCT
ap-8605	227	45	∂x2g11	∂x2g11	X
ap-8605	228	1	=	=	SYM
ap-8605	228	2	0	0	NUM
ap-8605	228	3	,	,	PUNCT
ap-8605	228	4	(	(	PUNCT
ap-8605	228	5	77	77	NUM
ap-8605	228	6	)	)	PUNCT
ap-8605	228	7	∂x2g12	∂x2g12	PROPN
ap-8605	229	1	=	=	PUNCT
ap-8605	229	2	∂x2g21	∂x2g21	PROPN
ap-8605	229	3	=	=	SYM
ap-8605	229	4	0	0	NUM
ap-8605	229	5	,	,	PUNCT
ap-8605	229	6	(	(	PUNCT
ap-8605	229	7	78	78	X
ap-8605	229	8	)	)	PUNCT
ap-8605	230	1	∂x2g22	∂x2g22	NOUN
ap-8605	230	2	=	=	SYM
ap-8605	230	3	0	0	NUM
ap-8605	230	4	,	,	PUNCT
ap-8605	230	5	(	(	PUNCT
ap-8605	230	6	79	79	NUM
ap-8605	230	7	)	)	PUNCT
ap-8605	230	8	where	where	SCONJ
ap-8605	230	9	:	:	PUNCT
ap-8605	230	10	β	β	X
ap-8605	230	11	=	=	SYM
ap-8605	230	12	4∑	4∑	NUM
ap-8605	230	13	i=2	i=2	PROPN
ap-8605	231	1	i	i	PRON
ap-8605	231	2	(	(	PUNCT
ap-8605	231	3	i−	i−	PROPN
ap-8605	231	4	1	1	NUM
ap-8605	231	5	)	)	PUNCT
ap-8605	231	6	ai	ai	VERB
ap-8605	231	7	(	(	PUNCT
ap-8605	231	8	x1)(i−2	x1)(i−2	PROPN
ap-8605	231	9	)	)	PUNCT
ap-8605	231	10	.	.	PUNCT
ap-8605	232	1	(	(	PUNCT
ap-8605	232	2	80	80	NUM
ap-8605	232	3	)	)	PUNCT
ap-8605	232	4	then	then	ADV
ap-8605	232	5	,	,	PUNCT
ap-8605	232	6	all	all	PRON
ap-8605	232	7	of	of	ADP
ap-8605	232	8	the	the	DET
ap-8605	232	9	christoffel	christoffel	ADJ
ap-8605	232	10	symbols	symbol	NOUN
ap-8605	232	11	are	be	AUX
ap-8605	232	12	equal	equal	ADJ
ap-8605	232	13	to	to	ADP
ap-8605	232	14	zero	zero	NUM
ap-8605	232	15	except	except	SCONJ
ap-8605	232	16	γ2	γ2	PROPN
ap-8605	232	17	11	11	NUM
ap-8605	232	18	=	=	SYM
ap-8605	232	19	β	β	X
ap-8605	232	20	.	.	PUNCT
ap-8605	233	1	having	have	VERB
ap-8605	233	2	all	all	PRON
ap-8605	233	3	of	of	ADP
ap-8605	233	4	these	these	DET
ap-8605	233	5	pieces	piece	NOUN
ap-8605	233	6	of	of	ADP
ap-8605	233	7	information	information	NOUN
ap-8605	233	8	,	,	PUNCT
ap-8605	233	9	the	the	DET
ap-8605	233	10	calculation	calculation	NOUN
ap-8605	233	11	of	of	ADP
ap-8605	233	12	the	the	DET
ap-8605	233	13	entropy	entropy	NOUN
ap-8605	233	14	production	production	NOUN
ap-8605	233	15	can	can	AUX
ap-8605	233	16	be	be	AUX
ap-8605	233	17	directly	directly	ADV
ap-8605	233	18	performed	perform	VERB
ap-8605	233	19	.	.	PUNCT
ap-8605	234	1	this	this	DET
ap-8605	234	2	calculation	calculation	NOUN
ap-8605	234	3	was	be	AUX
ap-8605	234	4	performed	perform	VERB
ap-8605	234	5	in	in	ADP
ap-8605	234	6	the	the	DET
ap-8605	234	7	region	region	NOUN
ap-8605	234	8	near	near	ADP
ap-8605	234	9	the	the	DET
ap-8605	234	10	blade	blade	NOUN
ap-8605	234	11	surface	surface	NOUN
ap-8605	234	12	(	(	PUNCT
ap-8605	234	13	out	out	ADP
ap-8605	234	14	of	of	ADP
ap-8605	234	15	the	the	DET
ap-8605	234	16	boundary	boundary	ADJ
ap-8605	234	17	layer	layer	NOUN
ap-8605	234	18	)	)	PUNCT
ap-8605	234	19	,	,	PUNCT
ap-8605	234	20	where	where	SCONJ
ap-8605	234	21	the	the	DET
ap-8605	234	22	gradients	gradient	NOUN
ap-8605	234	23	of	of	ADP
ap-8605	234	24	the	the	DET
ap-8605	234	25	parameters	parameter	NOUN
ap-8605	234	26	along	along	ADP
ap-8605	234	27	the	the	DET
ap-8605	234	28	coordinate	coordinate	NOUN
ap-8605	234	29	ζ2	ζ2	NOUN
ap-8605	234	30	were	be	AUX
ap-8605	234	31	considered	consider	VERB
ap-8605	234	32	only	only	ADV
ap-8605	234	33	(	(	PUNCT
ap-8605	234	34	in	in	ADP
ap-8605	234	35	other	other	ADJ
ap-8605	234	36	directions	direction	NOUN
ap-8605	234	37	,	,	PUNCT
ap-8605	234	38	their	their	PRON
ap-8605	234	39	values	value	NOUN
ap-8605	234	40	can	can	AUX
ap-8605	234	41	be	be	AUX
ap-8605	234	42	neglected	neglect	VERB
ap-8605	234	43	)	)	PUNCT
ap-8605	234	44	.	.	PUNCT
ap-8605	235	1	the	the	DET
ap-8605	235	2	boundary	boundary	ADJ
ap-8605	235	3	conditions	condition	NOUN
ap-8605	235	4	were	be	AUX
ap-8605	235	5	not	not	PART
ap-8605	235	6	specified	specify	VERB
ap-8605	235	7	in	in	ADP
ap-8605	235	8	the	the	DET
ap-8605	235	9	paper	paper	NOUN
ap-8605	236	1	[	[	X
ap-8605	236	2	11	11	NUM
ap-8605	236	3	]	]	PUNCT
ap-8605	236	4	,	,	PUNCT
ap-8605	236	5	i.e.	i.e.	X
ap-8605	236	6	both	both	CCONJ
ap-8605	236	7	the	the	DET
ap-8605	236	8	stagnation	stagnation	NOUN
ap-8605	236	9	temperature	temperature	NOUN
ap-8605	236	10	and	and	CCONJ
ap-8605	236	11	the	the	DET
ap-8605	236	12	pressure	pressure	NOUN
ap-8605	236	13	,	,	PUNCT
ap-8605	236	14	however	however	ADV
ap-8605	236	15	,	,	PUNCT
ap-8605	236	16	based	base	VERB
ap-8605	236	17	on	on	ADP
ap-8605	236	18	the	the	DET
ap-8605	236	19	wind	wind	NOUN
ap-8605	236	20	tunnel	tunnel	NOUN
ap-8605	236	21	type	type	NOUN
ap-8605	236	22	,	,	PUNCT
ap-8605	236	23	their	their	PRON
ap-8605	236	24	values	value	NOUN
ap-8605	236	25	can	can	AUX
ap-8605	236	26	be	be	AUX
ap-8605	236	27	estimated	estimate	VERB
ap-8605	236	28	as	as	ADP
ap-8605	236	29	t0	t0	X
ap-8605	236	30	=	=	PROPN
ap-8605	236	31	297.15	297.15	NUM
ap-8605	236	32	k	k	NOUN
ap-8605	236	33	and	and	CCONJ
ap-8605	236	34	p0	p0	NOUN
ap-8605	236	35	=	=	SYM
ap-8605	236	36	98000	98000	NUM
ap-8605	236	37	pa	pa	PROPN
ap-8605	236	38	.	.	PUNCT
ap-8605	237	1	the	the	DET
ap-8605	237	2	pressure	pressure	NOUN
ap-8605	237	3	distribution	distribution	NOUN
ap-8605	237	4	on	on	ADP
ap-8605	237	5	the	the	DET
ap-8605	237	6	blade	blade	NOUN
ap-8605	237	7	surface	surface	NOUN
ap-8605	237	8	(	(	PUNCT
ap-8605	237	9	denoted	denote	VERB
ap-8605	237	10	by	by	ADP
ap-8605	237	11	coordinate	coordinate	NOUN
ap-8605	237	12	s	s	NOUN
ap-8605	237	13	)	)	PUNCT
ap-8605	237	14	can	can	AUX
ap-8605	237	15	be	be	AUX
ap-8605	237	16	calculated	calculate	VERB
ap-8605	237	17	from	from	ADP
ap-8605	237	18	the	the	DET
ap-8605	237	19	mach	mach	NOUN
ap-8605	237	20	number	number	NOUN
ap-8605	237	21	distribution	distribution	NOUN
ap-8605	237	22	.	.	PUNCT
ap-8605	238	1	the	the	DET
ap-8605	238	2	pressure	pressure	NOUN
ap-8605	238	3	,	,	PUNCT
ap-8605	238	4	temperature	temperature	NOUN
ap-8605	238	5	,	,	PUNCT
ap-8605	238	6	and	and	CCONJ
ap-8605	238	7	velocity	velocity	NOUN
ap-8605	238	8	distributions	distribution	NOUN
ap-8605	238	9	are	be	AUX
ap-8605	238	10	shown	show	VERB
ap-8605	238	11	in	in	ADP
ap-8605	238	12	figure	figure	NOUN
ap-8605	238	13	3	3	NUM
ap-8605	238	14	.	.	PUNCT
ap-8605	239	1	distribution	distribution	NOUN
ap-8605	239	2	of	of	ADP
ap-8605	239	3	the	the	DET
ap-8605	239	4	entropy	entropy	NOUN
ap-8605	239	5	production	production	NOUN
ap-8605	239	6	ϱds	ϱds	PROPN
ap-8605	239	7	/	/	SYM
ap-8605	239	8	dt	dt	NOUN
ap-8605	239	9	along	along	ADP
ap-8605	239	10	the	the	DET
ap-8605	239	11	blade	blade	NOUN
ap-8605	239	12	surface	surface	NOUN
ap-8605	239	13	is	be	AUX
ap-8605	239	14	shown	show	VERB
ap-8605	239	15	in	in	ADP
ap-8605	239	16	figure	figure	NOUN
ap-8605	239	17	4	4	NUM
ap-8605	239	18	.	.	PUNCT
ap-8605	240	1	note	note	NOUN
ap-8605	240	2	,	,	PUNCT
ap-8605	240	3	that	that	SCONJ
ap-8605	240	4	the	the	DET
ap-8605	240	5	bulk	bulk	ADJ
ap-8605	240	6	viscosity	viscosity	NOUN
ap-8605	240	7	λ	λ	NOUN
ap-8605	240	8	was	be	AUX
ap-8605	240	9	obtained	obtain	VERB
ap-8605	240	10	by	by	ADP
ap-8605	240	11	the	the	DET
ap-8605	240	12	stokes	stoke	NOUN
ap-8605	240	13	hypothesis	hypothesis	NOUN
ap-8605	240	14	,	,	PUNCT
ap-8605	240	15	that	that	SCONJ
ap-8605	240	16	λ+	λ+	VERB
ap-8605	240	17	2/3µ	2/3µ	NUM
ap-8605	240	18	=	=	SYM
ap-8605	240	19	0	0	X
ap-8605	240	20	.	.	PUNCT
ap-8605	241	1	it	it	PRON
ap-8605	241	2	is	be	AUX
ap-8605	241	3	obvious	obvious	ADJ
ap-8605	241	4	that	that	SCONJ
ap-8605	241	5	most	most	ADJ
ap-8605	241	6	of	of	ADP
ap-8605	241	7	the	the	DET
ap-8605	241	8	entropy	entropy	NOUN
ap-8605	241	9	production	production	NOUN
ap-8605	241	10	occurred	occur	VERB
ap-8605	241	11	in	in	ADP
ap-8605	241	12	the	the	DET
ap-8605	241	13	leading	leading	ADJ
ap-8605	241	14	edge	edge	NOUN
ap-8605	241	15	region	region	NOUN
ap-8605	241	16	,	,	PUNCT
ap-8605	241	17	where	where	SCONJ
ap-8605	241	18	the	the	DET
ap-8605	241	19	flow	flow	NOUN
ap-8605	241	20	acceleration	acceleration	NOUN
ap-8605	241	21	was	be	AUX
ap-8605	241	22	the	the	DET
ap-8605	241	23	highest	high	ADJ
ap-8605	241	24	,	,	PUNCT
ap-8605	241	25	and	and	CCONJ
ap-8605	241	26	therefore	therefore	ADV
ap-8605	241	27	the	the	DET
ap-8605	241	28	velocity	velocity	NOUN
ap-8605	241	29	gradients	gradient	NOUN
ap-8605	241	30	were	be	AUX
ap-8605	241	31	the	the	DET
ap-8605	241	32	largest	large	ADJ
ap-8605	241	33	.	.	PUNCT
ap-8605	242	1	overall	overall	ADJ
ap-8605	242	2	entropy	entropy	PROPN
ap-8605	242	3	production	production	NOUN
ap-8605	242	4	along	along	ADP
ap-8605	242	5	the	the	DET
ap-8605	242	6	coordinate	coordinate	NOUN
ap-8605	242	7	ζ2	ζ2	NOUN
ap-8605	242	8	was	be	AUX
ap-8605	242	9	calculated	calculate	VERB
ap-8605	242	10	as	as	ADP
ap-8605	242	11	an	an	DET
ap-8605	242	12	integral	integral	ADJ
ap-8605	242	13	along	along	ADP
ap-8605	242	14	this	this	DET
ap-8605	242	15	curve	curve	NOUN
ap-8605	242	16	and	and	CCONJ
ap-8605	242	17	was	be	AUX
ap-8605	242	18	p	p	NOUN
ap-8605	242	19	=	=	NOUN
ap-8605	242	20	0.0327	0.0327	NUM
ap-8605	242	21	j·k−1·m−2·s−1	j·k−1·m−2·s−1	NOUN
ap-8605	242	22	.	.	PUNCT
ap-8605	243	1	108	108	NUM
ap-8605	243	2	vol	vol	NOUN
ap-8605	243	3	.	.	PUNCT
ap-8605	244	1	63	63	NUM
ap-8605	244	2	no	no	NOUN
ap-8605	244	3	.	.	PUNCT
ap-8605	245	1	2/2023	2/2023	NUM
ap-8605	245	2	derivation	derivation	NOUN
ap-8605	245	3	of	of	ADP
ap-8605	245	4	entropy	entropy	NOUN
ap-8605	245	5	production	production	NOUN
ap-8605	245	6	in	in	ADP
ap-8605	245	7	a	a	DET
ap-8605	245	8	fluid	fluid	ADJ
ap-8605	245	9	flow	flow	NOUN
ap-8605	245	10	0.0	0.0	NUM
ap-8605	245	11	0.2	0.2	NUM
ap-8605	245	12	0.4	0.4	NUM
ap-8605	245	13	0.6	0.6	NUM
ap-8605	245	14	0.8	0.8	NUM
ap-8605	245	15	1.0	1.0	NUM
ap-8605	245	16	s2	s2	PROPN
ap-8605	245	17	s2	s2	NOUN
ap-8605	245	18	max	max	PROPN
ap-8605	245	19	(	(	PUNCT
ap-8605	245	20	1	1	NUM
ap-8605	245	21	)	)	PUNCT
ap-8605	245	22	60000	60000	NUM
ap-8605	245	23	65000	65000	NUM
ap-8605	245	24	70000	70000	NUM
ap-8605	245	25	75000	75000	NUM
ap-8605	245	26	80000	80000	NUM
ap-8605	245	27	85000	85000	NUM
ap-8605	245	28	p	p	NOUN
ap-8605	245	29	(	(	PUNCT
ap-8605	245	30	p	p	NOUN
ap-8605	245	31	a	a	NOUN
ap-8605	245	32	)	)	PUNCT
ap-8605	245	33	(	(	PUNCT
ap-8605	245	34	a	a	NOUN
ap-8605	245	35	)	)	PUNCT
ap-8605	245	36	.	.	PUNCT
ap-8605	246	1	pressure	pressure	NOUN
ap-8605	246	2	distribution	distribution	NOUN
ap-8605	246	3	0.0	0.0	NUM
ap-8605	246	4	0.2	0.2	NUM
ap-8605	246	5	0.4	0.4	NUM
ap-8605	246	6	0.6	0.6	NUM
ap-8605	246	7	0.8	0.8	NUM
ap-8605	246	8	1.0	1.0	NUM
ap-8605	246	9	s2	s2	PROPN
ap-8605	246	10	s2	s2	NOUN
ap-8605	246	11	max	max	PROPN
ap-8605	246	12	(	(	PUNCT
ap-8605	246	13	1	1	NUM
ap-8605	246	14	)	)	PUNCT
ap-8605	246	15	250	250	NUM
ap-8605	246	16	260	260	NUM
ap-8605	246	17	270	270	NUM
ap-8605	246	18	280	280	NUM
ap-8605	246	19	290	290	NUM
ap-8605	246	20	t	t	NOUN
ap-8605	246	21	(	(	PUNCT
ap-8605	246	22	k	k	PROPN
ap-8605	246	23	)	)	PUNCT
ap-8605	246	24	(	(	PUNCT
ap-8605	246	25	b	b	NOUN
ap-8605	246	26	)	)	PUNCT
ap-8605	246	27	.	.	PUNCT
ap-8605	247	1	temperature	temperature	NOUN
ap-8605	247	2	distribution	distribution	NOUN
ap-8605	247	3	0.0	0.0	NUM
ap-8605	247	4	0.2	0.2	NUM
ap-8605	247	5	0.4	0.4	NUM
ap-8605	247	6	0.6	0.6	NUM
ap-8605	247	7	0.8	0.8	NUM
ap-8605	247	8	1.0	1.0	NUM
ap-8605	247	9	s2	s2	PROPN
ap-8605	247	10	s2	s2	NOUN
ap-8605	247	11	max	max	PROPN
ap-8605	247	12	(	(	PUNCT
ap-8605	247	13	1	1	NUM
ap-8605	247	14	)	)	PUNCT
ap-8605	247	15	160	160	NUM
ap-8605	247	16	180	180	NUM
ap-8605	247	17	200	200	NUM
ap-8605	247	18	220	220	NUM
ap-8605	247	19	240	240	NUM
ap-8605	247	20	260	260	NUM
ap-8605	247	21	u	u	NOUN
ap-8605	247	22	(	(	PUNCT
ap-8605	247	23	m	m	PROPN
ap-8605	247	24	·	·	PUNCT
ap-8605	247	25	s−	s−	PROPN
ap-8605	247	26	1	1	NUM
ap-8605	247	27	)	)	PUNCT
ap-8605	247	28	(	(	PUNCT
ap-8605	247	29	c	c	NOUN
ap-8605	247	30	)	)	PUNCT
ap-8605	247	31	.	.	PUNCT
ap-8605	248	1	velocity	velocity	NOUN
ap-8605	248	2	distribution	distribution	NOUN
ap-8605	248	3	figure	figure	NOUN
ap-8605	248	4	3	3	NUM
ap-8605	248	5	.	.	PUNCT
ap-8605	249	1	distribution	distribution	NOUN
ap-8605	249	2	of	of	ADP
ap-8605	249	3	the	the	DET
ap-8605	249	4	flow	flow	NOUN
ap-8605	249	5	parameters	parameter	NOUN
ap-8605	249	6	along	along	ADP
ap-8605	249	7	the	the	DET
ap-8605	249	8	blade	blade	NOUN
ap-8605	249	9	surface	surface	NOUN
ap-8605	249	10	.	.	PUNCT
ap-8605	250	1	0.0	0.0	NUM
ap-8605	250	2	0.2	0.2	NUM
ap-8605	250	3	0.4	0.4	NUM
ap-8605	250	4	0.6	0.6	NUM
ap-8605	250	5	0.8	0.8	NUM
ap-8605	250	6	1.0	1.0	NUM
ap-8605	250	7	s2	s2	PROPN
ap-8605	250	8	s2	s2	NOUN
ap-8605	250	9	max	max	PROPN
ap-8605	250	10	(	(	PUNCT
ap-8605	250	11	1	1	NUM
ap-8605	250	12	)	)	PUNCT
ap-8605	250	13	0	0	NUM
ap-8605	251	1	10	10	NUM
ap-8605	251	2	20	20	NUM
ap-8605	251	3	30	30	NUM
ap-8605	251	4	40	40	NUM
ap-8605	251	5	%	%	NOUN
ap-8605	251	6	d	d	X
ap-8605	251	7	s	s	PROPN
ap-8605	251	8	d	d	X
ap-8605	251	9	t	t	PROPN
ap-8605	251	10	(	(	PUNCT
ap-8605	251	11	j	j	PROPN
ap-8605	251	12	·	·	SYM
ap-8605	251	13	k	k	PROPN
ap-8605	251	14	−	−	PROPN
ap-8605	251	15	1	1	NUM
ap-8605	251	16	·	·	SYM
ap-8605	251	17	m	m	NOUN
ap-8605	251	18	−	−	NOUN
ap-8605	251	19	3	3	NUM
ap-8605	251	20	·	·	SYM
ap-8605	251	21	s	s	PART
ap-8605	251	22	−	−	NOUN
ap-8605	251	23	1	1	NUM
ap-8605	251	24	)	)	PUNCT
ap-8605	251	25	figure	figure	NOUN
ap-8605	251	26	4	4	NUM
ap-8605	251	27	.	.	PUNCT
ap-8605	251	28	entropy	entropy	PROPN
ap-8605	251	29	production	production	NOUN
ap-8605	251	30	.	.	PUNCT
ap-8605	252	1	8	8	X
ap-8605	252	2	.	.	X
ap-8605	252	3	conclusion	conclusion	VERB
ap-8605	252	4	a	a	DET
ap-8605	252	5	derivation	derivation	NOUN
ap-8605	252	6	of	of	ADP
ap-8605	252	7	the	the	DET
ap-8605	252	8	entropy	entropy	NOUN
ap-8605	252	9	production	production	NOUN
ap-8605	252	10	in	in	ADP
ap-8605	252	11	a	a	DET
ap-8605	252	12	flowing	flow	VERB
ap-8605	252	13	fluid	fluid	NOUN
ap-8605	252	14	in	in	ADP
ap-8605	252	15	a	a	DET
ap-8605	252	16	general	general	ADJ
ap-8605	252	17	curvilinear	curvilinear	NOUN
ap-8605	252	18	coordinate	coordinate	NOUN
ap-8605	252	19	system	system	NOUN
ap-8605	252	20	was	be	AUX
ap-8605	252	21	performed	perform	VERB
ap-8605	252	22	in	in	ADP
ap-8605	252	23	this	this	DET
ap-8605	252	24	paper	paper	NOUN
ap-8605	252	25	.	.	PUNCT
ap-8605	253	1	basic	basic	ADJ
ap-8605	253	2	relationships	relationship	NOUN
ap-8605	253	3	from	from	ADP
ap-8605	253	4	the	the	DET
ap-8605	253	5	differential	differential	ADJ
ap-8605	253	6	geometry	geometry	NOUN
ap-8605	253	7	used	use	VERB
ap-8605	253	8	during	during	ADP
ap-8605	253	9	the	the	DET
ap-8605	253	10	derivation	derivation	NOUN
ap-8605	253	11	were	be	AUX
ap-8605	253	12	presented	present	VERB
ap-8605	253	13	as	as	ADV
ap-8605	253	14	well	well	ADV
ap-8605	253	15	to	to	PART
ap-8605	253	16	clarify	clarify	VERB
ap-8605	253	17	used	used	ADJ
ap-8605	253	18	notations	notation	NOUN
ap-8605	253	19	.	.	PUNCT
ap-8605	254	1	curvilinear	curvilinear	PROPN
ap-8605	254	2	coordinates	coordinate	NOUN
ap-8605	254	3	were	be	AUX
ap-8605	254	4	chosen	choose	VERB
ap-8605	254	5	to	to	PART
ap-8605	254	6	describe	describe	VERB
ap-8605	254	7	this	this	DET
ap-8605	254	8	phenomenon	phenomenon	NOUN
ap-8605	254	9	in	in	ADP
ap-8605	254	10	a	a	DET
ap-8605	254	11	more	more	ADV
ap-8605	254	12	general	general	ADJ
ap-8605	254	13	case	case	NOUN
ap-8605	254	14	than	than	SCONJ
ap-8605	254	15	is	be	AUX
ap-8605	254	16	usually	usually	ADV
ap-8605	254	17	used	use	VERB
ap-8605	254	18	in	in	ADP
ap-8605	254	19	the	the	DET
ap-8605	254	20	literature	literature	NOUN
ap-8605	254	21	.	.	PUNCT
ap-8605	255	1	the	the	DET
ap-8605	255	2	results	result	NOUN
ap-8605	255	3	obtained	obtain	VERB
ap-8605	255	4	here	here	ADV
ap-8605	255	5	were	be	AUX
ap-8605	255	6	used	use	VERB
ap-8605	255	7	to	to	PART
ap-8605	255	8	describe	describe	VERB
ap-8605	255	9	the	the	DET
ap-8605	255	10	flow	flow	NOUN
ap-8605	255	11	within	within	ADP
ap-8605	255	12	the	the	DET
ap-8605	255	13	linear	linear	ADJ
ap-8605	255	14	blade	blade	NOUN
ap-8605	255	15	cascades	cascade	NOUN
ap-8605	255	16	in	in	ADP
ap-8605	255	17	a	a	DET
ap-8605	255	18	simplified	simplified	ADJ
ap-8605	255	19	manner	manner	NOUN
ap-8605	255	20	and	and	CCONJ
ap-8605	255	21	the	the	DET
ap-8605	255	22	distribution	distribution	NOUN
ap-8605	255	23	of	of	ADP
ap-8605	255	24	the	the	DET
ap-8605	255	25	entropy	entropy	NOUN
ap-8605	255	26	production	production	NOUN
ap-8605	255	27	along	along	ADP
ap-8605	255	28	one	one	NUM
ap-8605	255	29	coordinate	coordinate	NOUN
ap-8605	255	30	near	near	ADP
ap-8605	255	31	the	the	DET
ap-8605	255	32	blade	blade	NOUN
ap-8605	255	33	suction	suction	NOUN
ap-8605	255	34	surface	surface	NOUN
ap-8605	255	35	was	be	AUX
ap-8605	255	36	obtained	obtain	VERB
ap-8605	255	37	.	.	PUNCT
ap-8605	256	1	the	the	DET
ap-8605	256	2	integral	integral	ADJ
ap-8605	256	3	value	value	NOUN
ap-8605	256	4	of	of	ADP
ap-8605	256	5	the	the	DET
ap-8605	256	6	entropy	entropy	NOUN
ap-8605	256	7	production	production	NOUN
ap-8605	256	8	was	be	AUX
ap-8605	256	9	then	then	ADV
ap-8605	256	10	evaluated	evaluate	VERB
ap-8605	256	11	from	from	ADP
ap-8605	256	12	this	this	DET
ap-8605	256	13	distribution	distribution	NOUN
ap-8605	256	14	.	.	PUNCT
ap-8605	257	1	the	the	DET
ap-8605	257	2	aim	aim	NOUN
ap-8605	257	3	of	of	ADP
ap-8605	257	4	this	this	DET
ap-8605	257	5	paper	paper	NOUN
ap-8605	257	6	was	be	AUX
ap-8605	257	7	to	to	PART
ap-8605	257	8	prove	prove	VERB
ap-8605	257	9	that	that	SCONJ
ap-8605	257	10	this	this	DET
ap-8605	257	11	approach	approach	NOUN
ap-8605	257	12	is	be	AUX
ap-8605	257	13	capable	capable	ADJ
ap-8605	257	14	to	to	PART
ap-8605	257	15	evaluate	evaluate	VERB
ap-8605	257	16	some	some	DET
ap-8605	257	17	experimental	experimental	ADJ
ap-8605	257	18	data	datum	NOUN
ap-8605	257	19	along	along	ADP
ap-8605	257	20	the	the	DET
ap-8605	257	21	suction	suction	NOUN
ap-8605	257	22	side	side	NOUN
ap-8605	257	23	of	of	ADP
ap-8605	257	24	the	the	DET
ap-8605	257	25	blade	blade	NOUN
ap-8605	257	26	.	.	PUNCT
ap-8605	258	1	this	this	DET
ap-8605	258	2	approach	approach	NOUN
ap-8605	258	3	can	can	AUX
ap-8605	258	4	be	be	AUX
ap-8605	258	5	used	use	VERB
ap-8605	258	6	in	in	ADP
ap-8605	258	7	close	close	ADJ
ap-8605	258	8	proximity	proximity	NOUN
ap-8605	258	9	to	to	ADP
ap-8605	258	10	the	the	DET
ap-8605	258	11	blade	blade	NOUN
ap-8605	258	12	.	.	PUNCT
ap-8605	259	1	the	the	DET
ap-8605	259	2	polynomial	polynomial	ADJ
ap-8605	259	3	function	function	NOUN
ap-8605	259	4	will	will	AUX
ap-8605	259	5	be	be	AUX
ap-8605	259	6	changing	change	VERB
ap-8605	259	7	with	with	ADP
ap-8605	259	8	increasing	increase	VERB
ap-8605	259	9	distance	distance	NOUN
ap-8605	259	10	from	from	ADP
ap-8605	259	11	the	the	DET
ap-8605	259	12	blade	blade	NOUN
ap-8605	259	13	surface	surface	NOUN
ap-8605	259	14	,	,	PUNCT
ap-8605	259	15	as	as	SCONJ
ap-8605	259	16	the	the	DET
ap-8605	259	17	opposite	opposite	ADJ
ap-8605	259	18	surface	surface	NOUN
ap-8605	259	19	of	of	ADP
ap-8605	259	20	the	the	DET
ap-8605	259	21	blade	blade	NOUN
ap-8605	259	22	will	will	AUX
ap-8605	259	23	be	be	AUX
ap-8605	259	24	given	give	VERB
ap-8605	259	25	by	by	ADP
ap-8605	259	26	a	a	DET
ap-8605	259	27	polynomial	polynomial	NOUN
ap-8605	259	28	with	with	ADP
ap-8605	259	29	different	different	ADJ
ap-8605	259	30	coefficients	coefficient	NOUN
ap-8605	259	31	.	.	PUNCT
ap-8605	260	1	future	future	ADJ
ap-8605	260	2	work	work	NOUN
ap-8605	260	3	will	will	AUX
ap-8605	260	4	,	,	PUNCT
ap-8605	260	5	therefore	therefore	ADV
ap-8605	260	6	,	,	PUNCT
ap-8605	260	7	be	be	AUX
ap-8605	260	8	dealing	deal	VERB
ap-8605	260	9	with	with	ADP
ap-8605	260	10	the	the	DET
ap-8605	260	11	generalisation	generalisation	NOUN
ap-8605	260	12	of	of	ADP
ap-8605	260	13	this	this	DET
ap-8605	260	14	approach	approach	NOUN
ap-8605	260	15	to	to	ADP
ap-8605	260	16	a	a	DET
ap-8605	260	17	more	more	ADV
ap-8605	260	18	complicated	complicated	ADJ
ap-8605	260	19	situation	situation	NOUN
ap-8605	260	20	,	,	PUNCT
ap-8605	260	21	where	where	SCONJ
ap-8605	260	22	the	the	DET
ap-8605	260	23	polynomial	polynomial	ADJ
ap-8605	260	24	coefficients	coefficient	NOUN
ap-8605	260	25	ai	ai	VERB
ap-8605	260	26	will	will	AUX
ap-8605	260	27	not	not	PART
ap-8605	260	28	be	be	AUX
ap-8605	260	29	constants	constant	NOUN
ap-8605	260	30	.	.	PUNCT
ap-8605	261	1	list	list	NOUN
ap-8605	261	2	of	of	ADP
ap-8605	261	3	symbols	symbol	NOUN
ap-8605	261	4	ai	ai	VERB
ap-8605	261	5	components	component	NOUN
ap-8605	261	6	of	of	ADP
ap-8605	261	7	acceleration	acceleration	NOUN
ap-8605	261	8	vector	vector	NOUN
ap-8605	262	1	[	[	X
ap-8605	262	2	m	m	PROPN
ap-8605	262	3	s−2	s−2	PROPN
ap-8605	262	4	]	]	PUNCT
ap-8605	262	5	e	e	NOUN
ap-8605	262	6	strain	strain	NOUN
ap-8605	262	7	rate	rate	NOUN
ap-8605	262	8	tensor	tensor	NOUN
ap-8605	262	9	[	[	X
ap-8605	262	10	s−1	s−1	PROPN
ap-8605	262	11	]	]	X
ap-8605	262	12	f	f	PROPN
ap-8605	262	13	volume	volume	NOUN
ap-8605	262	14	force	force	NOUN
ap-8605	263	1	[	[	X
ap-8605	263	2	n	n	X
ap-8605	263	3	]	]	X
ap-8605	263	4	gi	gi	X
ap-8605	263	5	,	,	PUNCT
ap-8605	263	6	gi	gi	VERB
ap-8605	263	7	basis	basis	NOUN
ap-8605	263	8	and	and	CCONJ
ap-8605	263	9	co	co	NOUN
ap-8605	263	10	-	-	NOUN
ap-8605	263	11	basis	basis	NOUN
ap-8605	263	12	vectors	vector	NOUN
ap-8605	263	13	[	[	X
ap-8605	263	14	1	1	NUM
ap-8605	263	15	]	]	X
ap-8605	263	16	gij	gij	ADJ
ap-8605	263	17	,	,	PUNCT
ap-8605	263	18	gij	gij	ADJ
ap-8605	263	19	components	component	NOUN
ap-8605	263	20	of	of	ADP
ap-8605	263	21	metric	metric	ADJ
ap-8605	263	22	tensor	tensor	NOUN
ap-8605	263	23	[	[	NOUN
ap-8605	263	24	1	1	NUM
ap-8605	263	25	]	]	PUNCT
ap-8605	263	26	h	h	NOUN
ap-8605	263	27	specific	specific	ADJ
ap-8605	263	28	enthalpy	enthalpy	NOUN
ap-8605	263	29	[	[	X
ap-8605	263	30	j	j	PROPN
ap-8605	263	31	kg−1	kg−1	PROPN
ap-8605	263	32	]	]	X
ap-8605	263	33	j	j	PROPN
ap-8605	263	34	(	(	PUNCT
ap-8605	263	35	s	s	NOUN
ap-8605	263	36	)	)	PUNCT
ap-8605	263	37	entropy	entropy	PROPN
ap-8605	263	38	flux	flux	NOUN
ap-8605	264	1	[	[	X
ap-8605	264	2	j	j	X
ap-8605	264	3	kg−1	kg−1	PROPN
ap-8605	264	4	k−1	k−1	PROPN
ap-8605	264	5	s−1	s−1	PROPN
ap-8605	264	6	]	]	PUNCT
ap-8605	264	7	m	m	VERB
ap-8605	264	8	mass	mass	NOUN
ap-8605	265	1	[	[	X
ap-8605	265	2	kg	kg	X
ap-8605	265	3	]	]	X
ap-8605	265	4	m	m	VERB
ap-8605	265	5	momentum	momentum	NOUN
ap-8605	266	1	[	[	X
ap-8605	266	2	kg	kg	NOUN
ap-8605	266	3	m	m	VERB
ap-8605	266	4	s−1	s−1	PROPN
ap-8605	266	5	]	]	X
ap-8605	266	6	p	p	X
ap-8605	266	7	thermodynamic	thermodynamic	ADJ
ap-8605	266	8	pressure	pressure	NOUN
ap-8605	266	9	[	[	X
ap-8605	266	10	pa	pa	X
ap-8605	266	11	]	]	X
ap-8605	266	12	p(s	p(s	PROPN
ap-8605	266	13	)	)	PUNCT
ap-8605	266	14	local	local	ADJ
ap-8605	266	15	entropy	entropy	NOUN
ap-8605	266	16	production	production	NOUN
ap-8605	267	1	[	[	X
ap-8605	267	2	j	j	X
ap-8605	267	3	m−2	m−2	PROPN
ap-8605	267	4	s−1	s−1	PROPN
ap-8605	267	5	k−1	k−1	PROPN
ap-8605	267	6	]	]	X
ap-8605	267	7	109	109	NUM
ap-8605	267	8	erik	erik	PROPN
ap-8605	267	9	flídr	flídr	PROPN
ap-8605	267	10	acta	acta	PROPN
ap-8605	267	11	polytechnica	polytechnica	PROPN
ap-8605	267	12	p(s	p(s	PROPN
ap-8605	267	13	)	)	PUNCT
ap-8605	267	14	integral	integral	ADJ
ap-8605	267	15	entropy	entropy	NOUN
ap-8605	267	16	production	production	NOUN
ap-8605	267	17	[	[	X
ap-8605	267	18	j	j	X
ap-8605	267	19	m−2	m−2	PROPN
ap-8605	267	20	s−1	s−1	PROPN
ap-8605	267	21	k−1	k−1	PROPN
ap-8605	267	22	]	]	PUNCT
ap-8605	267	23	qi	qi	PROPN
ap-8605	267	24	components	component	NOUN
ap-8605	267	25	of	of	ADP
ap-8605	267	26	heat	heat	NOUN
ap-8605	267	27	flux	flux	NOUN
ap-8605	267	28	vector	vector	NOUN
ap-8605	268	1	[	[	X
ap-8605	268	2	jm−2	jm−2	PROPN
ap-8605	268	3	s−1	s−1	PROPN
ap-8605	268	4	]	]	X
ap-8605	268	5	s	s	PART
ap-8605	268	6	specific	specific	ADJ
ap-8605	268	7	entropy	entropy	NOUN
ap-8605	268	8	[	[	X
ap-8605	268	9	j	j	PROPN
ap-8605	268	10	kg−1	kg−1	PROPN
ap-8605	268	11	k−1	k−1	PROPN
ap-8605	268	12	]	]	X
ap-8605	268	13	s	s	PART
ap-8605	268	14	blade	blade	NOUN
ap-8605	268	15	surface	surface	NOUN
ap-8605	268	16	coordinate	coordinate	NOUN
ap-8605	269	1	[	[	X
ap-8605	269	2	m	m	X
ap-8605	269	3	]	]	X
ap-8605	269	4	t	t	NOUN
ap-8605	269	5	time	time	NOUN
ap-8605	269	6	[	[	X
ap-8605	269	7	s	s	X
ap-8605	269	8	]	]	X
ap-8605	269	9	t	t	X
ap-8605	269	10	thermodynamic	thermodynamic	ADJ
ap-8605	269	11	temperature	temperature	NOUN
ap-8605	270	1	[	[	X
ap-8605	270	2	k	k	X
ap-8605	270	3	]	]	X
ap-8605	270	4	ui	ui	PROPN
ap-8605	270	5	components	component	NOUN
ap-8605	270	6	of	of	ADP
ap-8605	270	7	velocity	velocity	NOUN
ap-8605	270	8	vector	vector	NOUN
ap-8605	270	9	[	[	X
ap-8605	270	10	m	m	NOUN
ap-8605	270	11	s−1	s−1	PROPN
ap-8605	270	12	]	]	PUNCT
ap-8605	270	13	v	v	NOUN
ap-8605	270	14	control	control	NOUN
ap-8605	270	15	volume	volume	NOUN
ap-8605	271	1	[	[	X
ap-8605	271	2	m3	m3	X
ap-8605	271	3	]	]	X
ap-8605	271	4	x	x	SYM
ap-8605	271	5	,	,	PUNCT
ap-8605	271	6	y	y	PROPN
ap-8605	271	7	,	,	PUNCT
ap-8605	271	8	z	z	NOUN
ap-8605	271	9	=	=	SYM
ap-8605	271	10	xi	xi	PROPN
ap-8605	271	11	cartesian	cartesian	ADJ
ap-8605	271	12	coordinates	coordinate	NOUN
ap-8605	272	1	[	[	X
ap-8605	272	2	m	m	X
ap-8605	272	3	]	]	X
ap-8605	272	4	γ	γ	PROPN
ap-8605	272	5	christoffel	christoffel	ADJ
ap-8605	272	6	symbols	symbol	NOUN
ap-8605	272	7	[	[	X
ap-8605	272	8	1	1	X
ap-8605	272	9	]	]	PUNCT
ap-8605	272	10	ζi	ζi	PROPN
ap-8605	272	11	curvilinear	curvilinear	ADJ
ap-8605	272	12	blade	blade	NOUN
ap-8605	272	13	coordinates	coordinate	NOUN
ap-8605	273	1	[	[	X
ap-8605	273	2	m	m	X
ap-8605	273	3	]	]	X
ap-8605	273	4	µ	µ	DET
ap-8605	273	5	dynamic	dynamic	ADJ
ap-8605	273	6	viscosity	viscosity	NOUN
ap-8605	273	7	[	[	X
ap-8605	273	8	pa	pa	PROPN
ap-8605	273	9	s	s	X
ap-8605	273	10	]	]	X
ap-8605	273	11	λ	λ	X
ap-8605	273	12	bulk	bulk	ADJ
ap-8605	273	13	viscosity	viscosity	NOUN
ap-8605	273	14	[	[	AUX
ap-8605	273	15	pa	pa	PROPN
ap-8605	273	16	s	s	X
ap-8605	273	17	]	]	X
ap-8605	273	18	ϱ	ϱ	ADP
ap-8605	273	19	density	density	NOUN
ap-8605	274	1	[	[	X
ap-8605	274	2	kg	kg	X
ap-8605	274	3	m−3	m−3	PROPN
ap-8605	274	4	]	]	X
ap-8605	274	5	references	reference	NOUN
ap-8605	274	6	[	[	X
ap-8605	274	7	1	1	NUM
ap-8605	274	8	]	]	PUNCT
ap-8605	274	9	c.	c.	PROPN
ap-8605	274	10	truesdell	truesdell	PROPN
ap-8605	274	11	.	.	PUNCT
ap-8605	275	1	the	the	DET
ap-8605	275	2	physical	physical	ADJ
ap-8605	275	3	components	component	NOUN
ap-8605	275	4	of	of	ADP
ap-8605	275	5	vectors	vector	NOUN
ap-8605	275	6	and	and	CCONJ
ap-8605	275	7	tensors	tensor	NOUN
ap-8605	275	8	.	.	PUNCT
ap-8605	276	1	journal	journal	NOUN
ap-8605	276	2	of	of	ADP
ap-8605	276	3	applied	apply	VERB
ap-8605	276	4	mathematics	mathematic	NOUN
ap-8605	276	5	and	and	CCONJ
ap-8605	276	6	mechanics	mechanic	NOUN
ap-8605	276	7	33(10–11):345–356	33(10–11):345–356	NUM
ap-8605	276	8	,	,	PUNCT
ap-8605	276	9	1953	1953	NUM
ap-8605	276	10	.	.	PUNCT
ap-8605	277	1	https://doi.org/10.1002/zamm.19530331005	https://doi.org/10.1002/zamm.19530331005	X
ap-8605	278	1	[	[	X
ap-8605	278	2	2	2	NUM
ap-8605	278	3	]	]	X
ap-8605	278	4	r.	r.	PROPN
ap-8605	278	5	aris	aris	PROPN
ap-8605	278	6	.	.	PUNCT
ap-8605	279	1	vectors	vector	NOUN
ap-8605	279	2	,	,	PUNCT
ap-8605	279	3	tensors	tensor	NOUN
ap-8605	279	4	and	and	CCONJ
ap-8605	279	5	the	the	DET
ap-8605	279	6	basic	basic	ADJ
ap-8605	279	7	equations	equation	NOUN
ap-8605	279	8	of	of	ADP
ap-8605	279	9	fluid	fluid	ADJ
ap-8605	279	10	mechanics	mechanic	NOUN
ap-8605	279	11	.	.	PUNCT
ap-8605	280	1	dover	dover	PROPN
ap-8605	280	2	publications	publications	PROPN
ap-8605	280	3	,	,	PUNCT
ap-8605	280	4	1989	1989	NUM
ap-8605	280	5	.	.	PUNCT
ap-8605	281	1	[	[	X
ap-8605	281	2	3	3	X
ap-8605	281	3	]	]	X
ap-8605	281	4	v.	v.	ADP
ap-8605	281	5	ivancevic	ivancevic	ADJ
ap-8605	281	6	,	,	PUNCT
ap-8605	281	7	t.	t.	PROPN
ap-8605	281	8	ivancevic	ivancevic	PROPN
ap-8605	281	9	.	.	PUNCT
ap-8605	282	1	applied	apply	VERB
ap-8605	282	2	differential	differential	NOUN
ap-8605	282	3	geometry	geometry	NOUN
ap-8605	282	4	:	:	PUNCT
ap-8605	282	5	a	a	DET
ap-8605	282	6	modern	modern	ADJ
ap-8605	282	7	introduction	introduction	NOUN
ap-8605	282	8	.	.	PUNCT
ap-8605	283	1	world	world	NOUN
ap-8605	283	2	scientific	scientific	ADJ
ap-8605	283	3	,	,	PUNCT
ap-8605	283	4	2007	2007	NUM
ap-8605	283	5	.	.	PUNCT
ap-8605	284	1	https://doi.org/10.1142/6420	https://doi.org/10.1142/6420	NOUN
ap-8605	285	1	[	[	X
ap-8605	285	2	4	4	X
ap-8605	285	3	]	]	PUNCT
ap-8605	285	4	s.	s.	PROPN
ap-8605	285	5	surattana	surattana	PROPN
ap-8605	285	6	.	.	PUNCT
ap-8605	286	1	transformation	transformation	NOUN
ap-8605	286	2	of	of	ADP
ap-8605	286	3	the	the	DET
ap-8605	286	4	navier	navier	NOUN
ap-8605	286	5	-	-	PUNCT
ap-8605	286	6	stokes	stoke	NOUN
ap-8605	286	7	equations	equation	NOUN
ap-8605	286	8	in	in	ADP
ap-8605	286	9	curvilinear	curvilinear	ADJ
ap-8605	286	10	coordinate	coordinate	NOUN
ap-8605	286	11	system	system	NOUN
ap-8605	286	12	with	with	ADP
ap-8605	286	13	mapel	mapel	NOUN
ap-8605	286	14	.	.	PUNCT
ap-8605	287	1	global	global	ADJ
ap-8605	287	2	journal	journal	PROPN
ap-8605	287	3	of	of	ADP
ap-8605	287	4	pure	pure	ADJ
ap-8605	287	5	and	and	CCONJ
ap-8605	287	6	applied	apply	VERB
ap-8605	287	7	mathematics	mathematic	NOUN
ap-8605	287	8	12(4):3315–3325	12(4):3315–3325	NUM
ap-8605	287	9	,	,	PUNCT
ap-8605	287	10	2016	2016	NUM
ap-8605	287	11	.	.	PUNCT
ap-8605	288	1	[	[	X
ap-8605	288	2	5	5	NUM
ap-8605	288	3	]	]	X
ap-8605	288	4	l.	l.	PROPN
ap-8605	288	5	swungoho	swungoho	PROPN
ap-8605	288	6	,	,	PUNCT
ap-8605	288	7	s.	s.	PROPN
ap-8605	288	8	bharat	bharat	PROPN
ap-8605	288	9	.	.	PUNCT
ap-8605	289	1	governing	govern	VERB
ap-8605	289	2	equations	equation	NOUN
ap-8605	289	3	of	of	ADP
ap-8605	289	4	fluid	fluid	ADJ
ap-8605	289	5	mechanics	mechanic	NOUN
ap-8605	289	6	in	in	ADP
ap-8605	289	7	physical	physical	ADJ
ap-8605	289	8	curvilinear	curvilinear	NOUN
ap-8605	289	9	coordinate	coordinate	NOUN
ap-8605	289	10	system	system	NOUN
ap-8605	289	11	.	.	PUNCT
ap-8605	290	1	in	in	ADP
ap-8605	290	2	third	third	ADJ
ap-8605	290	3	mississippi	mississippi	PROPN
ap-8605	290	4	state	state	NOUN
ap-8605	290	5	conference	conference	NOUN
ap-8605	290	6	on	on	ADP
ap-8605	290	7	difference	difference	NOUN
ap-8605	290	8	equations	equation	NOUN
ap-8605	290	9	and	and	CCONJ
ap-8605	290	10	computational	computational	ADJ
ap-8605	290	11	simulations	simulation	NOUN
ap-8605	290	12	,	,	PUNCT
ap-8605	290	13	pp	pp	ADJ
ap-8605	290	14	.	.	PUNCT
ap-8605	291	1	149–157	149–157	NUM
ap-8605	291	2	.	.	PUNCT
ap-8605	292	1	1997	1997	NUM
ap-8605	292	2	.	.	PUNCT
ap-8605	293	1	[	[	X
ap-8605	293	2	6	6	NUM
ap-8605	293	3	]	]	X
ap-8605	293	4	p.	p.	NOUN
ap-8605	293	5	asinari	asinari	PROPN
ap-8605	293	6	,	,	PUNCT
ap-8605	293	7	e.	e.	PROPN
ap-8605	293	8	chiavazzo	chiavazzo	PROPN
ap-8605	293	9	.	.	PUNCT
ap-8605	294	1	overview	overview	NOUN
ap-8605	294	2	of	of	ADP
ap-8605	294	3	the	the	DET
ap-8605	294	4	entropy	entropy	NOUN
ap-8605	294	5	production	production	NOUN
ap-8605	294	6	of	of	ADP
ap-8605	294	7	incompressible	incompressible	ADJ
ap-8605	294	8	and	and	CCONJ
ap-8605	294	9	compressible	compressible	ADJ
ap-8605	294	10	fluid	fluid	ADJ
ap-8605	294	11	dynamics	dynamic	NOUN
ap-8605	294	12	.	.	PUNCT
ap-8605	295	1	meccanica	meccanica	PROPN
ap-8605	295	2	51:1–10	51:1–10	NUM
ap-8605	295	3	,	,	PUNCT
ap-8605	295	4	2015	2015	NUM
ap-8605	295	5	.	.	PUNCT
ap-8605	296	1	https://doi.org/10.1007/s11012-015-0284-z	https://doi.org/10.1007/s11012-015-0284-z	PROPN
ap-8605	297	1	[	[	X
ap-8605	297	2	7	7	X
ap-8605	297	3	]	]	X
ap-8605	297	4	j.	j.	PROPN
ap-8605	297	5	kvasnica	kvasnica	PROPN
ap-8605	297	6	.	.	PUNCT
ap-8605	298	1	termodynamika	termodynamika	PROPN
ap-8605	298	2	.	.	PUNCT
ap-8605	299	1	sntl	sntl	PROPN
ap-8605	299	2	,	,	PUNCT
ap-8605	299	3	1965	1965	NUM
ap-8605	299	4	.	.	PUNCT
ap-8605	300	1	[	[	X
ap-8605	300	2	8	8	NUM
ap-8605	300	3	]	]	PUNCT
ap-8605	300	4	a.	a.	NOUN
ap-8605	300	5	bejan	bejan	PROPN
ap-8605	300	6	.	.	PUNCT
ap-8605	301	1	entropy	entropy	PROPN
ap-8605	301	2	generation	generation	NOUN
ap-8605	301	3	minimization	minimization	NOUN
ap-8605	301	4	.	.	PUNCT
ap-8605	302	1	crc	crc	PROPN
ap-8605	302	2	press	press	PROPN
ap-8605	302	3	lcc	lcc	PROPN
ap-8605	302	4	,	,	PUNCT
ap-8605	302	5	2013	2013	NUM
ap-8605	302	6	.	.	PUNCT
ap-8605	303	1	[	[	X
ap-8605	303	2	9	9	NUM
ap-8605	303	3	]	]	PUNCT
ap-8605	303	4	f.	f.	PROPN
ap-8605	303	5	maršík	maršík	PROPN
ap-8605	303	6	.	.	PUNCT
ap-8605	304	1	termodynamika	termodynamika	NOUN
ap-8605	304	2	kontinua	kontinua	PROPN
ap-8605	304	3	.	.	PUNCT
ap-8605	305	1	academia	academia	PROPN
ap-8605	305	2	,	,	PUNCT
ap-8605	305	3	1999	1999	NUM
ap-8605	305	4	.	.	PUNCT
ap-8605	306	1	[	[	X
ap-8605	306	2	10	10	NUM
ap-8605	306	3	]	]	X
ap-8605	306	4	l.	l.	PROPN
ap-8605	306	5	landau	landau	PROPN
ap-8605	306	6	,	,	PUNCT
ap-8605	306	7	e.	e.	PROPN
ap-8605	306	8	lifschitz	lifschitz	PROPN
ap-8605	306	9	.	.	PUNCT
ap-8605	307	1	fluid	fluid	ADJ
ap-8605	307	2	mechanics	mechanic	NOUN
ap-8605	307	3	.	.	PUNCT
ap-8605	308	1	pergamon	pergamon	PROPN
ap-8605	308	2	press	press	PROPN
ap-8605	308	3	,	,	PUNCT
ap-8605	308	4	1987	1987	NUM
ap-8605	308	5	.	.	PUNCT
ap-8605	309	1	[	[	X
ap-8605	309	2	11	11	NUM
ap-8605	309	3	]	]	PUNCT
ap-8605	309	4	a.	a.	NOUN
ap-8605	309	5	perdichizzi	perdichizzi	PROPN
ap-8605	309	6	,	,	PUNCT
ap-8605	309	7	v.	v.	ADP
ap-8605	309	8	dossena	dossena	NOUN
ap-8605	309	9	.	.	PUNCT
ap-8605	310	1	incidence	incidence	NOUN
ap-8605	310	2	angle	angle	NOUN
ap-8605	310	3	and	and	CCONJ
ap-8605	310	4	pitch	pitch	NOUN
ap-8605	310	5	–	–	PUNCT
ap-8605	310	6	chord	chord	NOUN
ap-8605	310	7	effects	effect	NOUN
ap-8605	310	8	on	on	ADP
ap-8605	310	9	secondary	secondary	ADJ
ap-8605	310	10	flows	flow	NOUN
ap-8605	310	11	downstream	downstream	ADV
ap-8605	310	12	of	of	ADP
ap-8605	310	13	a	a	DET
ap-8605	310	14	turbine	turbine	NOUN
ap-8605	310	15	cascade	cascade	NOUN
ap-8605	310	16	.	.	PUNCT
ap-8605	311	1	journal	journal	NOUN
ap-8605	311	2	of	of	ADP
ap-8605	311	3	turbomachinerytransactions	turbomachinerytransaction	NOUN
ap-8605	311	4	of	of	ADP
ap-8605	311	5	the	the	DET
ap-8605	311	6	asme	asme	PROPN
ap-8605	311	7	115(3):383–391	115(3):383–391	NUM
ap-8605	311	8	,	,	PUNCT
ap-8605	311	9	1993	1993	NUM
ap-8605	311	10	.	.	PUNCT
ap-8605	312	1	https://doi.org/10.1115/1.2929265	https://doi.org/10.1115/1.2929265	NOUN
ap-8605	313	1	110	110	NUM
ap-8605	313	2	https://doi.org/10.1002/zamm.19530331005	https://doi.org/10.1002/zamm.19530331005	NOUN
ap-8605	313	3	https://doi.org/10.1142/6420	https://doi.org/10.1142/6420	NOUN
ap-8605	313	4	https://doi.org/10.1007/s11012-015-0284-z	https://doi.org/10.1007/s11012-015-0284-z	PROPN
ap-8605	313	5	https://doi.org/10.1115/1.2929265	https://doi.org/10.1115/1.2929265	AUX
ap-8605	313	6	acta	acta	PROPN
ap-8605	313	7	polytechnica	polytechnica	PROPN
ap-8605	313	8	63(2):29–36	63(2):29–36	NUM
ap-8605	313	9	,	,	PUNCT
ap-8605	313	10	2023	2023	NUM
ap-8605	313	11	1	1	NUM
ap-8605	313	12	introduction	introduction	NOUN
ap-8605	313	13	2	2	NUM
ap-8605	313	14	basics	basic	NOUN
ap-8605	313	15	of	of	ADP
ap-8605	313	16	differential	differential	ADJ
ap-8605	313	17	geometry	geometry	NOUN
ap-8605	313	18	3	3	NUM
ap-8605	313	19	laws	law	NOUN
ap-8605	313	20	of	of	ADP
ap-8605	313	21	thermodynamics	thermodynamic	NOUN
ap-8605	313	22	3.1	3.1	NUM
ap-8605	313	23	the	the	DET
ap-8605	313	24	first	first	ADJ
ap-8605	313	25	law	law	NOUN
ap-8605	313	26	of	of	ADP
ap-8605	313	27	thermodynamics	thermodynamic	NOUN
ap-8605	313	28	3.2	3.2	NUM
ap-8605	313	29	the	the	DET
ap-8605	313	30	second	second	ADJ
ap-8605	313	31	law	law	NOUN
ap-8605	313	32	of	of	ADP
ap-8605	313	33	thermodynamics	thermodynamic	NOUN
ap-8605	313	34	4	4	NUM
ap-8605	313	35	balances	balance	NOUN
ap-8605	313	36	laws	law	NOUN
ap-8605	313	37	4.1	4.1	NUM
ap-8605	313	38	continuity	continuity	NOUN
ap-8605	313	39	equation	equation	NOUN
ap-8605	313	40	4.2	4.2	NUM
ap-8605	313	41	momentum	momentum	NOUN
ap-8605	313	42	conservation	conservation	NOUN
ap-8605	313	43	law	law	NOUN
ap-8605	313	44	4.3	4.3	NUM
ap-8605	313	45	energy	energy	NOUN
ap-8605	313	46	conservation	conservation	NOUN
ap-8605	313	47	law	law	NOUN
ap-8605	313	48	4.4	4.4	NUM
ap-8605	313	49	entropy	entropy	PROPN
ap-8605	313	50	balance	balance	NOUN
ap-8605	313	51	5	5	NUM
ap-8605	313	52	entropy	entropy	NOUN
ap-8605	313	53	production	production	NOUN
ap-8605	313	54	in	in	ADP
ap-8605	313	55	flowing	flow	VERB
ap-8605	313	56	fluid	fluid	ADJ
ap-8605	313	57	6	6	NUM
ap-8605	313	58	newtonian	newtonian	ADJ
ap-8605	313	59	fluid	fluid	NOUN
ap-8605	313	60	6.1	6.1	NUM
ap-8605	313	61	entropy	entropy	NOUN
ap-8605	313	62	production	production	NOUN
ap-8605	313	63	in	in	ADP
ap-8605	313	64	newtonian	newtonian	ADJ
ap-8605	313	65	fluid	fluid	ADJ
ap-8605	313	66	7	7	NUM
ap-8605	313	67	application	application	NOUN
ap-8605	313	68	to	to	PART
ap-8605	313	69	linear	linear	VERB
ap-8605	313	70	blade	blade	NOUN
ap-8605	313	71	cascade	cascade	NOUN
ap-8605	313	72	8	8	NUM
ap-8605	313	73	conclusion	conclusion	NOUN
ap-8605	313	74	list	list	NOUN
ap-8605	313	75	of	of	ADP
ap-8605	313	76	symbols	symbol	NOUN
ap-8605	313	77	references	reference	NOUN