id	sid	tid	token	lemma	pos
ap-10175	1	1	acta	acta	PROPN
ap-10175	1	2	polytechnica	polytechnica	PROPN
ap-10175	1	3	https://doi.org/10.14311/ap.2025.65.0334	https://doi.org/10.14311/ap.2025.65.0334	PROPN
ap-10175	1	4	acta	acta	PROPN
ap-10175	1	5	polytechnica	polytechnica	PROPN
ap-10175	1	6	65(3):334–340	65(3):334–340	PROPN
ap-10175	1	7	,	,	PUNCT
ap-10175	1	8	2025	2025	NUM
ap-10175	1	9	©	©	ADP
ap-10175	1	10	2025	2025	NUM
ap-10175	1	11	the	the	DET
ap-10175	1	12	author(s	author(s	NOUN
ap-10175	1	13	)	)	PUNCT
ap-10175	1	14	.	.	PUNCT
ap-10175	2	1	licensed	license	VERB
ap-10175	2	2	under	under	ADP
ap-10175	2	3	a	a	DET
ap-10175	2	4	cc	cc	NOUN
ap-10175	2	5	-	-	PUNCT
ap-10175	2	6	by	by	ADP
ap-10175	2	7	4.0	4.0	NUM
ap-10175	2	8	licence	licence	NOUN
ap-10175	2	9	published	publish	VERB
ap-10175	2	10	by	by	ADP
ap-10175	2	11	the	the	DET
ap-10175	2	12	czech	czech	PROPN
ap-10175	2	13	technical	technical	PROPN
ap-10175	2	14	university	university	PROPN
ap-10175	2	15	in	in	ADP
ap-10175	2	16	prague	prague	PROPN
ap-10175	2	17	wave	wave	NOUN
ap-10175	2	18	propagation	propagation	NOUN
ap-10175	2	19	in	in	ADP
ap-10175	2	20	a	a	DET
ap-10175	2	21	pipe	pipe	NOUN
ap-10175	2	22	conveying	convey	VERB
ap-10175	2	23	two	two	NUM
ap-10175	2	24	phase	phase	NOUN
ap-10175	2	25	flow	flow	NOUN
ap-10175	2	26	akintoye	akintoye	NOUN
ap-10175	2	27	o.	o.	NOUN
ap-10175	2	28	oyeladea,∗	oyeladea,∗	PROPN
ap-10175	2	29	,	,	PUNCT
ap-10175	2	30	adegboyega	adegboyega	PROPN
ap-10175	2	31	b.	b.	PROPN
ap-10175	2	32	ehinmowob	ehinmowob	PROPN
ap-10175	2	33	,	,	PUNCT
ap-10175	2	34	oluwasola	oluwasola	PROPN
ap-10175	2	35	oribayoc	oribayoc	NOUN
ap-10175	2	36	,	,	PUNCT
ap-10175	2	37	yetunde	yetunde	NOUN
ap-10175	2	38	o.	o.	PROPN
ap-10175	2	39	abioduna	abioduna	PROPN
ap-10175	2	40	a	a	DET
ap-10175	2	41	university	university	PROPN
ap-10175	2	42	of	of	ADP
ap-10175	2	43	lagos	lago	NOUN
ap-10175	2	44	,	,	PUNCT
ap-10175	2	45	faculty	faculty	NOUN
ap-10175	2	46	of	of	ADP
ap-10175	2	47	engineering	engineering	NOUN
ap-10175	2	48	,	,	PUNCT
ap-10175	2	49	department	department	NOUN
ap-10175	2	50	of	of	ADP
ap-10175	2	51	civil	civil	ADJ
ap-10175	2	52	and	and	CCONJ
ap-10175	2	53	environmental	environmental	ADJ
ap-10175	2	54	engineering	engineering	NOUN
ap-10175	2	55	,	,	PUNCT
ap-10175	2	56	100213	100213	NUM
ap-10175	2	57	lagos	lago	NOUN
ap-10175	2	58	,	,	PUNCT
ap-10175	2	59	nigeria	nigeria	PROPN
ap-10175	2	60	b	b	PROPN
ap-10175	2	61	university	university	PROPN
ap-10175	2	62	of	of	ADP
ap-10175	2	63	lagos	lagos	PROPN
ap-10175	2	64	,	,	PUNCT
ap-10175	2	65	faculty	faculty	NOUN
ap-10175	2	66	of	of	ADP
ap-10175	2	67	engineering	engineering	NOUN
ap-10175	2	68	,	,	PUNCT
ap-10175	2	69	department	department	NOUN
ap-10175	2	70	of	of	ADP
ap-10175	2	71	petroleum	petroleum	NOUN
ap-10175	2	72	and	and	CCONJ
ap-10175	2	73	gas	gas	NOUN
ap-10175	2	74	,	,	PUNCT
ap-10175	2	75	100213	100213	NUM
ap-10175	2	76	lagos	lago	NOUN
ap-10175	2	77	,	,	PUNCT
ap-10175	2	78	nigeria	nigeria	PROPN
ap-10175	2	79	c	c	PROPN
ap-10175	2	80	university	university	PROPN
ap-10175	2	81	of	of	ADP
ap-10175	2	82	lagos	lagos	PROPN
ap-10175	2	83	,	,	PUNCT
ap-10175	2	84	faculty	faculty	NOUN
ap-10175	2	85	of	of	ADP
ap-10175	2	86	engineering	engineering	NOUN
ap-10175	2	87	,	,	PUNCT
ap-10175	2	88	department	department	NOUN
ap-10175	2	89	of	of	ADP
ap-10175	2	90	chemical	chemical	PROPN
ap-10175	2	91	engineering	engineering	NOUN
ap-10175	2	92	,	,	PUNCT
ap-10175	2	93	100213	100213	NUM
ap-10175	2	94	lagos	lago	NOUN
ap-10175	2	95	,	,	PUNCT
ap-10175	2	96	nigeria	nigeria	PROPN
ap-10175	2	97	∗	∗	NOUN
ap-10175	2	98	corresponding	correspond	VERB
ap-10175	2	99	author	author	NOUN
ap-10175	2	100	:	:	PUNCT
ap-10175	2	101	aoyelade@unilag.edu.ng	aoyelade@unilag.edu.ng	ADJ
ap-10175	2	102	abstract	abstract	NOUN
ap-10175	2	103	.	.	PUNCT
ap-10175	3	1	the	the	DET
ap-10175	3	2	study	study	NOUN
ap-10175	3	3	of	of	ADP
ap-10175	3	4	wave	wave	NOUN
ap-10175	3	5	propagation	propagation	NOUN
ap-10175	3	6	in	in	ADP
ap-10175	3	7	pipes	pipe	NOUN
ap-10175	3	8	conveying	convey	VERB
ap-10175	3	9	a	a	DET
ap-10175	3	10	two	two	NUM
ap-10175	3	11	-	-	PUNCT
ap-10175	3	12	phase	phase	NOUN
ap-10175	3	13	flow	flow	NOUN
ap-10175	3	14	is	be	AUX
ap-10175	3	15	of	of	ADP
ap-10175	3	16	significant	significant	ADJ
ap-10175	3	17	importance	importance	NOUN
ap-10175	3	18	in	in	ADP
ap-10175	3	19	various	various	ADJ
ap-10175	3	20	engineering	engineering	NOUN
ap-10175	3	21	applications	application	NOUN
ap-10175	3	22	,	,	PUNCT
ap-10175	3	23	including	include	VERB
ap-10175	3	24	the	the	DET
ap-10175	3	25	oil	oil	NOUN
ap-10175	3	26	and	and	CCONJ
ap-10175	3	27	gas	gas	NOUN
ap-10175	3	28	,	,	PUNCT
ap-10175	3	29	chemical	chemical	NOUN
ap-10175	3	30	,	,	PUNCT
ap-10175	3	31	and	and	CCONJ
ap-10175	3	32	nuclear	nuclear	ADJ
ap-10175	3	33	industries	industry	NOUN
ap-10175	3	34	.	.	PUNCT
ap-10175	4	1	one	one	NUM
ap-10175	4	2	of	of	ADP
ap-10175	4	3	the	the	DET
ap-10175	4	4	most	most	ADV
ap-10175	4	5	significant	significant	ADJ
ap-10175	4	6	characteristics	characteristic	NOUN
ap-10175	4	7	of	of	ADP
ap-10175	4	8	a	a	DET
ap-10175	4	9	two	two	NUM
ap-10175	4	10	-	-	PUNCT
ap-10175	4	11	phase	phase	NOUN
ap-10175	4	12	flow	flow	NOUN
ap-10175	4	13	in	in	ADP
ap-10175	4	14	pipes	pipe	NOUN
ap-10175	4	15	is	be	AUX
ap-10175	4	16	the	the	DET
ap-10175	4	17	flow	flow	NOUN
ap-10175	4	18	velocity	velocity	NOUN
ap-10175	4	19	whose	whose	DET
ap-10175	4	20	estimation	estimation	NOUN
ap-10175	4	21	is	be	AUX
ap-10175	4	22	achieved	achieve	VERB
ap-10175	4	23	by	by	ADP
ap-10175	4	24	various	various	ADJ
ap-10175	4	25	means	mean	NOUN
ap-10175	4	26	.	.	PUNCT
ap-10175	5	1	however	however	ADV
ap-10175	5	2	,	,	PUNCT
ap-10175	5	3	such	such	ADJ
ap-10175	5	4	approaches	approach	NOUN
ap-10175	5	5	can	can	AUX
ap-10175	5	6	be	be	AUX
ap-10175	5	7	very	very	ADV
ap-10175	5	8	sensitive	sensitive	ADJ
ap-10175	5	9	to	to	ADP
ap-10175	5	10	the	the	DET
ap-10175	5	11	operational	operational	ADJ
ap-10175	5	12	and	and	CCONJ
ap-10175	5	13	boundary	boundary	ADJ
ap-10175	5	14	conditions	condition	NOUN
ap-10175	5	15	.	.	PUNCT
ap-10175	6	1	therefore	therefore	ADV
ap-10175	6	2	,	,	PUNCT
ap-10175	6	3	there	there	PRON
ap-10175	6	4	is	be	VERB
ap-10175	6	5	a	a	DET
ap-10175	6	6	need	need	NOUN
ap-10175	6	7	to	to	PART
ap-10175	6	8	develop	develop	VERB
ap-10175	6	9	a	a	DET
ap-10175	6	10	reliable	reliable	ADJ
ap-10175	6	11	approach	approach	NOUN
ap-10175	6	12	based	base	VERB
ap-10175	6	13	on	on	ADP
ap-10175	6	14	the	the	DET
ap-10175	6	15	local	local	ADJ
ap-10175	6	16	flow	flow	NOUN
ap-10175	6	17	dynamics	dynamic	NOUN
ap-10175	6	18	and	and	CCONJ
ap-10175	6	19	properties	property	NOUN
ap-10175	6	20	of	of	ADP
ap-10175	6	21	the	the	DET
ap-10175	6	22	pipe	pipe	NOUN
ap-10175	6	23	.	.	PUNCT
ap-10175	7	1	in	in	ADP
ap-10175	7	2	this	this	DET
ap-10175	7	3	work	work	NOUN
ap-10175	7	4	,	,	PUNCT
ap-10175	7	5	a	a	DET
ap-10175	7	6	wave	wave	NOUN
ap-10175	7	7	-	-	PUNCT
ap-10175	7	8	based	base	VERB
ap-10175	7	9	approach	approach	NOUN
ap-10175	7	10	for	for	ADP
ap-10175	7	11	estimating	estimate	VERB
ap-10175	7	12	the	the	DET
ap-10175	7	13	phase	phase	NOUN
ap-10175	7	14	and	and	CCONJ
ap-10175	7	15	group	group	NOUN
ap-10175	7	16	velocities	velocity	NOUN
ap-10175	7	17	was	be	AUX
ap-10175	7	18	developed	develop	VERB
ap-10175	7	19	.	.	PUNCT
ap-10175	8	1	the	the	DET
ap-10175	8	2	governing	govern	VERB
ap-10175	8	3	equation	equation	NOUN
ap-10175	8	4	of	of	ADP
ap-10175	8	5	the	the	DET
ap-10175	8	6	work	work	NOUN
ap-10175	8	7	was	be	AUX
ap-10175	8	8	derived	derive	VERB
ap-10175	8	9	based	base	VERB
ap-10175	8	10	on	on	ADP
ap-10175	8	11	hamilton	hamilton	PROPN
ap-10175	8	12	,	,	PUNCT
ap-10175	8	13	and	and	CCONJ
ap-10175	8	14	the	the	DET
ap-10175	8	15	chisolm	chisolm	ADJ
ap-10175	8	16	correlation	correlation	NOUN
ap-10175	8	17	model	model	NOUN
ap-10175	8	18	was	be	AUX
ap-10175	8	19	used	use	VERB
ap-10175	8	20	for	for	ADP
ap-10175	8	21	the	the	DET
ap-10175	8	22	two	two	NUM
ap-10175	8	23	-	-	PUNCT
ap-10175	8	24	phase	phase	NOUN
ap-10175	8	25	flow	flow	NOUN
ap-10175	8	26	.	.	PUNCT
ap-10175	9	1	the	the	DET
ap-10175	9	2	dispersion	dispersion	NOUN
ap-10175	9	3	relation	relation	NOUN
ap-10175	9	4	of	of	ADP
ap-10175	9	5	the	the	DET
ap-10175	9	6	governing	govern	VERB
ap-10175	9	7	equation	equation	NOUN
ap-10175	9	8	is	be	AUX
ap-10175	9	9	first	first	ADV
ap-10175	9	10	derived	derive	VERB
ap-10175	9	11	in	in	ADP
ap-10175	9	12	terms	term	NOUN
ap-10175	9	13	of	of	ADP
ap-10175	9	14	the	the	DET
ap-10175	9	15	traveling	travel	VERB
ap-10175	9	16	wave	wave	NOUN
ap-10175	9	17	feature	feature	NOUN
ap-10175	9	18	.	.	PUNCT
ap-10175	10	1	then	then	ADV
ap-10175	10	2	,	,	PUNCT
ap-10175	10	3	the	the	DET
ap-10175	10	4	exact	exact	ADJ
ap-10175	10	5	expressions	expression	NOUN
ap-10175	10	6	of	of	ADP
ap-10175	10	7	the	the	DET
ap-10175	10	8	phase	phase	NOUN
ap-10175	10	9	velocity	velocity	NOUN
ap-10175	10	10	and	and	CCONJ
ap-10175	10	11	group	group	NOUN
ap-10175	10	12	velocity	velocity	NOUN
ap-10175	10	13	for	for	ADP
ap-10175	10	14	the	the	DET
ap-10175	10	15	bending	bend	VERB
ap-10175	10	16	waves	wave	NOUN
ap-10175	10	17	are	be	AUX
ap-10175	10	18	obtained	obtain	VERB
ap-10175	10	19	.	.	PUNCT
ap-10175	11	1	furthermore	furthermore	ADV
ap-10175	11	2	,	,	PUNCT
ap-10175	11	3	the	the	DET
ap-10175	11	4	free	free	ADJ
ap-10175	11	5	vibration	vibration	NOUN
ap-10175	11	6	frequency	frequency	NOUN
ap-10175	11	7	characteristics	characteristic	NOUN
ap-10175	11	8	of	of	ADP
ap-10175	11	9	the	the	DET
ap-10175	11	10	two	two	NUM
ap-10175	11	11	phases	phase	NOUN
ap-10175	11	12	was	be	AUX
ap-10175	11	13	studied	study	VERB
ap-10175	11	14	.	.	PUNCT
ap-10175	12	1	the	the	DET
ap-10175	12	2	results	result	NOUN
ap-10175	12	3	indicate	indicate	VERB
ap-10175	12	4	that	that	SCONJ
ap-10175	12	5	in	in	ADP
ap-10175	12	6	a	a	DET
ap-10175	12	7	single	single	ADJ
ap-10175	12	8	-	-	PUNCT
ap-10175	12	9	phase	phase	NOUN
ap-10175	12	10	flow	flow	NOUN
ap-10175	12	11	,	,	PUNCT
ap-10175	12	12	wave	wave	NOUN
ap-10175	12	13	dispersion	dispersion	NOUN
ap-10175	12	14	occurs	occur	VERB
ap-10175	12	15	at	at	ADP
ap-10175	12	16	a	a	DET
ap-10175	12	17	wavenumber	wavenumber	NOUN
ap-10175	12	18	of	of	ADP
ap-10175	12	19	2.1	2.1	NUM
ap-10175	12	20	,	,	PUNCT
ap-10175	12	21	whereas	whereas	SCONJ
ap-10175	12	22	in	in	ADP
ap-10175	12	23	a	a	DET
ap-10175	12	24	two	two	NUM
ap-10175	12	25	-	-	PUNCT
ap-10175	12	26	phase	phase	NOUN
ap-10175	12	27	flow	flow	NOUN
ap-10175	12	28	with	with	ADP
ap-10175	12	29	a	a	DET
ap-10175	12	30	vapour	vapour	NOUN
ap-10175	12	31	quality	quality	NOUN
ap-10175	12	32	of	of	ADP
ap-10175	12	33	0.2	0.2	NUM
ap-10175	12	34	,	,	PUNCT
ap-10175	12	35	dispersion	dispersion	NOUN
ap-10175	12	36	occurs	occur	VERB
ap-10175	12	37	at	at	ADP
ap-10175	12	38	a	a	DET
ap-10175	12	39	higher	high	ADJ
ap-10175	12	40	wavenumber	wavenumber	NOUN
ap-10175	12	41	of	of	ADP
ap-10175	12	42	5.8	5.8	NUM
ap-10175	12	43	,	,	PUNCT
ap-10175	12	44	demonstrating	demonstrate	VERB
ap-10175	12	45	that	that	SCONJ
ap-10175	12	46	increasing	increase	VERB
ap-10175	12	47	vapour	vapour	PRON
ap-10175	12	48	quality	quality	NOUN
ap-10175	12	49	delays	delay	NOUN
ap-10175	12	50	the	the	DET
ap-10175	12	51	onset	onset	NOUN
ap-10175	12	52	of	of	ADP
ap-10175	12	53	dispersion	dispersion	NOUN
ap-10175	12	54	.	.	PUNCT
ap-10175	13	1	this	this	DET
ap-10175	13	2	work	work	NOUN
ap-10175	13	3	contributes	contribute	VERB
ap-10175	13	4	to	to	ADP
ap-10175	13	5	a	a	DET
ap-10175	13	6	better	well	ADJ
ap-10175	13	7	understanding	understanding	NOUN
ap-10175	13	8	of	of	ADP
ap-10175	13	9	wave	wave	NOUN
ap-10175	13	10	propagation	propagation	NOUN
ap-10175	13	11	in	in	ADP
ap-10175	13	12	a	a	DET
ap-10175	13	13	two	two	NUM
ap-10175	13	14	-	-	PUNCT
ap-10175	13	15	phase	phase	NOUN
ap-10175	13	16	flow	flow	NOUN
ap-10175	13	17	.	.	PUNCT
ap-10175	14	1	keywords	keyword	NOUN
ap-10175	14	2	:	:	PUNCT
ap-10175	14	3	wave	wave	NOUN
ap-10175	14	4	propagation	propagation	NOUN
ap-10175	14	5	,	,	PUNCT
ap-10175	14	6	phase	phase	NOUN
ap-10175	14	7	velocity	velocity	NOUN
ap-10175	14	8	,	,	PUNCT
ap-10175	14	9	group	group	NOUN
ap-10175	14	10	velocity	velocity	NOUN
ap-10175	14	11	,	,	PUNCT
ap-10175	14	12	two	two	NUM
ap-10175	14	13	phase	phase	NOUN
ap-10175	14	14	,	,	PUNCT
ap-10175	14	15	natural	natural	ADJ
ap-10175	14	16	frequency	frequency	NOUN
ap-10175	14	17	.	.	PUNCT
ap-10175	15	1	1	1	X
ap-10175	15	2	.	.	X
ap-10175	15	3	introduction	introduction	NOUN
ap-10175	15	4	numerous	numerous	ADJ
ap-10175	15	5	industries	industry	NOUN
ap-10175	15	6	,	,	PUNCT
ap-10175	15	7	including	include	VERB
ap-10175	15	8	the	the	DET
ap-10175	15	9	production	production	NOUN
ap-10175	15	10	of	of	ADP
ap-10175	15	11	oil	oil	NOUN
ap-10175	15	12	and	and	CCONJ
ap-10175	15	13	gas	gas	NOUN
ap-10175	15	14	,	,	PUNCT
ap-10175	15	15	nuclear	nuclear	ADJ
ap-10175	15	16	and	and	CCONJ
ap-10175	15	17	thermal	thermal	ADJ
ap-10175	15	18	power	power	NOUN
ap-10175	15	19	plants	plant	NOUN
ap-10175	15	20	,	,	PUNCT
ap-10175	15	21	and	and	CCONJ
ap-10175	15	22	the	the	DET
ap-10175	15	23	food	food	NOUN
ap-10175	15	24	processing	processing	NOUN
ap-10175	15	25	industry	industry	NOUN
ap-10175	15	26	,	,	PUNCT
ap-10175	15	27	frequently	frequently	ADV
ap-10175	15	28	make	make	VERB
ap-10175	15	29	use	use	NOUN
ap-10175	15	30	of	of	ADP
ap-10175	15	31	pipes	pipe	NOUN
ap-10175	15	32	in	in	ADP
ap-10175	15	33	conveying	convey	VERB
ap-10175	15	34	their	their	PRON
ap-10175	15	35	product	product	NOUN
ap-10175	15	36	from	from	ADP
ap-10175	15	37	one	one	NUM
ap-10175	15	38	point	point	NOUN
ap-10175	15	39	to	to	ADP
ap-10175	15	40	another	another	PRON
ap-10175	15	41	[	[	X
ap-10175	15	42	1–4	1–4	NOUN
ap-10175	15	43	]	]	X
ap-10175	15	44	.	.	PUNCT
ap-10175	16	1	oftentimes	oftentime	NOUN
ap-10175	16	2	,	,	PUNCT
ap-10175	16	3	these	these	DET
ap-10175	16	4	pipes	pipe	NOUN
ap-10175	16	5	convey	convey	VERB
ap-10175	16	6	more	more	ADJ
ap-10175	16	7	than	than	ADP
ap-10175	16	8	one	one	NUM
ap-10175	16	9	fluid	fluid	NOUN
ap-10175	16	10	;	;	PUNCT
ap-10175	16	11	hence	hence	ADV
ap-10175	16	12	multiphase	multiphase	NOUN
ap-10175	16	13	flow	flow	NOUN
ap-10175	16	14	occurs	occur	VERB
ap-10175	16	15	in	in	ADP
ap-10175	16	16	these	these	DET
ap-10175	16	17	pipes	pipe	NOUN
ap-10175	17	1	[	[	X
ap-10175	17	2	2	2	NUM
ap-10175	17	3	,	,	PUNCT
ap-10175	17	4	5–7	5–7	NOUN
ap-10175	17	5	]	]	PUNCT
ap-10175	17	6	.	.	PUNCT
ap-10175	18	1	many	many	ADJ
ap-10175	18	2	researchers	researcher	NOUN
ap-10175	18	3	have	have	AUX
ap-10175	18	4	investigated	investigate	VERB
ap-10175	18	5	the	the	DET
ap-10175	18	6	dynamics	dynamic	NOUN
ap-10175	18	7	of	of	ADP
ap-10175	18	8	these	these	DET
ap-10175	18	9	flows	flow	NOUN
ap-10175	18	10	and	and	CCONJ
ap-10175	18	11	proposed	propose	VERB
ap-10175	18	12	methods	method	NOUN
ap-10175	18	13	for	for	ADP
ap-10175	18	14	attenuating	attenuate	VERB
ap-10175	18	15	challenges	challenge	NOUN
ap-10175	18	16	arising	arise	VERB
ap-10175	18	17	from	from	ADP
ap-10175	18	18	such	such	ADJ
ap-10175	18	19	multiphase	multiphase	NOUN
ap-10175	18	20	transport	transport	NOUN
ap-10175	18	21	[	[	X
ap-10175	18	22	5	5	NUM
ap-10175	18	23	,	,	PUNCT
ap-10175	18	24	8–12	8–12	NOUN
ap-10175	18	25	]	]	PUNCT
ap-10175	18	26	.	.	PUNCT
ap-10175	19	1	in	in	ADP
ap-10175	19	2	the	the	DET
ap-10175	19	3	analysis	analysis	NOUN
ap-10175	19	4	of	of	ADP
ap-10175	19	5	these	these	DET
ap-10175	19	6	pipes	pipe	NOUN
ap-10175	19	7	,	,	PUNCT
ap-10175	19	8	various	various	ADJ
ap-10175	19	9	methods	method	NOUN
ap-10175	19	10	and	and	CCONJ
ap-10175	19	11	solutions	solution	NOUN
ap-10175	19	12	have	have	AUX
ap-10175	19	13	been	be	AUX
ap-10175	19	14	used	use	VERB
ap-10175	19	15	to	to	PART
ap-10175	19	16	study	study	VERB
ap-10175	19	17	the	the	DET
ap-10175	19	18	dynamics	dynamic	NOUN
ap-10175	19	19	of	of	ADP
ap-10175	19	20	vibrations	vibration	NOUN
ap-10175	19	21	in	in	ADP
ap-10175	19	22	these	these	DET
ap-10175	19	23	systems	system	NOUN
ap-10175	19	24	.	.	PUNCT
ap-10175	20	1	nonlinear	nonlinear	ADJ
ap-10175	20	2	vibration	vibration	NOUN
ap-10175	20	3	of	of	ADP
ap-10175	20	4	fluid	fluid	NOUN
ap-10175	20	5	-	-	PUNCT
ap-10175	20	6	conveying	convey	VERB
ap-10175	20	7	pipes	pipe	NOUN
ap-10175	20	8	can	can	AUX
ap-10175	20	9	be	be	AUX
ap-10175	20	10	analysed	analyse	VERB
ap-10175	20	11	using	use	VERB
ap-10175	20	12	galerkin	galerkin	ADJ
ap-10175	20	13	discretization	discretization	NOUN
ap-10175	21	1	[	[	X
ap-10175	21	2	13	13	NUM
ap-10175	21	3	,	,	PUNCT
ap-10175	21	4	14	14	NUM
ap-10175	21	5	]	]	PUNCT
ap-10175	21	6	,	,	PUNCT
ap-10175	21	7	numerical	numerical	PROPN
ap-10175	21	8	tool	tool	PROPN
ap-10175	21	9	ansys	ansys	PROPN
ap-10175	22	1	[	[	X
ap-10175	22	2	15	15	NUM
ap-10175	22	3	]	]	PUNCT
ap-10175	22	4	,	,	PUNCT
ap-10175	22	5	finite	finite	PROPN
ap-10175	22	6	element	element	NOUN
ap-10175	22	7	method	method	NOUN
ap-10175	22	8	[	[	X
ap-10175	22	9	8	8	NUM
ap-10175	22	10	,	,	PUNCT
ap-10175	22	11	9	9	NUM
ap-10175	22	12	]	]	PUNCT
ap-10175	22	13	,	,	PUNCT
ap-10175	22	14	wave	wave	NOUN
ap-10175	22	15	method	method	NOUN
ap-10175	22	16	approach	approach	NOUN
ap-10175	22	17	[	[	X
ap-10175	22	18	1	1	NUM
ap-10175	22	19	,	,	PUNCT
ap-10175	22	20	16	16	NUM
ap-10175	22	21	]	]	PUNCT
ap-10175	22	22	,	,	PUNCT
ap-10175	22	23	differential	differential	ADJ
ap-10175	22	24	transformation	transformation	NOUN
ap-10175	22	25	method	method	NOUN
ap-10175	23	1	[	[	X
ap-10175	23	2	17	17	NUM
ap-10175	23	3	]	]	PUNCT
ap-10175	23	4	,	,	PUNCT
ap-10175	23	5	transfer	transfer	NOUN
ap-10175	23	6	matrix	matrix	NOUN
ap-10175	23	7	method	method	NOUN
ap-10175	23	8	(	(	PUNCT
ap-10175	23	9	tmm	tmm	NOUN
ap-10175	23	10	)	)	PUNCT
ap-10175	24	1	[	[	X
ap-10175	24	2	18	18	NUM
ap-10175	24	3	,	,	PUNCT
ap-10175	24	4	19	19	NUM
ap-10175	24	5	]	]	PUNCT
ap-10175	24	6	,	,	PUNCT
ap-10175	24	7	and	and	CCONJ
ap-10175	24	8	differential	differential	ADJ
ap-10175	24	9	quadrature	quadrature	NOUN
ap-10175	24	10	method	method	NOUN
ap-10175	24	11	(	(	PUNCT
ap-10175	24	12	dqm	dqm	NOUN
ap-10175	24	13	)	)	PUNCT
ap-10175	24	14	[	[	X
ap-10175	24	15	20	20	NUM
ap-10175	24	16	]	]	PUNCT
ap-10175	24	17	.	.	PUNCT
ap-10175	25	1	wave	wave	NOUN
ap-10175	25	2	propagation	propagation	NOUN
ap-10175	25	3	approach	approach	NOUN
ap-10175	25	4	was	be	AUX
ap-10175	25	5	used	use	VERB
ap-10175	25	6	to	to	PART
ap-10175	25	7	analyse	analyse	VERB
ap-10175	25	8	finite	finite	ADJ
ap-10175	25	9	cylindrical	cylindrical	ADJ
ap-10175	25	10	pipes	pipe	NOUN
ap-10175	25	11	that	that	PRON
ap-10175	25	12	convey	convey	VERB
ap-10175	25	13	dense	dense	ADJ
ap-10175	25	14	fluids	fluid	NOUN
ap-10175	25	15	[	[	X
ap-10175	25	16	21	21	NUM
ap-10175	25	17	]	]	PUNCT
ap-10175	25	18	.	.	PUNCT
ap-10175	26	1	he	he	PRON
ap-10175	26	2	proved	prove	VERB
ap-10175	26	3	that	that	SCONJ
ap-10175	26	4	the	the	DET
ap-10175	26	5	fundamental	fundamental	ADJ
ap-10175	26	6	frequency	frequency	NOUN
ap-10175	26	7	transition	transition	NOUN
ap-10175	26	8	between	between	ADP
ap-10175	26	9	circumferential	circumferential	ADJ
ap-10175	26	10	modes	mode	NOUN
ap-10175	26	11	happens	happen	VERB
ap-10175	26	12	at	at	ADP
ap-10175	26	13	various	various	ADJ
ap-10175	26	14	height	height	NOUN
ap-10175	26	15	-	-	PUNCT
ap-10175	26	16	radius	radius	NOUN
ap-10175	26	17	ratios	ratio	NOUN
ap-10175	26	18	for	for	ADP
ap-10175	26	19	various	various	ADJ
ap-10175	26	20	boundary	boundary	ADJ
ap-10175	26	21	conditions	condition	NOUN
ap-10175	26	22	.	.	PUNCT
ap-10175	27	1	in	in	ADP
ap-10175	27	2	addition	addition	NOUN
ap-10175	27	3	,	,	PUNCT
ap-10175	27	4	wave	wave	NOUN
ap-10175	27	5	propagation	propagation	NOUN
ap-10175	27	6	and	and	CCONJ
ap-10175	27	7	band	band	NOUN
ap-10175	27	8	gap	gap	NOUN
ap-10175	27	9	properties	property	NOUN
ap-10175	27	10	of	of	ADP
ap-10175	27	11	long	long	ADJ
ap-10175	27	12	fluid	fluid	NOUN
ap-10175	27	13	-	-	PUNCT
ap-10175	27	14	conveying	convey	VERB
ap-10175	27	15	pipes	pipe	NOUN
ap-10175	27	16	was	be	AUX
ap-10175	27	17	investigated	investigate	VERB
ap-10175	27	18	[	[	PUNCT
ap-10175	27	19	22	22	NUM
ap-10175	27	20	]	]	PUNCT
ap-10175	27	21	.	.	PUNCT
ap-10175	28	1	in	in	ADP
ap-10175	28	2	the	the	DET
ap-10175	28	3	first	first	ADJ
ap-10175	28	4	part	part	NOUN
ap-10175	28	5	of	of	ADP
ap-10175	28	6	the	the	DET
ap-10175	28	7	work	work	NOUN
ap-10175	28	8	,	,	PUNCT
ap-10175	28	9	the	the	DET
ap-10175	28	10	traveling	travel	VERB
ap-10175	28	11	wave	wave	NOUN
ap-10175	28	12	characteristics	characteristic	NOUN
ap-10175	28	13	of	of	ADP
ap-10175	28	14	axially	axially	ADV
ap-10175	28	15	moving	move	VERB
ap-10175	28	16	structures	structure	NOUN
ap-10175	28	17	was	be	AUX
ap-10175	28	18	used	use	VERB
ap-10175	28	19	to	to	PART
ap-10175	28	20	derive	derive	VERB
ap-10175	28	21	the	the	DET
ap-10175	28	22	dispersion	dispersion	NOUN
ap-10175	28	23	relation	relation	NOUN
ap-10175	28	24	of	of	ADP
ap-10175	28	25	the	the	DET
ap-10175	28	26	corresponding	corresponding	ADJ
ap-10175	28	27	time	time	NOUN
ap-10175	28	28	-	-	PUNCT
ap-10175	28	29	variant	variant	ADJ
ap-10175	28	30	uniform	uniform	ADJ
ap-10175	28	31	pipe	pipe	NOUN
ap-10175	28	32	system	system	NOUN
ap-10175	28	33	.	.	PUNCT
ap-10175	29	1	the	the	DET
ap-10175	29	2	second	second	ADJ
ap-10175	29	3	section	section	NOUN
ap-10175	29	4	illustrated	illustrate	VERB
ap-10175	29	5	the	the	DET
ap-10175	29	6	significant	significant	ADJ
ap-10175	29	7	effects	effect	NOUN
ap-10175	29	8	of	of	ADP
ap-10175	29	9	flow	flow	NOUN
ap-10175	29	10	velocity	velocity	NOUN
ap-10175	29	11	and	and	CCONJ
ap-10175	29	12	deploying	deploy	VERB
ap-10175	29	13	speed	speed	NOUN
ap-10175	29	14	,	,	PUNCT
ap-10175	29	15	propagating	propagate	VERB
ap-10175	29	16	and	and	CCONJ
ap-10175	29	17	evanescent	evanescent	NOUN
ap-10175	29	18	waves	wave	NOUN
ap-10175	29	19	,	,	PUNCT
ap-10175	29	20	as	as	ADV
ap-10175	29	21	well	well	ADV
ap-10175	29	22	as	as	ADP
ap-10175	29	23	the	the	DET
ap-10175	29	24	phase	phase	NOUN
ap-10175	29	25	velocity	velocity	NOUN
ap-10175	29	26	and	and	CCONJ
ap-10175	29	27	group	group	NOUN
ap-10175	29	28	velocity	velocity	NOUN
ap-10175	29	29	of	of	ADP
ap-10175	29	30	propagating	propagate	VERB
ap-10175	29	31	waves	wave	NOUN
ap-10175	29	32	.	.	PUNCT
ap-10175	30	1	the	the	DET
ap-10175	30	2	dynamics	dynamic	NOUN
ap-10175	30	3	of	of	ADP
ap-10175	30	4	the	the	DET
ap-10175	30	5	fluid	fluid	NOUN
ap-10175	30	6	-	-	PUNCT
ap-10175	30	7	conveying	convey	VERB
ap-10175	30	8	pipe	pipe	NOUN
ap-10175	30	9	with	with	ADP
ap-10175	30	10	functionally	functionally	ADV
ap-10175	30	11	graded	grade	VERB
ap-10175	30	12	(	(	PUNCT
ap-10175	30	13	fg	fg	NOUN
ap-10175	30	14	)	)	PUNCT
ap-10175	30	15	materials	material	NOUN
ap-10175	30	16	were	be	AUX
ap-10175	30	17	explored	explore	VERB
ap-10175	30	18	[	[	PUNCT
ap-10175	30	19	16	16	NUM
ap-10175	30	20	]	]	PUNCT
ap-10175	30	21	.	.	PUNCT
ap-10175	31	1	in	in	ADP
ap-10175	31	2	this	this	DET
ap-10175	31	3	work	work	NOUN
ap-10175	31	4	,	,	PUNCT
ap-10175	31	5	the	the	DET
ap-10175	31	6	propagation	propagation	NOUN
ap-10175	31	7	characteristics	characteristic	NOUN
ap-10175	31	8	of	of	ADP
ap-10175	31	9	longitudinal	longitudinal	ADJ
ap-10175	31	10	and	and	CCONJ
ap-10175	31	11	flexural	flexural	ADJ
ap-10175	31	12	waves	wave	NOUN
ap-10175	31	13	in	in	ADP
ap-10175	31	14	the	the	DET
ap-10175	31	15	fluid	fluid	NOUN
ap-10175	31	16	-	-	PUNCT
ap-10175	31	17	conveying	convey	VERB
ap-10175	31	18	pipes	pipe	NOUN
ap-10175	31	19	were	be	AUX
ap-10175	31	20	studied	study	VERB
ap-10175	31	21	.	.	PUNCT
ap-10175	32	1	it	it	PRON
ap-10175	32	2	was	be	AUX
ap-10175	32	3	found	find	VERB
ap-10175	32	4	that	that	SCONJ
ap-10175	32	5	the	the	DET
ap-10175	32	6	temperature	temperature	NOUN
ap-10175	32	7	and	and	CCONJ
ap-10175	32	8	functional	functional	ADJ
ap-10175	32	9	gradient	gradient	NOUN
ap-10175	32	10	exponent	exponent	NOUN
ap-10175	32	11	decrease	decrease	NOUN
ap-10175	32	12	the	the	DET
ap-10175	32	13	phase	phase	NOUN
ap-10175	32	14	and	and	CCONJ
ap-10175	32	15	group	group	NOUN
ap-10175	32	16	velocities	velocity	NOUN
ap-10175	32	17	.	.	PUNCT
ap-10175	33	1	on	on	ADP
ap-10175	33	2	the	the	DET
ap-10175	33	3	contrary	contrary	NOUN
ap-10175	33	4	,	,	PUNCT
ap-10175	33	5	the	the	DET
ap-10175	33	6	liquid	liquid	ADJ
ap-10175	33	7	flow	flow	NOUN
ap-10175	33	8	velocity	velocity	NOUN
ap-10175	33	9	increases	increase	VERB
ap-10175	33	10	the	the	DET
ap-10175	33	11	phase	phase	NOUN
ap-10175	33	12	and	and	CCONJ
ap-10175	33	13	group	group	NOUN
ap-10175	33	14	velocities	velocity	NOUN
ap-10175	33	15	.	.	PUNCT
ap-10175	34	1	it	it	PRON
ap-10175	34	2	appears	appear	VERB
ap-10175	34	3	that	that	SCONJ
ap-10175	34	4	there	there	PRON
ap-10175	34	5	are	be	VERB
ap-10175	34	6	relatively	relatively	ADV
ap-10175	34	7	fewer	few	ADJ
ap-10175	34	8	works	work	NOUN
ap-10175	34	9	in	in	ADP
ap-10175	34	10	the	the	DET
ap-10175	34	11	literature	literature	NOUN
ap-10175	34	12	on	on	ADP
ap-10175	34	13	wave	wave	NOUN
ap-10175	34	14	propagation	propagation	NOUN
ap-10175	34	15	for	for	ADP
ap-10175	34	16	a	a	DET
ap-10175	34	17	two	two	NUM
ap-10175	34	18	phase	phase	NOUN
ap-10175	34	19	flow	flow	NOUN
ap-10175	34	20	in	in	ADP
ap-10175	34	21	pipes	pipe	NOUN
ap-10175	34	22	.	.	PUNCT
ap-10175	35	1	in	in	ADP
ap-10175	35	2	order	order	NOUN
ap-10175	35	3	to	to	PART
ap-10175	35	4	properly	properly	ADV
ap-10175	35	5	address	address	VERB
ap-10175	35	6	this	this	DET
ap-10175	35	7	lacuna	lacuna	NOUN
ap-10175	35	8	in	in	ADP
ap-10175	35	9	literature	literature	NOUN
ap-10175	35	10	,	,	PUNCT
ap-10175	35	11	the	the	DET
ap-10175	35	12	present	present	ADJ
ap-10175	35	13	study	study	NOUN
ap-10175	35	14	aims	aim	VERB
ap-10175	35	15	to	to	PART
ap-10175	35	16	show	show	VERB
ap-10175	35	17	that	that	SCONJ
ap-10175	35	18	the	the	DET
ap-10175	35	19	dynamics	dynamic	NOUN
ap-10175	35	20	of	of	ADP
ap-10175	35	21	a	a	DET
ap-10175	35	22	pipe	pipe	NOUN
ap-10175	35	23	conveying	convey	VERB
ap-10175	35	24	a	a	DET
ap-10175	35	25	two	two	NUM
ap-10175	35	26	phase	phase	NOUN
ap-10175	35	27	flow	flow	NOUN
ap-10175	35	28	can	can	AUX
ap-10175	35	29	be	be	AUX
ap-10175	35	30	analysed	analyse	VERB
ap-10175	35	31	by	by	ADP
ap-10175	35	32	the	the	DET
ap-10175	35	33	elastic	elastic	ADJ
ap-10175	35	34	wave	wave	NOUN
ap-10175	35	35	propagation	propagation	NOUN
ap-10175	35	36	.	.	PUNCT
ap-10175	36	1	the	the	DET
ap-10175	36	2	characteristics	characteristic	NOUN
ap-10175	36	3	of	of	ADP
ap-10175	36	4	flexural	flexural	ADJ
ap-10175	36	5	waves	wave	NOUN
ap-10175	36	6	in	in	ADP
ap-10175	36	7	the	the	DET
ap-10175	36	8	conveying	convey	VERB
ap-10175	36	9	fluid	fluid	ADJ
ap-10175	36	10	pipes	pipe	NOUN
ap-10175	36	11	are	be	AUX
ap-10175	36	12	studied	study	VERB
ap-10175	36	13	.	.	PUNCT
ap-10175	37	1	334	334	NUM
ap-10175	37	2	https://doi.org/10.14311/ap.2025.65.0334	https://doi.org/10.14311/ap.2025.65.0334	NOUN
ap-10175	37	3	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-10175	37	4	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-10175	37	5	vol	vol	NOUN
ap-10175	37	6	.	.	PROPN
ap-10175	38	1	65	65	NUM
ap-10175	38	2	no	no	NOUN
ap-10175	38	3	.	.	PUNCT
ap-10175	39	1	3/2025	3/2025	NUM
ap-10175	39	2	wave	wave	NOUN
ap-10175	39	3	propagation	propagation	NOUN
ap-10175	39	4	in	in	ADP
ap-10175	39	5	a	a	DET
ap-10175	39	6	pipe	pipe	NOUN
ap-10175	39	7	conveying	convey	VERB
ap-10175	39	8	two	two	NUM
ap-10175	39	9	phase	phase	NOUN
ap-10175	39	10	flow	flow	NOUN
ap-10175	39	11	figure	figure	NOUN
ap-10175	39	12	1	1	NUM
ap-10175	39	13	.	.	PUNCT
ap-10175	39	14	mechanical	mechanical	ADJ
ap-10175	39	15	model	model	NOUN
ap-10175	39	16	of	of	ADP
ap-10175	39	17	a	a	DET
ap-10175	39	18	pipe	pipe	NOUN
ap-10175	39	19	conveying	convey	VERB
ap-10175	39	20	two	two	NUM
ap-10175	39	21	phase	phase	NOUN
ap-10175	39	22	flow	flow	NOUN
ap-10175	39	23	.	.	PUNCT
ap-10175	40	1	2	2	X
ap-10175	40	2	.	.	X
ap-10175	40	3	derivation	derivation	NOUN
ap-10175	40	4	of	of	ADP
ap-10175	40	5	the	the	DET
ap-10175	40	6	equation	equation	NOUN
ap-10175	40	7	of	of	ADP
ap-10175	40	8	motion	motion	NOUN
ap-10175	40	9	the	the	DET
ap-10175	40	10	system	system	NOUN
ap-10175	40	11	under	under	ADP
ap-10175	40	12	consideration	consideration	NOUN
ap-10175	40	13	consists	consist	VERB
ap-10175	40	14	of	of	ADP
ap-10175	40	15	a	a	DET
ap-10175	40	16	pipe	pipe	NOUN
ap-10175	40	17	conveying	convey	VERB
ap-10175	40	18	a	a	DET
ap-10175	40	19	two	two	NUM
ap-10175	40	20	phase	phase	NOUN
ap-10175	40	21	flow	flow	NOUN
ap-10175	40	22	(	(	PUNCT
ap-10175	40	23	figure	figure	NOUN
ap-10175	40	24	1	1	NUM
ap-10175	40	25	)	)	PUNCT
ap-10175	40	26	.	.	PUNCT
ap-10175	41	1	the	the	DET
ap-10175	41	2	governing	govern	VERB
ap-10175	41	3	equation	equation	NOUN
ap-10175	41	4	in	in	ADP
ap-10175	41	5	transverse	transverse	NOUN
ap-10175	41	6	direction	direction	NOUN
ap-10175	41	7	is	be	AUX
ap-10175	41	8	given	give	VERB
ap-10175	41	9	as	as	ADP
ap-10175	41	10	[	[	X
ap-10175	41	11	6	6	NUM
ap-10175	41	12	,	,	PUNCT
ap-10175	41	13	23	23	NUM
ap-10175	41	14	]	]	PUNCT
ap-10175	41	15	:	:	PUNCT
ap-10175	41	16	(	(	PUNCT
ap-10175	41	17	mp	mp	NOUN
ap-10175	41	18	+	+	CCONJ
ap-10175	41	19	ml	ml	X
ap-10175	42	1	+	+	ADJ
ap-10175	42	2	mg	mg	NOUN
ap-10175	42	3	)	)	PUNCT
ap-10175	42	4	¨̄w	¨̄w	NOUN
ap-10175	43	1	+	+	CCONJ
ap-10175	43	2	2(mlv̄l	2(mlv̄l	NUM
ap-10175	43	3	+	+	NOUN
ap-10175	43	4	mgv̄g	mgv̄g	NUM
ap-10175	43	5	)	)	PUNCT
ap-10175	43	6	˙̄w′	˙̄w′	PUNCT
ap-10175	44	1	+	+	CCONJ
ap-10175	44	2	(	(	PUNCT
ap-10175	44	3	mlv̄2	mlv̄2	ADJ
ap-10175	44	4	l	l	NOUN
ap-10175	44	5	+	+	CCONJ
ap-10175	44	6	mgv̄2	mgv̄2	ADJ
ap-10175	44	7	g)w̄′′	g)w̄′′	NOUN
ap-10175	44	8	+	+	CCONJ
ap-10175	44	9	eiw̄iv	eiw̄iv	PROPN
ap-10175	44	10	−	−	NOUN
ap-10175	44	11	ei(2w̄′2w̄iv	ei(2w̄′2w̄iv	NOUN
ap-10175	44	12	+	+	NUM
ap-10175	44	13	8w̄′w̄′′w̄′′′	8w̄′w̄′′w̄′′′	NUM
ap-10175	44	14	+	+	SYM
ap-10175	44	15	2w̄′′w̄′′w̄′′	2w̄′′w̄′′w̄′′	NUM
ap-10175	44	16	)	)	PUNCT
ap-10175	44	17	−	−	PROPN
ap-10175	45	1	ea	ea	NOUN
ap-10175	45	2	(	(	PUNCT
ap-10175	45	3	3	3	NUM
ap-10175	45	4	2	2	NUM
ap-10175	45	5	w̄′2(w̄′′	w̄′2(w̄′′	NOUN
ap-10175	45	6	+	+	CCONJ
ap-10175	45	7	ȳ	ȳ	PROPN
ap-10175	45	8	′′	′′	PROPN
ap-10175	45	9	0	0	NUM
ap-10175	45	10	)	)	PUNCT
ap-10175	46	1	+	+	CCONJ
ap-10175	46	2	3w̄′w̄′′ȳ	3w̄′w̄′′ȳ	NUM
ap-10175	46	3	′	′	NUM
ap-10175	46	4	0	0	NUM
ap-10175	47	1	+	+	CCONJ
ap-10175	47	2	ȳ	ȳ	ADJ
ap-10175	47	3	′2	′2	X
ap-10175	47	4	0	0	NUM
ap-10175	47	5	w̄′′	w̄′′	PROPN
ap-10175	47	6	+2ȳ	+2ȳ	PROPN
ap-10175	48	1	′	′	NOUN
ap-10175	48	2	0	0	NUM
ap-10175	49	1	ȳ	ȳ	PROPN
ap-10175	49	2	′′	′′	PROPN
ap-10175	49	3	0	0	PUNCT
ap-10175	49	4	w̄′	w̄′	PROPN
ap-10175	49	5	−	−	PROPN
ap-10175	49	6	αθ̄′(w̄′	αθ̄′(w̄′	PROPN
ap-10175	50	1	+	+	CCONJ
ap-10175	50	2	ȳ	ȳ	NUM
ap-10175	50	3	′	′	NUM
ap-10175	50	4	0	0	NUM
ap-10175	50	5	)	)	PUNCT
ap-10175	51	1	+	+	CCONJ
ap-10175	51	2	(	(	PUNCT
ap-10175	51	3	t̄	t̄	PROPN
ap-10175	51	4	ea	ea	PROPN
ap-10175	51	5	−	−	NOUN
ap-10175	51	6	p̄	p̄	PROPN
ap-10175	51	7	e	e	PROPN
ap-10175	51	8	)	)	PUNCT
ap-10175	51	9	(	(	PUNCT
ap-10175	51	10	w̄′′	w̄′′	NOUN
ap-10175	51	11	+	+	CCONJ
ap-10175	51	12	ȳ	ȳ	PROPN
ap-10175	51	13	′′	′′	PROPN
ap-10175	51	14	0	0	NUM
ap-10175	51	15	)	)	PUNCT
ap-10175	52	1	−αθ̄(w̄′′	−αθ̄(w̄′′	NOUN
ap-10175	53	1	+	+	CCONJ
ap-10175	53	2	ȳ	ȳ	PROPN
ap-10175	53	3	′′	′′	PROPN
ap-10175	53	4	0	0	NUM
ap-10175	53	5	)	)	PUNCT
ap-10175	53	6	)	)	PUNCT
ap-10175	54	1	=	=	SYM
ap-10175	54	2	0	0	PUNCT
ap-10175	54	3	(	(	PUNCT
ap-10175	54	4	1	1	NUM
ap-10175	54	5	)	)	PUNCT
ap-10175	54	6	2.1	2.1	NUM
ap-10175	54	7	.	.	PUNCT
ap-10175	55	1	dimensionless	dimensionless	NOUN
ap-10175	55	2	quantities	quantity	NOUN
ap-10175	55	3	introducing	introduce	VERB
ap-10175	55	4	dimensionless	dimensionless	ADJ
ap-10175	55	5	quantities	quantity	NOUN
ap-10175	55	6	:	:	PUNCT
ap-10175	55	7	w̄	w̄	X
ap-10175	55	8	=	=	SYM
ap-10175	55	9	wr	wr	X
ap-10175	55	10	,	,	PUNCT
ap-10175	55	11	ū	ū	NOUN
ap-10175	55	12	=	=	SYM
ap-10175	55	13	ul	ul	INTJ
ap-10175	55	14	,	,	PUNCT
ap-10175	55	15	x̄	x̄	PUNCT
ap-10175	55	16	=	=	SYM
ap-10175	55	17	xl	xl	PROPN
ap-10175	55	18	,	,	PUNCT
ap-10175	55	19	ȳ0	ȳ0	PUNCT
ap-10175	55	20	=	=	SYM
ap-10175	55	21	y0r	y0r	PROPN
ap-10175	55	22	,	,	PUNCT
ap-10175	55	23	t̄	t̄	PROPN
ap-10175	55	24	=	=	SYM
ap-10175	55	25	t	t	PROPN
ap-10175	55	26	√	√	PROPN
ap-10175	55	27	mp	mp	PROPN
ap-10175	56	1	+	+	CCONJ
ap-10175	56	2	ml	ml	PROPN
ap-10175	57	1	+	+	CCONJ
ap-10175	57	2	mg	mg	NOUN
ap-10175	57	3	ei	ei	NOUN
ap-10175	57	4	l2	l2	PROPN
ap-10175	57	5	,	,	PUNCT
ap-10175	57	6	t̄	t̄	PROPN
ap-10175	57	7	=	=	SYM
ap-10175	57	8	t	t	PROPN
ap-10175	57	9	ei	ei	NOUN
ap-10175	57	10	l2	l2	NOUN
ap-10175	57	11	,	,	PUNCT
ap-10175	57	12	p̄	p̄	NOUN
ap-10175	58	1	=	=	PRON
ap-10175	59	1	p	p	NOUN
ap-10175	59	2	ei	ei	X
ap-10175	59	3	al2	al2	PROPN
ap-10175	59	4	,	,	PUNCT
ap-10175	59	5	θ̄	θ̄	ADJ
ap-10175	59	6	=	=	SYM
ap-10175	59	7	θ	θ	NOUN
ap-10175	60	1	i	i	PRON
ap-10175	60	2	αal2	αal2	PROPN
ap-10175	60	3	,	,	PUNCT
ap-10175	60	4	v̄l	v̄l	PROPN
ap-10175	60	5	=	=	SYM
ap-10175	60	6	vl	vl	PROPN
ap-10175	60	7	√	√	INTJ
ap-10175	60	8	ei	ei	INTJ
ap-10175	60	9	ml	ml	NOUN
ap-10175	60	10	1	1	NUM
ap-10175	60	11	l	l	NOUN
ap-10175	60	12	,	,	PUNCT
ap-10175	60	13	v̄g	v̄g	NOUN
ap-10175	60	14	=	=	NOUN
ap-10175	60	15	vg	vg	NOUN
ap-10175	60	16	√	√	NUM
ap-10175	60	17	ei	ei	NOUN
ap-10175	60	18	mg	mg	PROPN
ap-10175	60	19	1	1	NUM
ap-10175	60	20	l	l	NOUN
ap-10175	60	21	,	,	PUNCT
ap-10175	60	22	(	(	PUNCT
ap-10175	60	23	2	2	NUM
ap-10175	60	24	)	)	PUNCT
ap-10175	60	25	and	and	CCONJ
ap-10175	60	26	these	these	DET
ap-10175	60	27	terms	term	NOUN
ap-10175	60	28	are	be	AUX
ap-10175	60	29	defined	define	VERB
ap-10175	60	30	:	:	PUNCT
ap-10175	60	31	βl	βl	NOUN
ap-10175	60	32	=	=	PUNCT
ap-10175	60	33	ml	ml	PART
ap-10175	60	34	mp	mp	NOUN
ap-10175	61	1	+	+	CCONJ
ap-10175	61	2	ml	ml	PROPN
ap-10175	62	1	+	+	CCONJ
ap-10175	62	2	mg	mg	ADJ
ap-10175	62	3	,	,	PUNCT
ap-10175	62	4	βg	βg	ADV
ap-10175	62	5	=	=	PUNCT
ap-10175	62	6	mg	mg	NUM
ap-10175	62	7	mp	mp	PROPN
ap-10175	63	1	+	+	CCONJ
ap-10175	63	2	ml	ml	PROPN
ap-10175	64	1	+	+	CCONJ
ap-10175	64	2	mg	mg	PROPN
ap-10175	64	3	,	,	PUNCT
ap-10175	64	4	η	η	PROPN
ap-10175	64	5	=	=	PROPN
ap-10175	64	6	r	r	NOUN
ap-10175	64	7	l	l	NOUN
ap-10175	64	8	.	.	PUNCT
ap-10175	65	1	(	(	PUNCT
ap-10175	65	2	3	3	X
ap-10175	65	3	)	)	PUNCT
ap-10175	65	4	using	use	VERB
ap-10175	65	5	the	the	DET
ap-10175	65	6	dimensionless	dimensionless	NOUN
ap-10175	65	7	quantities	quantity	NOUN
ap-10175	65	8	defined	define	VERB
ap-10175	65	9	in	in	ADP
ap-10175	65	10	equation	equation	NOUN
ap-10175	65	11	(	(	PUNCT
ap-10175	65	12	2	2	NUM
ap-10175	65	13	)	)	PUNCT
ap-10175	65	14	,	,	PUNCT
ap-10175	65	15	the	the	DET
ap-10175	65	16	transverse	transverse	NOUN
ap-10175	65	17	vibration	vibration	NOUN
ap-10175	65	18	equation	equation	NOUN
ap-10175	65	19	(	(	PUNCT
ap-10175	65	20	1	1	X
ap-10175	65	21	)	)	PUNCT
ap-10175	65	22	becomes	become	VERB
ap-10175	65	23	:	:	PUNCT
ap-10175	65	24	ẅ	ẅ	X
ap-10175	66	1	+	+	CCONJ
ap-10175	66	2	2	2	NUM
ap-10175	66	3	(	(	PUNCT
ap-10175	66	4	vl	vl	INTJ
ap-10175	66	5	√	√	PROPN
ap-10175	66	6	βl	βl	NOUN
ap-10175	67	1	+	+	ADJ
ap-10175	67	2	vg	vg	NOUN
ap-10175	67	3	√	√	NUM
ap-10175	67	4	βg	βg	NOUN
ap-10175	67	5	)	)	PUNCT
ap-10175	67	6	ẇ′	ẇ′	NOUN
ap-10175	67	7	+	+	CCONJ
ap-10175	67	8	wiv	wiv	NOUN
ap-10175	67	9	+	+	CCONJ
ap-10175	67	10	(	(	PUNCT
ap-10175	67	11	v2	v2	NOUN
ap-10175	67	12	l	l	NOUN
ap-10175	67	13	+	+	CCONJ
ap-10175	67	14	v2	v2	NOUN
ap-10175	67	15	g	g	NOUN
ap-10175	67	16	−	−	PROPN
ap-10175	68	1	t	t	NOUN
ap-10175	69	1	+	+	CCONJ
ap-10175	69	2	p	p	X
ap-10175	69	3	+	+	NUM
ap-10175	69	4	θ	θ	NOUN
ap-10175	69	5	)	)	PUNCT
ap-10175	69	6	w′′	w′′	NOUN
ap-10175	69	7	−	−	PROPN
ap-10175	69	8	η2	η2	PROPN
ap-10175	69	9	(	(	PUNCT
ap-10175	69	10	2w′2wiv	2w′2wiv	NUM
ap-10175	69	11	+	+	CCONJ
ap-10175	69	12	8w′w′′w′′′	8w′w′′w′′′	NUM
ap-10175	69	13	+	+	NUM
ap-10175	69	14	2w′′w′′w′′	2w′′w′′w′′	NUM
ap-10175	69	15	)	)	PUNCT
ap-10175	69	16	−	−	NOUN
ap-10175	69	17	{	{	PUNCT
ap-10175	69	18	3	3	NUM
ap-10175	69	19	2w′2	2w′2	NUM
ap-10175	69	20	(	(	PUNCT
ap-10175	69	21	w′′	w′′	NOUN
ap-10175	69	22	+	+	CCONJ
ap-10175	69	23	y	y	PROPN
ap-10175	69	24	′′	′′	PROPN
ap-10175	69	25	0	0	NUM
ap-10175	69	26	)	)	PUNCT
ap-10175	70	1	+	+	CCONJ
ap-10175	70	2	3w′w′′y	3w′w′′y	ADJ
ap-10175	70	3	′	′	NOUN
ap-10175	70	4	0	0	PUNCT
ap-10175	71	1	+	+	ADV
ap-10175	71	2	y	y	PROPN
ap-10175	71	3	′	′	ADJ
ap-10175	71	4	0	0	NUM
ap-10175	71	5	2	2	NUM
ap-10175	71	6	w′′	w′′	NOUN
ap-10175	71	7	+	+	CCONJ
ap-10175	71	8	2y	2y	NUM
ap-10175	71	9	′	′	NUM
ap-10175	71	10	0y	0y	NUM
ap-10175	72	1	′′	′′	PROPN
ap-10175	72	2	0	0	NUM
ap-10175	72	3	w′	w′	NOUN
ap-10175	72	4	}	}	PUNCT
ap-10175	72	5	−	−	PROPN
ap-10175	73	1	(	(	PUNCT
ap-10175	73	2	t	t	PROPN
ap-10175	73	3	−	−	PROPN
ap-10175	73	4	p	p	NOUN
ap-10175	73	5	−	−	PROPN
ap-10175	73	6	θ	θ	PROPN
ap-10175	73	7	)	)	PUNCT
ap-10175	73	8	y	y	PROPN
ap-10175	73	9	′′	′′	PROPN
ap-10175	73	10	0	0	PUNCT
ap-10175	74	1	=	=	SYM
ap-10175	74	2	0	0	PROPN
ap-10175	74	3	.	.	PUNCT
ap-10175	75	1	(	(	PUNCT
ap-10175	75	2	4	4	NUM
ap-10175	75	3	)	)	PUNCT
ap-10175	75	4	for	for	ADP
ap-10175	75	5	a	a	DET
ap-10175	75	6	straight	straight	ADJ
ap-10175	75	7	pipe	pipe	NOUN
ap-10175	75	8	,	,	PUNCT
ap-10175	75	9	y0	y0	NOUN
ap-10175	75	10	=	=	SYM
ap-10175	75	11	0	0	NUM
ap-10175	75	12	,	,	PUNCT
ap-10175	75	13	and	and	CCONJ
ap-10175	75	14	η	η	PROPN
ap-10175	75	15	has	have	AUX
ap-10175	75	16	been	be	AUX
ap-10175	75	17	established	establish	VERB
ap-10175	75	18	to	to	PART
ap-10175	75	19	have	have	VERB
ap-10175	75	20	negligible	negligible	ADJ
ap-10175	75	21	effect	effect	NOUN
ap-10175	75	22	on	on	ADP
ap-10175	75	23	the	the	DET
ap-10175	75	24	dynamic	dynamic	ADJ
ap-10175	75	25	response	response	NOUN
ap-10175	75	26	of	of	ADP
ap-10175	75	27	the	the	DET
ap-10175	75	28	pipe	pipe	NOUN
ap-10175	75	29	conveying	convey	VERB
ap-10175	75	30	the	the	DET
ap-10175	75	31	fluid	fluid	NOUN
ap-10175	75	32	,	,	PUNCT
ap-10175	75	33	hence	hence	ADV
ap-10175	75	34	,	,	PUNCT
ap-10175	75	35	equation	equation	NOUN
ap-10175	75	36	(	(	PUNCT
ap-10175	75	37	4	4	X
ap-10175	75	38	)	)	PUNCT
ap-10175	75	39	becomes	become	VERB
ap-10175	75	40	:	:	PUNCT
ap-10175	75	41	ẅ	ẅ	X
ap-10175	76	1	+	+	CCONJ
ap-10175	76	2	2	2	NUM
ap-10175	76	3	(	(	PUNCT
ap-10175	76	4	vl	vl	INTJ
ap-10175	76	5	√	√	PROPN
ap-10175	76	6	βl	βl	NOUN
ap-10175	77	1	+	+	ADJ
ap-10175	77	2	vg	vg	NOUN
ap-10175	77	3	√	√	NUM
ap-10175	77	4	βg	βg	NOUN
ap-10175	77	5	)	)	PUNCT
ap-10175	77	6	ẇ′	ẇ′	NOUN
ap-10175	77	7	+	+	CCONJ
ap-10175	77	8	wiv	wiv	NOUN
ap-10175	77	9	+	+	CCONJ
ap-10175	77	10	(	(	PUNCT
ap-10175	77	11	v2	v2	NOUN
ap-10175	77	12	l	l	NOUN
ap-10175	77	13	+	+	CCONJ
ap-10175	77	14	v2	v2	NOUN
ap-10175	77	15	g	g	NOUN
ap-10175	77	16	−	−	PROPN
ap-10175	78	1	t	t	NOUN
ap-10175	79	1	+	+	CCONJ
ap-10175	79	2	p	p	X
ap-10175	79	3	+	+	NUM
ap-10175	79	4	θ	θ	NOUN
ap-10175	79	5	)	)	PUNCT
ap-10175	80	1	w′′	w′′	NOUN
ap-10175	80	2	−	−	PROPN
ap-10175	80	3	3	3	NUM
ap-10175	80	4	2w′2w′′	2w′2w′′	NUM
ap-10175	80	5	=	=	SYM
ap-10175	80	6	0	0	NUM
ap-10175	80	7	.	.	PUNCT
ap-10175	81	1	(	(	PUNCT
ap-10175	81	2	5	5	NUM
ap-10175	81	3	)	)	PUNCT
ap-10175	81	4	in	in	ADP
ap-10175	81	5	a	a	DET
ap-10175	81	6	two	two	NUM
ap-10175	81	7	-	-	PUNCT
ap-10175	81	8	phase	phase	NOUN
ap-10175	81	9	flow	flow	NOUN
ap-10175	81	10	,	,	PUNCT
ap-10175	81	11	the	the	DET
ap-10175	81	12	relationship	relationship	NOUN
ap-10175	81	13	between	between	ADP
ap-10175	81	14	the	the	DET
ap-10175	81	15	velocity	velocity	NOUN
ap-10175	81	16	of	of	ADP
ap-10175	81	17	the	the	DET
ap-10175	81	18	gas	gas	NOUN
ap-10175	81	19	with	with	ADP
ap-10175	81	20	liquid	liquid	NOUN
ap-10175	81	21	is	be	AUX
ap-10175	81	22	given	give	VERB
ap-10175	81	23	as	as	ADP
ap-10175	81	24	[	[	X
ap-10175	81	25	8	8	NUM
ap-10175	81	26	,	,	PUNCT
ap-10175	81	27	23	23	NUM
ap-10175	81	28	]	]	SYM
ap-10175	81	29	:	:	PUNCT
ap-10175	81	30	vg	vg	NOUN
ap-10175	81	31	=	=	SYM
ap-10175	81	32	ksvl	ksvl	NOUN
ap-10175	81	33	√	√	NOUN
ap-10175	81	34	ρgαg	ρgαg	NOUN
ap-10175	81	35	ρl(1	ρl(1	PROPN
ap-10175	81	36	−	−	PROPN
ap-10175	81	37	αg	αg	NOUN
ap-10175	81	38	)	)	PUNCT
ap-10175	81	39	,	,	PUNCT
ap-10175	81	40	(	(	PUNCT
ap-10175	81	41	6	6	NUM
ap-10175	81	42	)	)	PUNCT
ap-10175	81	43	where	where	SCONJ
ap-10175	81	44	αg	αg	NOUN
ap-10175	81	45	is	be	AUX
ap-10175	81	46	the	the	DET
ap-10175	81	47	gas	gas	NOUN
ap-10175	81	48	void	void	NOUN
ap-10175	81	49	fraction	fraction	NOUN
ap-10175	81	50	,	,	PUNCT
ap-10175	81	51	ρg	ρg	NOUN
ap-10175	81	52	and	and	CCONJ
ap-10175	81	53	ρl	ρl	ADV
ap-10175	81	54	is	be	AUX
ap-10175	81	55	the	the	DET
ap-10175	81	56	density	density	NOUN
ap-10175	81	57	of	of	ADP
ap-10175	81	58	the	the	DET
ap-10175	81	59	gas	gas	NOUN
ap-10175	81	60	and	and	CCONJ
ap-10175	81	61	the	the	DET
ap-10175	81	62	liquid	liquid	NOUN
ap-10175	81	63	,	,	PUNCT
ap-10175	81	64	respectively	respectively	ADV
ap-10175	81	65	,	,	PUNCT
ap-10175	81	66	and	and	CCONJ
ap-10175	81	67	ks	ks	PROPN
ap-10175	81	68	is	be	AUX
ap-10175	81	69	the	the	DET
ap-10175	81	70	slip	slip	NOUN
ap-10175	81	71	ratio	ratio	NOUN
ap-10175	81	72	.	.	PUNCT
ap-10175	82	1	the	the	DET
ap-10175	82	2	relationship	relationship	NOUN
ap-10175	82	3	between	between	ADP
ap-10175	82	4	dimensional	dimensional	ADJ
ap-10175	82	5	term	term	NOUN
ap-10175	82	6	βg	βg	NOUN
ap-10175	82	7	and	and	CCONJ
ap-10175	82	8	βl	βl	ADV
ap-10175	82	9	is	be	AUX
ap-10175	82	10	[	[	X
ap-10175	82	11	5	5	NUM
ap-10175	82	12	]	]	PUNCT
ap-10175	82	13	:	:	PUNCT
ap-10175	83	1	βg	βg	ADP
ap-10175	83	2	=	=	SYM
ap-10175	83	3	ρgαgβl	ρgαgβl	PROPN
ap-10175	83	4	ρl(1	ρl(1	PROPN
ap-10175	83	5	−	−	PROPN
ap-10175	83	6	αg	αg	NOUN
ap-10175	83	7	)	)	PUNCT
ap-10175	83	8	.	.	PUNCT
ap-10175	84	1	(	(	PUNCT
ap-10175	84	2	7	7	X
ap-10175	84	3	)	)	PUNCT
ap-10175	84	4	inserting	insert	VERB
ap-10175	84	5	equations	equation	NOUN
ap-10175	84	6	(	(	PUNCT
ap-10175	84	7	6	6	NUM
ap-10175	84	8	)	)	PUNCT
ap-10175	84	9	and	and	CCONJ
ap-10175	84	10	(	(	PUNCT
ap-10175	84	11	7	7	X
ap-10175	84	12	)	)	PUNCT
ap-10175	84	13	into	into	ADP
ap-10175	84	14	equation	equation	NOUN
ap-10175	84	15	(	(	PUNCT
ap-10175	84	16	5	5	X
ap-10175	84	17	)	)	PUNCT
ap-10175	84	18	yields	yield	VERB
ap-10175	84	19	the	the	DET
ap-10175	84	20	governing	govern	VERB
ap-10175	84	21	equations	equation	NOUN
ap-10175	84	22	of	of	ADP
ap-10175	84	23	motion	motion	NOUN
ap-10175	84	24	as	as	ADP
ap-10175	84	25	:	:	PUNCT
ap-10175	84	26	ẅ	ẅ	PROPN
ap-10175	85	1	+	+	CCONJ
ap-10175	85	2	2vl	2vl	ADJ
ap-10175	85	3	√	√	ADJ
ap-10175	85	4	βl	βl	NOUN
ap-10175	85	5	(	(	PUNCT
ap-10175	85	6	1	1	X
ap-10175	85	7	+	+	NUM
ap-10175	85	8	ks	ks	NOUN
ap-10175	85	9	αgρg	αgρg	NOUN
ap-10175	85	10	ρl(1	ρl(1	PROPN
ap-10175	85	11	−	−	PROPN
ap-10175	85	12	αg	αg	NOUN
ap-10175	85	13	)	)	PUNCT
ap-10175	85	14	)	)	PUNCT
ap-10175	86	1	ẇ′	ẇ′	NOUN
ap-10175	86	2	+	+	CCONJ
ap-10175	86	3	wiv	wiv	NOUN
ap-10175	86	4	+	+	CCONJ
ap-10175	86	5	(	(	PUNCT
ap-10175	86	6	v2	v2	NOUN
ap-10175	86	7	l	l	NOUN
ap-10175	86	8	+	+	CCONJ
ap-10175	86	9	v2	v2	PROPN
ap-10175	86	10	l	l	NOUN
ap-10175	86	11	ρg	ρg	PROPN
ap-10175	86	12	ρl	ρl	PROPN
ap-10175	86	13	k2	k2	PROPN
ap-10175	86	14	s	s	PART
ap-10175	86	15	αg	αg	PROPN
ap-10175	86	16	left(1	left(1	NOUN
ap-10175	86	17	−	−	PROPN
ap-10175	86	18	αg	αg	NOUN
ap-10175	86	19	)	)	PUNCT
ap-10175	86	20	−	−	PROPN
ap-10175	86	21	t	t	NOUN
ap-10175	86	22	+	+	CCONJ
ap-10175	86	23	p	p	X
ap-10175	86	24	+	+	NUM
ap-10175	86	25	θ	θ	NOUN
ap-10175	86	26	)	)	PUNCT
ap-10175	87	1	w′′	w′′	NOUN
ap-10175	87	2	−	−	PROPN
ap-10175	87	3	3	3	NUM
ap-10175	87	4	2w′2w′′	2w′2w′′	NUM
ap-10175	87	5	=	=	SYM
ap-10175	87	6	0	0	NUM
ap-10175	87	7	.	.	PUNCT
ap-10175	88	1	(	(	PUNCT
ap-10175	88	2	8)	8)	NUM
ap-10175	88	3	the	the	DET
ap-10175	88	4	gas	gas	NOUN
ap-10175	88	5	void	void	NOUN
ap-10175	88	6	fraction	fraction	NOUN
ap-10175	88	7	plays	play	VERB
ap-10175	88	8	a	a	DET
ap-10175	88	9	significant	significant	ADJ
ap-10175	88	10	role	role	NOUN
ap-10175	88	11	in	in	ADP
ap-10175	88	12	determining	determine	VERB
ap-10175	88	13	several	several	ADJ
ap-10175	88	14	multiphase	multiphase	NOUN
ap-10175	88	15	flow	flow	NOUN
ap-10175	88	16	parameters	parameter	NOUN
ap-10175	88	17	[	[	X
ap-10175	88	18	24	24	NUM
ap-10175	88	19	]	]	PUNCT
ap-10175	88	20	.	.	PUNCT
ap-10175	89	1	the	the	DET
ap-10175	89	2	void	void	ADJ
ap-10175	89	3	fraction	fraction	NOUN
ap-10175	89	4	and	and	CCONJ
ap-10175	89	5	slip	slip	NOUN
ap-10175	89	6	correlations	correlation	NOUN
ap-10175	89	7	according	accord	VERB
ap-10175	89	8	to	to	ADP
ap-10175	89	9	chisolm	chisolm	NOUN
ap-10175	89	10	[	[	X
ap-10175	89	11	25	25	NUM
ap-10175	89	12	]	]	PUNCT
ap-10175	89	13	will	will	AUX
ap-10175	89	14	be	be	AUX
ap-10175	89	15	adopted	adopt	VERB
ap-10175	89	16	in	in	ADP
ap-10175	89	17	this	this	DET
ap-10175	89	18	work	work	NOUN
ap-10175	89	19	:	:	PUNCT
ap-10175	89	20	αg	αg	NOUN
ap-10175	89	21	=	=	PUNCT
ap-10175	90	1	[	[	X
ap-10175	90	2	√	√	ADJ
ap-10175	90	3	1	1	NUM
ap-10175	90	4	+	+	NUM
ap-10175	90	5	xg	xg	NOUN
ap-10175	90	6	(	(	PUNCT
ap-10175	90	7	ρl	ρl	PROPN
ap-10175	90	8	ρg	ρg	ADP
ap-10175	90	9	−	−	NOUN
ap-10175	90	10	1	1	NUM
ap-10175	90	11	)	)	PUNCT
ap-10175	90	12	(	(	PUNCT
ap-10175	90	13	1	1	NUM
ap-10175	90	14	−	−	PROPN
ap-10175	90	15	xg	xg	PROPN
ap-10175	90	16	xg	xg	PROPN
ap-10175	90	17	)	)	PUNCT
ap-10175	91	1	(	(	PUNCT
ap-10175	91	2	ρg	ρg	ADP
ap-10175	91	3	ρl	ρl	NOUN
ap-10175	91	4	)	)	PUNCT
ap-10175	92	1	]	]	X
ap-10175	92	2	−1	−1	NOUN
ap-10175	92	3	,	,	PUNCT
ap-10175	92	4	ks	ks	PROPN
ap-10175	92	5	=	=	PUNCT
ap-10175	92	6	√	√	PROPN
ap-10175	92	7	1	1	NUM
ap-10175	92	8	+	+	NUM
ap-10175	92	9	xg	xg	NOUN
ap-10175	92	10	(	(	PUNCT
ap-10175	92	11	ρl	ρl	PROPN
ap-10175	92	12	ρg	ρg	ADP
ap-10175	92	13	−	−	NOUN
ap-10175	92	14	1	1	NUM
ap-10175	92	15	)	)	PUNCT
ap-10175	92	16	,	,	PUNCT
ap-10175	92	17	(	(	PUNCT
ap-10175	92	18	9	9	X
ap-10175	92	19	)	)	PUNCT
ap-10175	92	20	where	where	SCONJ
ap-10175	92	21	xg	xg	PROPN
ap-10175	92	22	is	be	AUX
ap-10175	92	23	the	the	DET
ap-10175	92	24	void	void	ADJ
ap-10175	92	25	quality	quality	NOUN
ap-10175	92	26	,	,	PUNCT
ap-10175	92	27	ρl	ρl	PROPN
ap-10175	92	28	is	be	AUX
ap-10175	92	29	the	the	DET
ap-10175	92	30	density	density	NOUN
ap-10175	92	31	of	of	ADP
ap-10175	92	32	the	the	DET
ap-10175	92	33	liquid	liquid	NOUN
ap-10175	92	34	,	,	PUNCT
ap-10175	92	35	and	and	CCONJ
ap-10175	92	36	ρg	ρg	NOUN
ap-10175	92	37	,	,	PUNCT
ap-10175	92	38	then	then	ADV
ap-10175	92	39	the	the	DET
ap-10175	92	40	density	density	NOUN
ap-10175	92	41	of	of	ADP
ap-10175	92	42	the	the	DET
ap-10175	92	43	gas	gas	NOUN
ap-10175	92	44	.	.	PUNCT
ap-10175	93	1	335	335	NUM
ap-10175	93	2	a.	a.	NOUN
ap-10175	93	3	o.	o.	PROPN
ap-10175	93	4	oyelade	oyelade	PROPN
ap-10175	93	5	,	,	PUNCT
ap-10175	93	6	a.	a.	PROPN
ap-10175	93	7	b.	b.	PROPN
ap-10175	93	8	ehinmowo	ehinmowo	PROPN
ap-10175	93	9	,	,	PUNCT
ap-10175	93	10	o.	o.	PROPN
ap-10175	93	11	oribayo	oribayo	PROPN
ap-10175	93	12	,	,	PUNCT
ap-10175	93	13	y.	y.	PROPN
ap-10175	93	14	o.	o.	PROPN
ap-10175	93	15	abiodun	abiodun	PROPN
ap-10175	93	16	acta	acta	PROPN
ap-10175	93	17	polytechnica	polytechnica	PROPN
ap-10175	93	18	3	3	NUM
ap-10175	93	19	.	.	PROPN
ap-10175	93	20	wave	wave	NOUN
ap-10175	93	21	propagation	propagation	NOUN
ap-10175	93	22	approach	approach	NOUN
ap-10175	93	23	we	we	PRON
ap-10175	93	24	first	first	ADV
ap-10175	93	25	consider	consider	VERB
ap-10175	93	26	the	the	DET
ap-10175	93	27	wave	wave	NOUN
ap-10175	93	28	propagation	propagation	NOUN
ap-10175	93	29	problem	problem	NOUN
ap-10175	93	30	,	,	PUNCT
ap-10175	93	31	assuming	assume	VERB
ap-10175	93	32	that	that	SCONJ
ap-10175	93	33	the	the	DET
ap-10175	93	34	equation	equation	NOUN
ap-10175	93	35	has	have	VERB
ap-10175	93	36	a	a	DET
ap-10175	93	37	traveling	travel	VERB
ap-10175	93	38	waves	wave	NOUN
ap-10175	93	39	solution	solution	NOUN
ap-10175	93	40	.	.	PUNCT
ap-10175	94	1	the	the	DET
ap-10175	94	2	harmonic	harmonic	ADJ
ap-10175	94	3	solution	solution	NOUN
ap-10175	94	4	in	in	ADP
ap-10175	94	5	the	the	DET
ap-10175	94	6	form	form	NOUN
ap-10175	94	7	of	of	ADP
ap-10175	94	8	a	a	DET
ap-10175	94	9	traveling	travel	VERB
ap-10175	94	10	wave	wave	NOUN
ap-10175	94	11	is	be	AUX
ap-10175	94	12	given	give	VERB
ap-10175	94	13	as	as	ADP
ap-10175	94	14	[	[	X
ap-10175	94	15	22	22	NUM
ap-10175	94	16	]	]	X
ap-10175	94	17	:	:	PUNCT
ap-10175	94	18	w	w	X
ap-10175	94	19	=	=	PUNCT
ap-10175	94	20	wnei(κx−ωt	wnei(κx−ωt	NOUN
ap-10175	94	21	)	)	PUNCT
ap-10175	94	22	,	,	PUNCT
ap-10175	94	23	(	(	PUNCT
ap-10175	94	24	10	10	NUM
ap-10175	94	25	)	)	PUNCT
ap-10175	94	26	where	where	SCONJ
ap-10175	94	27	wn	wn	PROPN
ap-10175	94	28	and	and	CCONJ
ap-10175	94	29	ω	ω	PROPN
ap-10175	94	30	are	be	AUX
ap-10175	94	31	the	the	DET
ap-10175	94	32	amplitude	amplitude	NOUN
ap-10175	94	33	and	and	CCONJ
ap-10175	94	34	angular	angular	ADJ
ap-10175	94	35	frequency	frequency	NOUN
ap-10175	94	36	of	of	ADP
ap-10175	94	37	the	the	DET
ap-10175	94	38	wave	wave	NOUN
ap-10175	94	39	,	,	PUNCT
ap-10175	94	40	respectively	respectively	ADV
ap-10175	94	41	.	.	PUNCT
ap-10175	95	1	κ	κ	PROPN
ap-10175	95	2	is	be	AUX
ap-10175	95	3	the	the	DET
ap-10175	95	4	wavenumber	wavenumber	NOUN
ap-10175	95	5	and	and	CCONJ
ap-10175	95	6	i	i	PRON
ap-10175	95	7	the	the	DET
ap-10175	95	8	imaginary	imaginary	ADJ
ap-10175	95	9	unit	unit	NOUN
ap-10175	95	10	.	.	PUNCT
ap-10175	96	1	in	in	ADP
ap-10175	96	2	addition	addition	NOUN
ap-10175	96	3	,	,	PUNCT
ap-10175	96	4	according	accord	VERB
ap-10175	96	5	to	to	ADP
ap-10175	96	6	the	the	DET
ap-10175	96	7	stress	stress	NOUN
ap-10175	96	8	wave	wave	NOUN
ap-10175	96	9	theory	theory	NOUN
ap-10175	96	10	,	,	PUNCT
ap-10175	96	11	the	the	DET
ap-10175	96	12	wave	wave	NOUN
ap-10175	96	13	phase	phase	NOUN
ap-10175	96	14	velocity	velocity	NOUN
ap-10175	96	15	is	be	AUX
ap-10175	96	16	equal	equal	ADJ
ap-10175	96	17	to	to	ADP
ap-10175	96	18	the	the	DET
ap-10175	96	19	circular	circular	ADJ
ap-10175	96	20	frequency	frequency	NOUN
ap-10175	96	21	divided	divide	VERB
ap-10175	96	22	by	by	ADP
ap-10175	96	23	the	the	DET
ap-10175	96	24	wave	wave	NOUN
ap-10175	96	25	number	number	NOUN
ap-10175	96	26	,	,	PUNCT
ap-10175	96	27	i.e.	i.e.	X
ap-10175	96	28	:	:	PUNCT
ap-10175	96	29	cp	cp	PROPN
ap-10175	96	30	=	=	SYM
ap-10175	96	31	ω	ω	PROPN
ap-10175	96	32	κ	κ	PROPN
ap-10175	96	33	.	.	PUNCT
ap-10175	97	1	(	(	PUNCT
ap-10175	97	2	11	11	NUM
ap-10175	97	3	)	)	PUNCT
ap-10175	97	4	by	by	ADP
ap-10175	97	5	rearranging	rearrange	VERB
ap-10175	97	6	equation	equation	NOUN
ap-10175	97	7	(	(	PUNCT
ap-10175	97	8	11	11	NUM
ap-10175	97	9	)	)	PUNCT
ap-10175	97	10	,	,	PUNCT
ap-10175	97	11	we	we	PRON
ap-10175	97	12	obtained	obtain	VERB
ap-10175	97	13	:	:	PUNCT
ap-10175	97	14	ω	ω	NUM
ap-10175	97	15	=	=	PUNCT
ap-10175	97	16	κvp	κvp	VERB
ap-10175	97	17	,	,	PUNCT
ap-10175	97	18	(	(	PUNCT
ap-10175	97	19	12	12	NUM
ap-10175	97	20	)	)	PUNCT
ap-10175	97	21	the	the	DET
ap-10175	97	22	group	group	NOUN
ap-10175	97	23	velocity	velocity	NOUN
ap-10175	97	24	is	be	AUX
ap-10175	97	25	equal	equal	ADJ
ap-10175	97	26	to	to	ADP
ap-10175	97	27	the	the	DET
ap-10175	97	28	derivative	derivative	NOUN
ap-10175	97	29	of	of	ADP
ap-10175	97	30	the	the	DET
ap-10175	97	31	circular	circular	ADJ
ap-10175	97	32	frequency	frequency	NOUN
ap-10175	97	33	with	with	ADP
ap-10175	97	34	respect	respect	NOUN
ap-10175	97	35	to	to	ADP
ap-10175	97	36	the	the	DET
ap-10175	97	37	wavenumber	wavenumber	NOUN
ap-10175	97	38	,	,	PUNCT
ap-10175	97	39	hence	hence	ADV
ap-10175	97	40	:	:	PUNCT
ap-10175	97	41	vg	vg	NOUN
ap-10175	97	42	=	=	PUNCT
ap-10175	97	43	vp	vp	PROPN
ap-10175	97	44	+	+	CCONJ
ap-10175	97	45	κ	κ	PROPN
ap-10175	97	46	dvp	dvp	PROPN
ap-10175	97	47	dκ	dκ	PROPN
ap-10175	97	48	.	.	PUNCT
ap-10175	98	1	(	(	PUNCT
ap-10175	98	2	13	13	NUM
ap-10175	98	3	)	)	PUNCT
ap-10175	98	4	substitution	substitution	NOUN
ap-10175	98	5	of	of	ADP
ap-10175	98	6	equation	equation	NOUN
ap-10175	98	7	(	(	PUNCT
ap-10175	98	8	10	10	NUM
ap-10175	98	9	)	)	PUNCT
ap-10175	98	10	into	into	ADP
ap-10175	98	11	equation	equation	NOUN
ap-10175	98	12	(	(	PUNCT
ap-10175	98	13	8)	8)	NUM
ap-10175	98	14	leads	lead	VERB
ap-10175	98	15	to	to	ADP
ap-10175	98	16	the	the	DET
ap-10175	98	17	dispersion	dispersion	NOUN
ap-10175	98	18	equation	equation	NOUN
ap-10175	98	19	as	as	ADP
ap-10175	98	20	:	:	PUNCT
ap-10175	98	21	κ4	κ4	NOUN
ap-10175	98	22	−	−	PROPN
ap-10175	99	1	ω2	ω2	ADJ
ap-10175	100	1	+	+	CCONJ
ap-10175	100	2	2κωvl	2κωvl	NUM
ap-10175	100	3	√	√	NUM
ap-10175	100	4	βl	βl	NOUN
ap-10175	100	5	(	(	PUNCT
ap-10175	100	6	1	1	NUM
ap-10175	100	7	+	+	NUM
ap-10175	100	8	ksvl	ksvl	NOUN
ap-10175	100	9	αgρg	αgρg	NOUN
ap-10175	100	10	ρl(1	ρl(1	PROPN
ap-10175	100	11	−	−	PROPN
ap-10175	100	12	αg	αg	NOUN
ap-10175	100	13	)	)	PUNCT
ap-10175	100	14	)	)	PUNCT
ap-10175	101	1	−	−	PROPN
ap-10175	101	2	κ2	κ2	NOUN
ap-10175	101	3	(	(	PUNCT
ap-10175	101	4	v2	v2	NOUN
ap-10175	101	5	l	l	NOUN
ap-10175	101	6	+	+	CCONJ
ap-10175	101	7	v2	v2	PROPN
ap-10175	101	8	l	l	NOUN
ap-10175	101	9	ρg	ρg	PROPN
ap-10175	101	10	ρl	ρl	PROPN
ap-10175	101	11	k2	k2	PROPN
ap-10175	101	12	s	s	PART
ap-10175	101	13	αg	αg	NOUN
ap-10175	101	14	(	(	PUNCT
ap-10175	101	15	1	1	NUM
ap-10175	101	16	−	−	NOUN
ap-10175	101	17	αg	αg	NOUN
ap-10175	101	18	)	)	PUNCT
ap-10175	101	19	−	−	PROPN
ap-10175	101	20	t	t	NOUN
ap-10175	101	21	+	+	CCONJ
ap-10175	101	22	p	p	X
ap-10175	101	23	+	+	NUM
ap-10175	101	24	θ	θ	NOUN
ap-10175	101	25	)	)	PUNCT
ap-10175	102	1	=	=	SYM
ap-10175	102	2	0	0	X
ap-10175	102	3	.	.	PUNCT
ap-10175	103	1	(	(	PUNCT
ap-10175	103	2	14	14	NUM
ap-10175	103	3	)	)	PUNCT
ap-10175	103	4	there	there	PRON
ap-10175	103	5	are	be	VERB
ap-10175	103	6	four	four	NUM
ap-10175	103	7	different	different	ADJ
ap-10175	103	8	wavenumber	wavenumber	NOUN
ap-10175	103	9	roots	root	NOUN
ap-10175	103	10	for	for	ADP
ap-10175	103	11	equation	equation	NOUN
ap-10175	103	12	(	(	PUNCT
ap-10175	103	13	14	14	NUM
ap-10175	103	14	)	)	PUNCT
ap-10175	103	15	,	,	PUNCT
ap-10175	103	16	involving	involve	VERB
ap-10175	103	17	two	two	NUM
ap-10175	103	18	real	real	ADJ
ap-10175	103	19	and	and	CCONJ
ap-10175	103	20	a	a	DET
ap-10175	103	21	conjugate	conjugate	ADJ
ap-10175	103	22	pair	pair	NOUN
ap-10175	103	23	of	of	ADP
ap-10175	103	24	imaginary	imaginary	ADJ
ap-10175	103	25	ones	one	NOUN
ap-10175	103	26	.	.	PUNCT
ap-10175	104	1	the	the	DET
ap-10175	104	2	two	two	NUM
ap-10175	104	3	real	real	NOUN
ap-10175	104	4	describe	describe	VERB
ap-10175	104	5	the	the	DET
ap-10175	104	6	downstream	downstream	ADJ
ap-10175	104	7	and	and	CCONJ
ap-10175	104	8	upstream	upstream	ADJ
ap-10175	104	9	propagating	propagating	NOUN
ap-10175	104	10	waves	wave	NOUN
ap-10175	104	11	,	,	PUNCT
ap-10175	104	12	respectively	respectively	ADV
ap-10175	104	13	,	,	PUNCT
ap-10175	104	14	and	and	CCONJ
ap-10175	104	15	the	the	DET
ap-10175	104	16	imaginary	imaginary	ADJ
ap-10175	104	17	describe	describe	VERB
ap-10175	104	18	evanescent	evanescent	NOUN
ap-10175	104	19	waves	wave	NOUN
ap-10175	104	20	.	.	PUNCT
ap-10175	105	1	by	by	ADP
ap-10175	105	2	rearranging	rearrange	VERB
ap-10175	105	3	equation	equation	NOUN
ap-10175	105	4	(	(	PUNCT
ap-10175	105	5	14	14	NUM
ap-10175	105	6	)	)	PUNCT
ap-10175	105	7	,	,	PUNCT
ap-10175	105	8	we	we	PRON
ap-10175	105	9	can	can	AUX
ap-10175	105	10	easily	easily	ADV
ap-10175	105	11	get	get	VERB
ap-10175	105	12	:	:	PUNCT
ap-10175	106	1	κ2	κ2	NOUN
ap-10175	106	2	−	−	PROPN
ap-10175	106	3	c2	c2	PROPN
ap-10175	106	4	p	p	PROPN
ap-10175	107	1	+	+	PROPN
ap-10175	107	2	2cpvl	2cpvl	NUM
ap-10175	107	3	√	√	PROPN
ap-10175	107	4	βl	βl	NOUN
ap-10175	107	5	(	(	PUNCT
ap-10175	107	6	1	1	NUM
ap-10175	107	7	+	+	NUM
ap-10175	107	8	ksvl	ksvl	NOUN
ap-10175	107	9	αgρg	αgρg	NOUN
ap-10175	107	10	ρl(1	ρl(1	PROPN
ap-10175	107	11	−	−	PROPN
ap-10175	107	12	αg	αg	NOUN
ap-10175	107	13	)	)	PUNCT
ap-10175	107	14	)	)	PUNCT
ap-10175	108	1	−	−	PROPN
ap-10175	109	1	(	(	PUNCT
ap-10175	109	2	v2	v2	NOUN
ap-10175	109	3	l	l	NOUN
ap-10175	109	4	+	+	CCONJ
ap-10175	109	5	v2	v2	PROPN
ap-10175	109	6	l	l	NOUN
ap-10175	109	7	ρg	ρg	PROPN
ap-10175	109	8	ρl	ρl	PROPN
ap-10175	109	9	k2	k2	PROPN
ap-10175	109	10	s	s	PART
ap-10175	109	11	αg	αg	NOUN
ap-10175	109	12	(	(	PUNCT
ap-10175	109	13	1	1	NUM
ap-10175	109	14	−	−	NOUN
ap-10175	109	15	αg	αg	NOUN
ap-10175	109	16	)	)	PUNCT
ap-10175	109	17	−	−	PROPN
ap-10175	109	18	t	t	NOUN
ap-10175	109	19	+	+	CCONJ
ap-10175	109	20	p	p	X
ap-10175	109	21	+	+	NUM
ap-10175	109	22	θ	θ	NOUN
ap-10175	109	23	)	)	PUNCT
ap-10175	110	1	=	=	SYM
ap-10175	110	2	0	0	PUNCT
ap-10175	110	3	(	(	PUNCT
ap-10175	110	4	15	15	NUM
ap-10175	110	5	)	)	PUNCT
ap-10175	110	6	then	then	ADV
ap-10175	110	7	,	,	PUNCT
ap-10175	110	8	the	the	DET
ap-10175	110	9	expressions	expression	NOUN
ap-10175	110	10	for	for	ADP
ap-10175	110	11	phase	phase	NOUN
ap-10175	110	12	velocity	velocity	NOUN
ap-10175	110	13	and	and	CCONJ
ap-10175	110	14	group	group	NOUN
ap-10175	110	15	velocity	velocity	NOUN
ap-10175	110	16	are	be	AUX
ap-10175	110	17	defined	define	VERB
ap-10175	110	18	as	as	ADP
ap-10175	110	19	:	:	PUNCT
ap-10175	110	20	cp	cp	NOUN
ap-10175	110	21	=	=	SYM
ap-10175	110	22	1	1	NUM
ap-10175	110	23	2	2	NUM
ap-10175	110	24	√	√	NUM
ap-10175	110	25	4	4	NUM
ap-10175	110	26	(	(	PUNCT
ap-10175	110	27	vl	vl	INTJ
ap-10175	110	28	√	√	PROPN
ap-10175	110	29	βl	βl	NOUN
ap-10175	111	1	+	+	CCONJ
ap-10175	111	2	vl	vl	INTJ
ap-10175	111	3	√	√	NUM
ap-10175	111	4	βl	βl	NOUN
ap-10175	111	5	αgρg	αgρg	NOUN
ap-10175	111	6	ρl(1	ρl(1	NOUN
ap-10175	111	7	−	−	PROPN
ap-10175	111	8	αg	αg	NOUN
ap-10175	111	9	)	)	PUNCT
ap-10175	111	10	)	)	PUNCT
ap-10175	111	11	2	2	NUM
ap-10175	112	1	+	+	NUM
ap-10175	112	2	4γ	4γ	NOUN
ap-10175	112	3	+	+	CCONJ
ap-10175	112	4	2vl	2vl	ADJ
ap-10175	112	5	√	√	ADJ
ap-10175	112	6	βl	βl	NOUN
ap-10175	112	7	(	(	PUNCT
ap-10175	112	8	1	1	NUM
ap-10175	112	9	+	+	NUM
ap-10175	112	10	αgρg	αgρg	NOUN
ap-10175	112	11	ρl(1	ρl(1	NOUN
ap-10175	112	12	−	−	PROPN
ap-10175	112	13	αg	αg	NOUN
ap-10175	112	14	)	)	PUNCT
ap-10175	112	15	)	)	PUNCT
ap-10175	112	16	,	,	PUNCT
ap-10175	112	17	(	(	PUNCT
ap-10175	112	18	16	16	NUM
ap-10175	112	19	)	)	PUNCT
ap-10175	112	20	vg	vg	NOUN
ap-10175	112	21	=	=	PUNCT
ap-10175	112	22	cp	cp	PROPN
ap-10175	112	23	+	+	NOUN
ap-10175	112	24	2κ2√	2κ2√	NUM
ap-10175	112	25	4	4	NUM
ap-10175	112	26	(	(	PUNCT
ap-10175	112	27	vl	vl	INTJ
ap-10175	112	28	√	√	PROPN
ap-10175	112	29	βl	βl	NOUN
ap-10175	113	1	+	+	CCONJ
ap-10175	113	2	vl	vl	INTJ
ap-10175	113	3	√	√	PROPN
ap-10175	113	4	βl	βl	PROPN
ap-10175	113	5	αgρg	αgρg	PROPN
ap-10175	113	6	ρl(1−αg	ρl(1−αg	PROPN
ap-10175	113	7	)	)	PUNCT
ap-10175	113	8	)	)	PUNCT
ap-10175	114	1	2	2	NUM
ap-10175	115	1	+	+	NUM
ap-10175	115	2	4γ	4γ	NOUN
ap-10175	115	3	,	,	PUNCT
ap-10175	115	4	(	(	PUNCT
ap-10175	115	5	17	17	NUM
ap-10175	115	6	)	)	PUNCT
ap-10175	115	7	where	where	SCONJ
ap-10175	115	8	γ	γ	PROPN
ap-10175	115	9	=	=	SYM
ap-10175	115	10	κ2	κ2	PROPN
ap-10175	115	11	−	−	PROPN
ap-10175	115	12	p	p	PROPN
ap-10175	116	1	+	+	PROPN
ap-10175	116	2	t	t	PROPN
ap-10175	116	3	−	−	NUM
ap-10175	116	4	θ	θ	NOUN
ap-10175	116	5	−	−	PROPN
ap-10175	117	1	v2	v2	NOUN
ap-10175	117	2	l	l	NOUN
ap-10175	117	3	−	−	PROPN
ap-10175	117	4	v2	v2	NOUN
ap-10175	117	5	l	l	NOUN
ap-10175	117	6	ρg	ρg	PROPN
ap-10175	117	7	ρl	ρl	PROPN
ap-10175	117	8	k2	k2	PROPN
ap-10175	117	9	s	s	PART
ap-10175	117	10	αg	αg	NOUN
ap-10175	117	11	(	(	PUNCT
ap-10175	117	12	1	1	NUM
ap-10175	117	13	−	−	NOUN
ap-10175	117	14	αg	αg	NOUN
ap-10175	117	15	)	)	PUNCT
ap-10175	117	16	.	.	PUNCT
ap-10175	118	1	for	for	ADP
ap-10175	118	2	the	the	DET
ap-10175	118	3	free	free	ADJ
ap-10175	118	4	vibration	vibration	NOUN
ap-10175	118	5	problem	problem	NOUN
ap-10175	118	6	,	,	PUNCT
ap-10175	118	7	based	base	VERB
ap-10175	118	8	on	on	ADP
ap-10175	118	9	the	the	DET
ap-10175	118	10	navier	navier	NOUN
ap-10175	118	11	solution	solution	NOUN
ap-10175	118	12	method	method	NOUN
ap-10175	118	13	,	,	PUNCT
ap-10175	118	14	we	we	PRON
ap-10175	118	15	assume	assume	VERB
ap-10175	118	16	equation	equation	NOUN
ap-10175	118	17	(	(	PUNCT
ap-10175	118	18	8)	8)	NUM
ap-10175	118	19	has	have	VERB
ap-10175	118	20	the	the	DET
ap-10175	118	21	following	follow	VERB
ap-10175	118	22	form	form	NOUN
ap-10175	118	23	solutions	solution	NOUN
ap-10175	118	24	:	:	PUNCT
ap-10175	118	25	w	w	X
ap-10175	118	26	(	(	PUNCT
ap-10175	118	27	x	x	PROPN
ap-10175	118	28	,	,	PUNCT
ap-10175	118	29	t	t	PROPN
ap-10175	118	30	)	)	PUNCT
ap-10175	118	31	=	=	SYM
ap-10175	119	1	∞∑	∞∑	NUM
ap-10175	119	2	n=1	n=1	PROPN
ap-10175	119	3	wneiωnt	wneiωnt	PROPN
ap-10175	119	4	sin	sin	NOUN
ap-10175	119	5	(	(	PUNCT
ap-10175	119	6	nπ	nπ	VERB
ap-10175	119	7	l	l	NOUN
ap-10175	119	8	x	x	PUNCT
ap-10175	119	9	)	)	PUNCT
ap-10175	119	10	.	.	PUNCT
ap-10175	120	1	(	(	PUNCT
ap-10175	120	2	18	18	NUM
ap-10175	120	3	)	)	PUNCT
ap-10175	120	4	substituting	substitute	VERB
ap-10175	120	5	equation	equation	NOUN
ap-10175	120	6	(	(	PUNCT
ap-10175	120	7	18	18	NUM
ap-10175	120	8	)	)	PUNCT
ap-10175	120	9	into	into	ADP
ap-10175	120	10	equation	equation	NOUN
ap-10175	120	11	(	(	PUNCT
ap-10175	120	12	8)	8)	NUM
ap-10175	120	13	,	,	PUNCT
ap-10175	120	14	the	the	DET
ap-10175	120	15	expression	expression	NOUN
ap-10175	120	16	for	for	ADP
ap-10175	120	17	the	the	DET
ap-10175	120	18	frequency	frequency	NOUN
ap-10175	120	19	relation	relation	NOUN
ap-10175	120	20	is	be	AUX
ap-10175	120	21	obtained	obtain	VERB
ap-10175	120	22	as	as	ADP
ap-10175	120	23	:	:	PUNCT
ap-10175	120	24	ωn	ωn	PROPN
ap-10175	120	25	=	=	PUNCT
ap-10175	120	26	inπ	inπ	NOUN
ap-10175	120	27	√√√√√√√√√√√	√√√√√√√√√√√	ADP
ap-10175	120	28	l2k2	l2k2	X
ap-10175	120	29	s	s	PART
ap-10175	120	30	v2	v2	NOUN
ap-10175	120	31	lαgρg	lαgρg	NOUN
ap-10175	121	1	+	+	CCONJ
ap-10175	121	2	(	(	PUNCT
ap-10175	121	3	−	−	X
ap-10175	121	4	n2π2	n2π2	INTJ
ap-10175	122	1	+	+	NUM
ap-10175	122	2	l2(p	l2(p	X
ap-10175	122	3	−	−	PROPN
ap-10175	122	4	t	t	PROPN
ap-10175	122	5	+	+	CCONJ
ap-10175	122	6	θ	θ	NOUN
ap-10175	122	7	)	)	PUNCT
ap-10175	122	8	−	−	NOUN
ap-10175	122	9	l2v2	l2v2	X
ap-10175	122	10	l(αg	l(αg	ADJ
ap-10175	122	11	−	−	NOUN
ap-10175	122	12	1	1	NUM
ap-10175	122	13	)	)	PUNCT
ap-10175	122	14	+	+	CCONJ
ap-10175	122	15	(	(	PUNCT
ap-10175	122	16	n2π2	n2π2	X
ap-10175	122	17	+	+	CCONJ
ap-10175	122	18	l2(t	l2(t	VERB
ap-10175	122	19	−	−	PROPN
ap-10175	122	20	p	p	NOUN
ap-10175	122	21	)	)	PUNCT
ap-10175	122	22	)	)	PUNCT
ap-10175	122	23	αg	αg	NOUN
ap-10175	122	24	)	)	PUNCT
ap-10175	122	25	ρl	ρl	ADP
ap-10175	122	26	×	×	NOUN
ap-10175	122	27	(	(	PUNCT
ap-10175	122	28	√	√	INTJ
ap-10175	122	29	l2(1	l2(1	NOUN
ap-10175	122	30	−	−	NOUN
ap-10175	122	31	αg)ρl	αg)ρl	NUM
ap-10175	122	32	)	)	PUNCT
ap-10175	122	33	−1	−1	NOUN
ap-10175	122	34	.	.	PUNCT
ap-10175	123	1	(	(	PUNCT
ap-10175	123	2	19	19	NUM
ap-10175	123	3	)	)	PUNCT
ap-10175	123	4	4	4	NUM
ap-10175	123	5	.	.	NOUN
ap-10175	123	6	results	result	NOUN
ap-10175	123	7	and	and	CCONJ
ap-10175	123	8	discussion	discussion	NOUN
ap-10175	123	9	in	in	ADP
ap-10175	123	10	the	the	DET
ap-10175	123	11	following	follow	VERB
ap-10175	123	12	numerical	numerical	ADJ
ap-10175	123	13	examples	example	NOUN
ap-10175	123	14	,	,	PUNCT
ap-10175	123	15	the	the	DET
ap-10175	123	16	two	two	NUM
ap-10175	123	17	-	-	PUNCT
ap-10175	123	18	phase	phase	NOUN
ap-10175	123	19	flow	flow	NOUN
ap-10175	123	20	constituents	constituent	NOUN
ap-10175	123	21	;	;	PUNCT
ap-10175	123	22	water	water	NOUN
ap-10175	123	23	and	and	CCONJ
ap-10175	123	24	air	air	NOUN
ap-10175	123	25	,	,	PUNCT
ap-10175	123	26	have	have	VERB
ap-10175	123	27	these	these	DET
ap-10175	123	28	densities	density	NOUN
ap-10175	123	29	ρl	ρl	ADP
ap-10175	123	30	=	=	SYM
ap-10175	123	31	1	1	NUM
ap-10175	123	32	000	000	NUM
ap-10175	123	33	kg	kg	NOUN
ap-10175	123	34	m−3	m−3	PROPN
ap-10175	123	35	and	and	CCONJ
ap-10175	123	36	ρg	ρg	PROPN
ap-10175	123	37	=	=	NOUN
ap-10175	123	38	1.2	1.2	NUM
ap-10175	123	39	kg	kg	NOUN
ap-10175	123	40	m−3	m−3	PROPN
ap-10175	123	41	,	,	PUNCT
ap-10175	123	42	respectively	respectively	ADV
ap-10175	123	43	.	.	PUNCT
ap-10175	124	1	these	these	DET
ap-10175	124	2	parameters	parameter	NOUN
ap-10175	124	3	are	be	AUX
ap-10175	124	4	used	use	VERB
ap-10175	124	5	except	except	SCONJ
ap-10175	124	6	stated	state	VERB
ap-10175	124	7	otherwise	otherwise	ADV
ap-10175	124	8	,	,	PUNCT
ap-10175	124	9	p	p	X
ap-10175	124	10	=	=	NOUN
ap-10175	124	11	0	0	NUM
ap-10175	124	12	,	,	PUNCT
ap-10175	124	13	t	t	NOUN
ap-10175	124	14	=	=	SYM
ap-10175	124	15	0	0	NUM
ap-10175	124	16	,	,	PUNCT
ap-10175	124	17	θ	θ	PROPN
ap-10175	124	18	=	=	SYM
ap-10175	124	19	0	0	PROPN
ap-10175	124	20	,	,	PUNCT
ap-10175	124	21	β	β	X
ap-10175	124	22	=	=	SYM
ap-10175	124	23	0.5	0.5	NUM
ap-10175	124	24	.	.	NOUN
ap-10175	124	25	4.1	4.1	NUM
ap-10175	124	26	.	.	PUNCT
ap-10175	125	1	validation	validation	NOUN
ap-10175	125	2	of	of	ADP
ap-10175	125	3	the	the	DET
ap-10175	125	4	result	result	NOUN
ap-10175	125	5	the	the	DET
ap-10175	125	6	accuracy	accuracy	NOUN
ap-10175	125	7	of	of	ADP
ap-10175	125	8	the	the	DET
ap-10175	125	9	wave	wave	NOUN
ap-10175	125	10	propagation	propagation	NOUN
ap-10175	125	11	approach	approach	NOUN
ap-10175	125	12	for	for	ADP
ap-10175	125	13	the	the	DET
ap-10175	125	14	pipe	pipe	NOUN
ap-10175	125	15	conveying	convey	VERB
ap-10175	125	16	a	a	DET
ap-10175	125	17	two	two	NUM
ap-10175	125	18	phase	phase	NOUN
ap-10175	125	19	flow	flow	NOUN
ap-10175	125	20	is	be	AUX
ap-10175	125	21	validated	validate	VERB
ap-10175	125	22	with	with	ADP
ap-10175	125	23	the	the	DET
ap-10175	125	24	work	work	NOUN
ap-10175	125	25	of	of	ADP
ap-10175	125	26	liang	liang	PROPN
ap-10175	125	27	et	et	PROPN
ap-10175	125	28	al	al	PROPN
ap-10175	125	29	.	.	PUNCT
ap-10175	126	1	[	[	X
ap-10175	126	2	26	26	NUM
ap-10175	126	3	]	]	PUNCT
ap-10175	126	4	.	.	PUNCT
ap-10175	127	1	for	for	ADP
ap-10175	127	2	the	the	DET
ap-10175	127	3	single	single	ADJ
ap-10175	127	4	-	-	PUNCT
ap-10175	127	5	phase	phase	NOUN
ap-10175	127	6	flow	flow	NOUN
ap-10175	127	7	,	,	PUNCT
ap-10175	127	8	the	the	DET
ap-10175	127	9	results	result	NOUN
ap-10175	127	10	obtained	obtain	VERB
ap-10175	127	11	from	from	ADP
ap-10175	127	12	the	the	DET
ap-10175	127	13	present	present	ADJ
ap-10175	127	14	model	model	NOUN
ap-10175	127	15	are	be	AUX
ap-10175	127	16	in	in	ADP
ap-10175	127	17	good	good	ADJ
ap-10175	127	18	agreement	agreement	NOUN
ap-10175	127	19	with	with	ADP
ap-10175	127	20	those	those	PRON
ap-10175	127	21	from	from	ADP
ap-10175	127	22	the	the	DET
ap-10175	127	23	reference	reference	NOUN
ap-10175	127	24	(	(	PUNCT
ap-10175	127	25	figure	figure	NOUN
ap-10175	127	26	2	2	NUM
ap-10175	127	27	)	)	PUNCT
ap-10175	127	28	.	.	PUNCT
ap-10175	128	1	these	these	DET
ap-10175	128	2	results	result	NOUN
ap-10175	128	3	show	show	VERB
ap-10175	128	4	that	that	SCONJ
ap-10175	128	5	the	the	DET
ap-10175	128	6	formulation	formulation	NOUN
ap-10175	128	7	can	can	AUX
ap-10175	128	8	give	give	VERB
ap-10175	128	9	a	a	DET
ap-10175	128	10	reliable	reliable	ADJ
ap-10175	128	11	description	description	NOUN
ap-10175	128	12	for	for	ADP
ap-10175	128	13	wave	wave	NOUN
ap-10175	128	14	propagation	propagation	NOUN
ap-10175	128	15	in	in	ADP
ap-10175	128	16	a	a	DET
ap-10175	128	17	pipe	pipe	NOUN
ap-10175	128	18	conveying	convey	VERB
ap-10175	128	19	a	a	DET
ap-10175	128	20	two	two	NUM
ap-10175	128	21	phase	phase	NOUN
ap-10175	128	22	flow	flow	NOUN
ap-10175	128	23	.	.	PUNCT
ap-10175	129	1	4.2	4.2	NUM
ap-10175	129	2	.	.	PUNCT
ap-10175	129	3	effect	effect	NOUN
ap-10175	129	4	of	of	ADP
ap-10175	129	5	two	two	NUM
ap-10175	129	6	-	-	PUNCT
ap-10175	129	7	phase	phase	NOUN
ap-10175	129	8	flow	flow	NOUN
ap-10175	129	9	on	on	ADP
ap-10175	129	10	phase	phase	NOUN
ap-10175	129	11	and	and	CCONJ
ap-10175	129	12	group	group	NOUN
ap-10175	129	13	velocities	velocity	NOUN
ap-10175	129	14	the	the	DET
ap-10175	129	15	effects	effect	NOUN
ap-10175	129	16	of	of	ADP
ap-10175	129	17	the	the	DET
ap-10175	129	18	two	two	NUM
ap-10175	129	19	-	-	PUNCT
ap-10175	129	20	phase	phase	NOUN
ap-10175	129	21	flow	flow	NOUN
ap-10175	129	22	on	on	ADP
ap-10175	129	23	wave	wave	NOUN
ap-10175	129	24	propagation	propagation	NOUN
ap-10175	129	25	are	be	AUX
ap-10175	129	26	shown	show	VERB
ap-10175	129	27	in	in	ADP
ap-10175	129	28	figures	figure	NOUN
ap-10175	129	29	3	3	NUM
ap-10175	129	30	and	and	CCONJ
ap-10175	129	31	4	4	NUM
ap-10175	129	32	at	at	ADP
ap-10175	129	33	a	a	DET
ap-10175	129	34	liquid	liquid	ADJ
ap-10175	129	35	velocity	velocity	NOUN
ap-10175	129	36	of	of	ADP
ap-10175	129	37	3	3	NUM
ap-10175	129	38	.	.	PUNCT
ap-10175	130	1	it	it	PRON
ap-10175	130	2	can	can	AUX
ap-10175	130	3	be	be	AUX
ap-10175	130	4	observed	observe	VERB
ap-10175	130	5	that	that	SCONJ
ap-10175	130	6	the	the	DET
ap-10175	130	7	wave	wave	NOUN
ap-10175	130	8	phase	phase	NOUN
ap-10175	130	9	velocity	velocity	NOUN
ap-10175	130	10	remains	remain	VERB
ap-10175	130	11	constant	constant	ADJ
ap-10175	130	12	across	across	ADP
ap-10175	130	13	all	all	DET
ap-10175	130	14	phases	phase	NOUN
ap-10175	130	15	for	for	ADP
ap-10175	130	16	a	a	DET
ap-10175	130	17	range	range	NOUN
ap-10175	130	18	of	of	ADP
ap-10175	130	19	wavenumbers	wavenumber	NOUN
ap-10175	130	20	until	until	SCONJ
ap-10175	130	21	dispersion	dispersion	NOUN
ap-10175	130	22	occurs	occur	VERB
ap-10175	130	23	.	.	PUNCT
ap-10175	131	1	for	for	ADP
ap-10175	131	2	the	the	DET
ap-10175	131	3	constant	constant	ADJ
ap-10175	131	4	phase	phase	NOUN
ap-10175	131	5	velocity	velocity	NOUN
ap-10175	131	6	,	,	PUNCT
ap-10175	131	7	the	the	DET
ap-10175	131	8	wave	wave	NOUN
ap-10175	131	9	is	be	AUX
ap-10175	131	10	non	non	ADJ
ap-10175	131	11	-	-	ADJ
ap-10175	131	12	dispersive	dispersive	ADJ
ap-10175	131	13	and	and	CCONJ
ap-10175	131	14	the	the	DET
ap-10175	131	15	wave	wave	NOUN
ap-10175	131	16	velocity	velocity	NOUN
ap-10175	131	17	depends	depend	VERB
ap-10175	131	18	only	only	ADV
ap-10175	131	19	on	on	ADP
ap-10175	131	20	the	the	DET
ap-10175	131	21	medium	medium	NOUN
ap-10175	131	22	’s	’s	PART
ap-10175	131	23	bulk	bulk	ADJ
ap-10175	131	24	properties	property	NOUN
ap-10175	131	25	and	and	CCONJ
ap-10175	131	26	not	not	PART
ap-10175	131	27	on	on	ADP
ap-10175	131	28	frequency	frequency	NOUN
ap-10175	131	29	.	.	PUNCT
ap-10175	132	1	for	for	ADP
ap-10175	132	2	instance	instance	NOUN
ap-10175	132	3	,	,	PUNCT
ap-10175	132	4	in	in	ADP
ap-10175	132	5	a	a	DET
ap-10175	132	6	single	single	ADJ
ap-10175	132	7	-	-	PUNCT
ap-10175	132	8	phase	phase	NOUN
ap-10175	132	9	flow	flow	NOUN
ap-10175	132	10	,	,	PUNCT
ap-10175	132	11	the	the	DET
ap-10175	132	12	wave	wave	NOUN
ap-10175	132	13	velocity	velocity	NOUN
ap-10175	132	14	is	be	AUX
ap-10175	132	15	constant	constant	ADJ
ap-10175	132	16	from	from	ADP
ap-10175	132	17	zero	zero	NUM
ap-10175	132	18	to	to	ADP
ap-10175	132	19	a	a	DET
ap-10175	132	20	wavenumber	wavenumber	NOUN
ap-10175	132	21	of	of	ADP
ap-10175	132	22	2	2	NUM
ap-10175	132	23	,	,	PUNCT
ap-10175	132	24	with	with	ADP
ap-10175	132	25	dispersion	dispersion	NOUN
ap-10175	132	26	occurring	occur	VERB
ap-10175	132	27	at	at	ADP
ap-10175	132	28	a	a	DET
ap-10175	132	29	wavenumber	wavenumber	NOUN
ap-10175	132	30	of	of	ADP
ap-10175	132	31	2.1	2.1	NUM
ap-10175	132	32	.	.	PUNCT
ap-10175	133	1	however	however	ADV
ap-10175	133	2	,	,	PUNCT
ap-10175	133	3	for	for	ADP
ap-10175	133	4	a	a	DET
ap-10175	133	5	two	two	NUM
ap-10175	133	6	-	-	PUNCT
ap-10175	133	7	phase	phase	NOUN
ap-10175	133	8	flow	flow	NOUN
ap-10175	133	9	with	with	ADP
ap-10175	133	10	a	a	DET
ap-10175	133	11	vapour	vapour	NOUN
ap-10175	133	12	quality	quality	NOUN
ap-10175	133	13	xg	xg	PROPN
ap-10175	133	14	=	=	NOUN
ap-10175	133	15	0.2	0.2	NUM
ap-10175	133	16	,	,	PUNCT
ap-10175	133	17	wave	wave	NOUN
ap-10175	133	18	dispersion	dispersion	NOUN
ap-10175	133	19	occurs	occur	VERB
ap-10175	133	20	at	at	ADP
ap-10175	133	21	a	a	DET
ap-10175	133	22	wavenumber	wavenumber	NOUN
ap-10175	133	23	of	of	ADP
ap-10175	133	24	5.8	5.8	NUM
ap-10175	133	25	.	.	PUNCT
ap-10175	134	1	at	at	ADP
ap-10175	134	2	the	the	DET
ap-10175	134	3	dispersion	dispersion	NOUN
ap-10175	134	4	points	point	NOUN
ap-10175	134	5	,	,	PUNCT
ap-10175	134	6	the	the	DET
ap-10175	134	7	wave	wave	NOUN
ap-10175	134	8	velocity	velocity	NOUN
ap-10175	134	9	depends	depend	VERB
ap-10175	134	10	on	on	ADP
ap-10175	134	11	the	the	DET
ap-10175	134	12	frequency	frequency	NOUN
ap-10175	134	13	of	of	ADP
ap-10175	134	14	the	the	DET
ap-10175	134	15	propagation	propagation	NOUN
ap-10175	134	16	.	.	PUNCT
ap-10175	135	1	therefore	therefore	ADV
ap-10175	135	2	,	,	PUNCT
ap-10175	135	3	as	as	ADP
ap-10175	135	4	vapour	vapour	NOUN
ap-10175	135	5	quality	quality	NOUN
ap-10175	135	6	increases	increase	NOUN
ap-10175	135	7	,	,	PUNCT
ap-10175	135	8	the	the	DET
ap-10175	135	9	wavenumber	wavenumber	NOUN
ap-10175	135	10	at	at	ADP
ap-10175	135	11	which	which	PRON
ap-10175	135	12	the	the	DET
ap-10175	135	13	propagating	propagate	VERB
ap-10175	135	14	wave	wave	NOUN
ap-10175	135	15	becomes	becomes	AUX
ap-10175	135	16	dispersed	disperse	VERB
ap-10175	135	17	also	also	ADV
ap-10175	135	18	increases	increase	VERB
ap-10175	135	19	.	.	PUNCT
ap-10175	136	1	the	the	DET
ap-10175	136	2	corresponding	correspond	VERB
ap-10175	136	3	group	group	NOUN
ap-10175	136	4	velocity	velocity	NOUN
ap-10175	136	5	for	for	ADP
ap-10175	136	6	the	the	DET
ap-10175	136	7	same	same	ADJ
ap-10175	136	8	wave	wave	NOUN
ap-10175	136	9	is	be	AUX
ap-10175	136	10	shown	show	VERB
ap-10175	136	11	in	in	ADP
ap-10175	136	12	figure	figure	NOUN
ap-10175	136	13	4	4	NUM
ap-10175	136	14	.	.	PUNCT
ap-10175	137	1	in	in	ADP
ap-10175	137	2	figure	figure	NOUN
ap-10175	137	3	4	4	NUM
ap-10175	137	4	,	,	PUNCT
ap-10175	137	5	there	there	PRON
ap-10175	137	6	is	be	VERB
ap-10175	137	7	a	a	DET
ap-10175	137	8	critical	critical	ADJ
ap-10175	137	9	point	point	NOUN
ap-10175	137	10	where	where	SCONJ
ap-10175	137	11	the	the	DET
ap-10175	137	12	group	group	NOUN
ap-10175	137	13	velocity	velocity	NOUN
ap-10175	137	14	jumps	jump	VERB
ap-10175	137	15	to	to	PART
ap-10175	137	16	infinity	infinity	VERB
ap-10175	137	17	for	for	ADP
ap-10175	137	18	a	a	DET
ap-10175	137	19	particular	particular	ADJ
ap-10175	137	20	wavenumber	wavenumber	NOUN
ap-10175	137	21	.	.	PUNCT
ap-10175	138	1	this	this	DET
ap-10175	138	2	point	point	NOUN
ap-10175	138	3	likely	likely	ADV
ap-10175	138	4	corresponds	correspond	VERB
ap-10175	138	5	to	to	ADP
ap-10175	138	6	stationary	stationary	ADJ
ap-10175	138	7	waves	wave	NOUN
ap-10175	138	8	or	or	CCONJ
ap-10175	138	9	indicates	indicate	VERB
ap-10175	138	10	that	that	SCONJ
ap-10175	138	11	the	the	DET
ap-10175	138	12	wave	wave	NOUN
ap-10175	138	13	has	have	VERB
ap-10175	138	14	a	a	DET
ap-10175	138	15	very	very	ADV
ap-10175	138	16	localised	localise	VERB
ap-10175	138	17	energy	energy	NOUN
ap-10175	138	18	distribution	distribution	NOUN
ap-10175	138	19	[	[	X
ap-10175	138	20	22	22	NUM
ap-10175	138	21	]	]	PUNCT
ap-10175	138	22	.	.	PUNCT
ap-10175	139	1	336	336	NUM
ap-10175	139	2	vol	vol	NOUN
ap-10175	139	3	.	.	PUNCT
ap-10175	140	1	65	65	NUM
ap-10175	140	2	no	no	NOUN
ap-10175	140	3	.	.	PUNCT
ap-10175	141	1	3/2025	3/2025	NUM
ap-10175	141	2	wave	wave	NOUN
ap-10175	141	3	propagation	propagation	NOUN
ap-10175	141	4	in	in	ADP
ap-10175	141	5	a	a	DET
ap-10175	141	6	pipe	pipe	NOUN
ap-10175	141	7	conveying	convey	VERB
ap-10175	141	8	two	two	NUM
ap-10175	141	9	phase	phase	NOUN
ap-10175	141	10	flow	flow	NOUN
ap-10175	141	11	0	0	NUM
ap-10175	141	12	1	1	NUM
ap-10175	141	13	2	2	NUM
ap-10175	141	14	3	3	NUM
ap-10175	141	15	4	4	NUM
ap-10175	141	16	5	5	NUM
ap-10175	141	17	6	6	NUM
ap-10175	141	18	0	0	NUM
ap-10175	141	19	2	2	NUM
ap-10175	141	20	4	4	NUM
ap-10175	141	21	6	6	NUM
ap-10175	141	22	8	8	NUM
ap-10175	141	23	10	10	NUM
ap-10175	141	24	liang	liang	PROPN
ap-10175	141	25	et	et	PROPN
ap-10175	141	26	al	al	PROPN
ap-10175	141	27	.	.	PUNCT
ap-10175	142	1	current	current	ADJ
ap-10175	142	2	r	r	NOUN
ap-10175	142	3	e	e	NOUN
ap-10175	142	4	(	(	PUNCT
ap-10175	142	5	)	)	PUNCT
ap-10175	142	6	flow	flow	NOUN
ap-10175	142	7	velocity	velocity	NOUN
ap-10175	142	8	(	(	PUNCT
ap-10175	142	9	a	a	NOUN
ap-10175	142	10	)	)	PUNCT
ap-10175	142	11	.	.	PUNCT
ap-10175	143	1	real	real	ADJ
ap-10175	143	2	.	.	PUNCT
ap-10175	144	1	0	0	NUM
ap-10175	145	1	2	2	NUM
ap-10175	145	2	4	4	NUM
ap-10175	145	3	6	6	NUM
ap-10175	145	4	-15	-15	NUM
ap-10175	145	5	-10	-10	PUNCT
ap-10175	145	6	-5	-5	NOUN
ap-10175	145	7	0	0	NUM
ap-10175	145	8	5	5	NUM
ap-10175	145	9	10	10	NUM
ap-10175	145	10	15	15	NUM
ap-10175	145	11	20	20	NUM
ap-10175	145	12	i	i	PRON
ap-10175	145	13	m	m	VERB
ap-10175	145	14	ag	ag	PROPN
ap-10175	145	15	(	(	PUNCT
ap-10175	145	16	)	)	PUNCT
ap-10175	145	17	flow	flow	NOUN
ap-10175	145	18	velocity	velocity	NOUN
ap-10175	145	19	liang	liang	PROPN
ap-10175	145	20	et	et	PROPN
ap-10175	145	21	al	al	PROPN
ap-10175	145	22	.	.	PROPN
ap-10175	146	1	current	current	ADJ
ap-10175	146	2	(	(	PUNCT
ap-10175	146	3	b	b	NOUN
ap-10175	146	4	)	)	PUNCT
ap-10175	146	5	.	.	PUNCT
ap-10175	147	1	imaginary	imaginary	ADJ
ap-10175	147	2	.	.	PUNCT
ap-10175	147	3	figure	figure	NOUN
ap-10175	147	4	2	2	NUM
ap-10175	147	5	.	.	PUNCT
ap-10175	148	1	the	the	DET
ap-10175	148	2	first	first	ADJ
ap-10175	148	3	-	-	PUNCT
ap-10175	148	4	order	order	NOUN
ap-10175	148	5	frequency	frequency	NOUN
ap-10175	148	6	diagrams	diagram	NOUN
ap-10175	148	7	for	for	ADP
ap-10175	148	8	the	the	DET
ap-10175	148	9	fluid	fluid	ADJ
ap-10175	148	10	conveying	conveying	NOUN
ap-10175	148	11	pipes	pipe	NOUN
ap-10175	148	12	.	.	PUNCT
ap-10175	149	1	0	0	NUM
ap-10175	149	2	2	2	NUM
ap-10175	149	3	4	4	NUM
ap-10175	149	4	6	6	NUM
ap-10175	149	5	8	8	NUM
ap-10175	149	6	1	1	NUM
ap-10175	149	7	0	0	NUM
ap-10175	149	8	2	2	NUM
ap-10175	149	9	4	4	NUM
ap-10175	149	10	6	6	NUM
ap-10175	149	11	8	8	NUM
ap-10175	149	12	1	1	NUM
ap-10175	149	13	0	0	NUM
ap-10175	149	14	1	1	NUM
ap-10175	149	15	2	2	NUM
ap-10175	149	16	ph	ph	NOUN
ap-10175	149	17	as	as	ADP
ap-10175	149	18	e	e	NOUN
ap-10175	149	19	v	v	NOUN
ap-10175	149	20	elo	elo	NOUN
ap-10175	149	21	cit	cit	PROPN
ap-10175	149	22	y	y	PROPN
ap-10175	149	23	w	w	PROPN
ap-10175	149	24	a	a	PRON
ap-10175	149	25	v	v	X
ap-10175	149	26	e	e	NOUN
ap-10175	149	27	n	n	CCONJ
ap-10175	149	28	u	u	NOUN
ap-10175	149	29	m	m	NOUN
ap-10175	149	30	b	b	NOUN
ap-10175	149	31	e	e	NOUN
ap-10175	149	32	r	r	NOUN
ap-10175	149	33	x	x	SYM
ap-10175	149	34	g	g	NOUN
ap-10175	149	35	=	=	NOUN
ap-10175	149	36	0	0	NUM
ap-10175	149	37	.	.	PUNCT
ap-10175	149	38	0	0	NUM
ap-10175	150	1	0	0	NUM
ap-10175	150	2	0	0	NUM
ap-10175	150	3	1	1	NUM
ap-10175	150	4	x	x	SYM
ap-10175	150	5	g	g	NOUN
ap-10175	150	6	=	=	NOUN
ap-10175	150	7	0	0	NUM
ap-10175	150	8	.	.	PUNCT
ap-10175	151	1	1	1	NUM
ap-10175	151	2	x	x	SYM
ap-10175	151	3	g	g	NOUN
ap-10175	151	4	=	=	NOUN
ap-10175	151	5	0	0	NUM
ap-10175	151	6	.	.	PUNCT
ap-10175	151	7	2	2	NUM
ap-10175	151	8	figure	figure	NOUN
ap-10175	151	9	3	3	NUM
ap-10175	151	10	.	.	NOUN
ap-10175	151	11	phase	phase	NOUN
ap-10175	151	12	velocity	velocity	NOUN
ap-10175	151	13	versus	versus	ADP
ap-10175	151	14	wavenumber	wavenumber	NOUN
ap-10175	151	15	with	with	ADP
ap-10175	151	16	different	different	ADJ
ap-10175	151	17	vapour	vapour	NOUN
ap-10175	151	18	quality	quality	NOUN
ap-10175	151	19	p	p	X
ap-10175	151	20	=	=	PROPN
ap-10175	151	21	0	0	NUM
ap-10175	151	22	,	,	PUNCT
ap-10175	151	23	t	t	NOUN
ap-10175	151	24	=	=	SYM
ap-10175	151	25	0	0	NUM
ap-10175	151	26	,	,	PUNCT
ap-10175	151	27	v	v	NOUN
ap-10175	151	28	=	=	SYM
ap-10175	151	29	3	3	NUM
ap-10175	151	30	,	,	PUNCT
ap-10175	151	31	β	β	X
ap-10175	151	32	=	=	SYM
ap-10175	151	33	0.5	0.5	NUM
ap-10175	151	34	.	.	NOUN
ap-10175	151	35	0	0	NUM
ap-10175	151	36	2	2	NUM
ap-10175	151	37	4	4	NUM
ap-10175	151	38	6	6	NUM
ap-10175	151	39	8	8	NUM
ap-10175	151	40	1	1	NUM
ap-10175	151	41	00	00	NUM
ap-10175	151	42	1	1	NUM
ap-10175	151	43	0	0	NUM
ap-10175	151	44	2	2	NUM
ap-10175	151	45	0	0	NUM
ap-10175	151	46	3	3	NUM
ap-10175	151	47	0	0	NUM
ap-10175	151	48	4	4	NUM
ap-10175	151	49	0	0	NUM
ap-10175	151	50	gr	gr	NUM
ap-10175	151	51	ou	ou	ADP
ap-10175	151	52	p	p	PROPN
ap-10175	151	53	v	v	PROPN
ap-10175	151	54	elo	elo	NOUN
ap-10175	151	55	cit	cit	PROPN
ap-10175	151	56	y	y	PROPN
ap-10175	151	57	w	w	PROPN
ap-10175	151	58	a	a	PRON
ap-10175	151	59	v	v	X
ap-10175	151	60	e	e	NOUN
ap-10175	151	61	n	n	CCONJ
ap-10175	151	62	u	u	NOUN
ap-10175	151	63	m	m	NOUN
ap-10175	151	64	b	b	NOUN
ap-10175	151	65	e	e	NOUN
ap-10175	151	66	r	r	NOUN
ap-10175	151	67	x	x	SYM
ap-10175	151	68	g	g	NOUN
ap-10175	151	69	=	=	NOUN
ap-10175	151	70	0	0	NUM
ap-10175	151	71	.	.	PUNCT
ap-10175	151	72	0	0	NUM
ap-10175	152	1	0	0	NUM
ap-10175	152	2	0	0	NUM
ap-10175	152	3	1	1	NUM
ap-10175	152	4	x	x	SYM
ap-10175	152	5	g	g	NOUN
ap-10175	152	6	=	=	NOUN
ap-10175	152	7	0	0	NUM
ap-10175	152	8	.	.	PUNCT
ap-10175	153	1	1	1	NUM
ap-10175	153	2	x	x	SYM
ap-10175	153	3	g	g	NOUN
ap-10175	153	4	=	=	NOUN
ap-10175	153	5	0	0	NUM
ap-10175	153	6	.	.	PUNCT
ap-10175	153	7	2	2	NUM
ap-10175	153	8	figure	figure	NOUN
ap-10175	153	9	4	4	NUM
ap-10175	153	10	.	.	PUNCT
ap-10175	153	11	group	group	NOUN
ap-10175	153	12	velocity	velocity	NOUN
ap-10175	153	13	versus	versus	ADP
ap-10175	153	14	wavenumber	wavenumber	NOUN
ap-10175	153	15	with	with	ADP
ap-10175	153	16	different	different	ADJ
ap-10175	153	17	vapour	vapour	NOUN
ap-10175	153	18	quality	quality	NOUN
ap-10175	153	19	v	v	ADP
ap-10175	153	20	=	=	SYM
ap-10175	153	21	3	3	NUM
ap-10175	153	22	.	.	NOUN
ap-10175	153	23	0	0	NUM
ap-10175	153	24	2	2	NUM
ap-10175	153	25	4	4	NUM
ap-10175	153	26	6	6	NUM
ap-10175	153	27	8	8	NUM
ap-10175	153	28	1	1	NUM
ap-10175	153	29	0	0	NUM
ap-10175	153	30	0	0	NUM
ap-10175	153	31	4	4	NUM
ap-10175	153	32	8	8	NUM
ap-10175	153	33	1	1	NUM
ap-10175	153	34	2	2	NUM
ap-10175	153	35	ph	ph	NOUN
ap-10175	153	36	as	as	ADP
ap-10175	153	37	e	e	NOUN
ap-10175	153	38	v	v	NOUN
ap-10175	153	39	elo	elo	NOUN
ap-10175	153	40	cit	cit	PROPN
ap-10175	153	41	y	y	PROPN
ap-10175	153	42	w	w	PROPN
ap-10175	153	43	a	a	PRON
ap-10175	153	44	v	v	X
ap-10175	153	45	e	e	NOUN
ap-10175	153	46	n	n	CCONJ
ap-10175	153	47	u	u	NOUN
ap-10175	153	48	m	m	PROPN
ap-10175	153	49	b	b	PROPN
ap-10175	153	50	e	e	NOUN
ap-10175	153	51	r	r	NOUN
ap-10175	153	52	�	�	PROPN
ap-10175	153	53	=	=	SYM
ap-10175	153	54	0	0	NUM
ap-10175	153	55	�	�	PROPN
ap-10175	153	56	=	=	SYM
ap-10175	153	57	2	2	NUM
ap-10175	153	58	�	�	NOUN
ap-10175	153	59	=	=	SYM
ap-10175	153	60	4	4	NUM
ap-10175	153	61	figure	figure	NOUN
ap-10175	153	62	5	5	NUM
ap-10175	153	63	.	.	PUNCT
ap-10175	153	64	group	group	NOUN
ap-10175	153	65	velocity	velocity	NOUN
ap-10175	153	66	versus	versus	ADP
ap-10175	153	67	wavenumber	wavenumber	NOUN
ap-10175	153	68	for	for	ADP
ap-10175	153	69	different	different	ADJ
ap-10175	153	70	temperature	temperature	NOUN
ap-10175	153	71	values	value	NOUN
ap-10175	153	72	xg	xg	NOUN
ap-10175	154	1	=	=	NOUN
ap-10175	154	2	0.1	0.1	NUM
ap-10175	154	3	,	,	PUNCT
ap-10175	154	4	v	v	NOUN
ap-10175	154	5	=	=	SYM
ap-10175	154	6	3	3	NUM
ap-10175	154	7	.	.	NUM
ap-10175	154	8	4.3	4.3	NUM
ap-10175	154	9	.	.	PUNCT
ap-10175	154	10	effect	effect	NOUN
ap-10175	154	11	of	of	ADP
ap-10175	154	12	temperature	temperature	NOUN
ap-10175	154	13	on	on	ADP
ap-10175	154	14	phase	phase	NOUN
ap-10175	154	15	and	and	CCONJ
ap-10175	154	16	group	group	NOUN
ap-10175	154	17	velocities	velocity	NOUN
ap-10175	154	18	the	the	DET
ap-10175	154	19	evolution	evolution	NOUN
ap-10175	154	20	of	of	ADP
ap-10175	154	21	the	the	DET
ap-10175	154	22	phase	phase	NOUN
ap-10175	154	23	and	and	CCONJ
ap-10175	154	24	group	group	NOUN
ap-10175	154	25	velocities	velocity	NOUN
ap-10175	154	26	with	with	ADP
ap-10175	154	27	increasing	increase	VERB
ap-10175	154	28	wave	wave	NOUN
ap-10175	154	29	number	number	NOUN
ap-10175	154	30	is	be	AUX
ap-10175	154	31	shown	show	VERB
ap-10175	154	32	in	in	ADP
ap-10175	154	33	figures	figure	NOUN
ap-10175	154	34	5	5	NUM
ap-10175	154	35	and	and	CCONJ
ap-10175	154	36	6	6	NUM
ap-10175	154	37	for	for	ADP
ap-10175	154	38	various	various	ADJ
ap-10175	154	39	temperature	temperature	NOUN
ap-10175	154	40	changes	change	NOUN
ap-10175	154	41	.	.	PUNCT
ap-10175	155	1	it	it	PRON
ap-10175	155	2	is	be	AUX
ap-10175	155	3	observed	observe	VERB
ap-10175	155	4	that	that	SCONJ
ap-10175	155	5	an	an	DET
ap-10175	155	6	increase	increase	NOUN
ap-10175	155	7	in	in	ADP
ap-10175	155	8	temperature	temperature	NOUN
ap-10175	155	9	affects	affect	VERB
ap-10175	155	10	the	the	DET
ap-10175	155	11	transition	transition	NOUN
ap-10175	155	12	point	point	NOUN
ap-10175	155	13	between	between	ADP
ap-10175	155	14	the	the	DET
ap-10175	155	15	non	non	ADJ
ap-10175	155	16	-	-	ADJ
ap-10175	155	17	dispersive	dispersive	ADJ
ap-10175	155	18	and	and	CCONJ
ap-10175	155	19	dispersive	dispersive	ADJ
ap-10175	155	20	wave	wave	NOUN
ap-10175	155	21	behaviour	behaviour	NOUN
ap-10175	155	22	.	.	PUNCT
ap-10175	156	1	for	for	ADP
ap-10175	156	2	the	the	DET
ap-10175	156	3	two	two	NUM
ap-10175	156	4	-	-	PUNCT
ap-10175	156	5	phase	phase	NOUN
ap-10175	156	6	flow	flow	NOUN
ap-10175	156	7	,	,	PUNCT
ap-10175	156	8	an	an	DET
ap-10175	156	9	increase	increase	NOUN
ap-10175	156	10	in	in	ADP
ap-10175	156	11	temperature	temperature	NOUN
ap-10175	156	12	tends	tend	VERB
ap-10175	156	13	to	to	PART
ap-10175	156	14	shift	shift	VERB
ap-10175	156	15	the	the	DET
ap-10175	156	16	dispersive	dispersive	ADJ
ap-10175	156	17	position	position	NOUN
ap-10175	156	18	to	to	ADP
ap-10175	156	19	a	a	DET
ap-10175	156	20	higher	high	ADJ
ap-10175	156	21	wavenumber	wavenumber	NOUN
ap-10175	156	22	.	.	PUNCT
ap-10175	157	1	4.4	4.4	NUM
ap-10175	157	2	.	.	PUNCT
ap-10175	157	3	effect	effect	NOUN
ap-10175	157	4	of	of	ADP
ap-10175	157	5	wavenumber	wavenumber	NOUN
ap-10175	157	6	on	on	ADP
ap-10175	157	7	phase	phase	NOUN
ap-10175	157	8	velocity	velocity	NOUN
ap-10175	157	9	figures	figure	NOUN
ap-10175	157	10	7	7	NUM
ap-10175	157	11	and	and	CCONJ
ap-10175	157	12	8	8	NUM
ap-10175	157	13	illustrate	illustrate	VERB
ap-10175	157	14	how	how	SCONJ
ap-10175	157	15	the	the	DET
ap-10175	157	16	phase	phase	NOUN
ap-10175	157	17	velocity	velocity	NOUN
ap-10175	157	18	of	of	ADP
ap-10175	157	19	a	a	DET
ap-10175	157	20	wave	wave	NOUN
ap-10175	157	21	in	in	ADP
ap-10175	157	22	a	a	DET
ap-10175	157	23	two	two	NUM
ap-10175	157	24	-	-	PUNCT
ap-10175	157	25	phase	phase	NOUN
ap-10175	157	26	flow	flow	NOUN
ap-10175	157	27	system	system	NOUN
ap-10175	157	28	varies	vary	VERB
ap-10175	157	29	with	with	ADP
ap-10175	157	30	the	the	DET
ap-10175	157	31	velocity	velocity	NOUN
ap-10175	157	32	of	of	ADP
ap-10175	157	33	the	the	DET
ap-10175	157	34	liquid	liquid	NOUN
ap-10175	157	35	and	and	CCONJ
ap-10175	157	36	how	how	SCONJ
ap-10175	157	37	this	this	DET
ap-10175	157	38	relationship	relationship	NOUN
ap-10175	157	39	is	be	AUX
ap-10175	157	40	influenced	influence	VERB
ap-10175	157	41	by	by	ADP
ap-10175	157	42	the	the	DET
ap-10175	157	43	wavenumber	wavenumber	NOUN
ap-10175	157	44	.	.	PUNCT
ap-10175	158	1	when	when	SCONJ
ap-10175	158	2	there	there	PRON
ap-10175	158	3	is	be	VERB
ap-10175	158	4	no	no	DET
ap-10175	158	5	real	real	ADJ
ap-10175	158	6	wave	wave	NOUN
ap-10175	158	7	propagation	propagation	NOUN
ap-10175	158	8	(	(	PUNCT
ap-10175	158	9	κ	κ	NOUN
ap-10175	158	10	=	=	NOUN
ap-10175	158	11	0	0	NUM
ap-10175	158	12	)	)	PUNCT
ap-10175	158	13	,	,	PUNCT
ap-10175	158	14	there	there	PRON
ap-10175	158	15	is	be	VERB
ap-10175	158	16	a	a	DET
ap-10175	158	17	linear	linear	ADJ
ap-10175	158	18	relationship	relationship	NOUN
ap-10175	158	19	between	between	ADP
ap-10175	158	20	the	the	DET
ap-10175	158	21	fluid	fluid	ADJ
ap-10175	158	22	velocity	velocity	NOUN
ap-10175	158	23	and	and	CCONJ
ap-10175	158	24	both	both	CCONJ
ap-10175	158	25	the	the	DET
ap-10175	158	26	wave	wave	NOUN
ap-10175	158	27	phase	phase	NOUN
ap-10175	158	28	velocity	velocity	NOUN
ap-10175	158	29	and	and	CCONJ
ap-10175	158	30	wave	wave	NOUN
ap-10175	158	31	group	group	NOUN
ap-10175	158	32	velocity	velocity	NOUN
ap-10175	158	33	.	.	PUNCT
ap-10175	159	1	for	for	ADP
ap-10175	159	2	non	non	ADJ
ap-10175	159	3	-	-	ADJ
ap-10175	159	4	zero	zero	NUM
ap-10175	159	5	wavenumbers	wavenumber	NOUN
ap-10175	159	6	,	,	PUNCT
ap-10175	159	7	the	the	DET
ap-10175	159	8	phase	phase	NOUN
ap-10175	159	9	velocity	velocity	NOUN
ap-10175	159	10	initially	initially	ADV
ap-10175	159	11	increases	increase	VERB
ap-10175	159	12	with	with	ADP
ap-10175	159	13	the	the	DET
ap-10175	159	14	liquid	liquid	ADJ
ap-10175	159	15	velocity	velocity	NOUN
ap-10175	159	16	,	,	PUNCT
ap-10175	159	17	reaches	reach	VERB
ap-10175	159	18	a	a	DET
ap-10175	159	19	peak	peak	NOUN
ap-10175	159	20	,	,	PUNCT
ap-10175	159	21	and	and	CCONJ
ap-10175	159	22	then	then	ADV
ap-10175	159	23	337	337	NUM
ap-10175	159	24	a.	a.	NOUN
ap-10175	159	25	o.	o.	NOUN
ap-10175	159	26	oyelade	oyelade	NOUN
ap-10175	159	27	,	,	PUNCT
ap-10175	159	28	a.	a.	PROPN
ap-10175	159	29	b.	b.	PROPN
ap-10175	159	30	ehinmowo	ehinmowo	PROPN
ap-10175	159	31	,	,	PUNCT
ap-10175	159	32	o.	o.	PROPN
ap-10175	159	33	oribayo	oribayo	PROPN
ap-10175	159	34	,	,	PUNCT
ap-10175	159	35	y.	y.	PROPN
ap-10175	159	36	o.	o.	PROPN
ap-10175	159	37	abiodun	abiodun	PROPN
ap-10175	159	38	acta	acta	PROPN
ap-10175	159	39	polytechnica	polytechnica	PROPN
ap-10175	159	40	0	0	NUM
ap-10175	160	1	2	2	NUM
ap-10175	160	2	4	4	NUM
ap-10175	160	3	6	6	NUM
ap-10175	160	4	8	8	NUM
ap-10175	160	5	1	1	NUM
ap-10175	160	6	0	0	NUM
ap-10175	160	7	0	0	NUM
ap-10175	160	8	1	1	NUM
ap-10175	160	9	0	0	NUM
ap-10175	160	10	2	2	NUM
ap-10175	160	11	0	0	NUM
ap-10175	160	12	3	3	NUM
ap-10175	160	13	0	0	NUM
ap-10175	160	14	4	4	NUM
ap-10175	160	15	0	0	NUM
ap-10175	160	16	gr	gr	NUM
ap-10175	160	17	ou	ou	ADP
ap-10175	160	18	p	p	PROPN
ap-10175	160	19	v	v	PROPN
ap-10175	160	20	elo	elo	NOUN
ap-10175	160	21	cit	cit	PROPN
ap-10175	160	22	y	y	PROPN
ap-10175	160	23	w	w	PROPN
ap-10175	160	24	a	a	PRON
ap-10175	160	25	v	v	X
ap-10175	160	26	e	e	NOUN
ap-10175	160	27	n	n	CCONJ
ap-10175	160	28	u	u	NOUN
ap-10175	160	29	m	m	PROPN
ap-10175	160	30	b	b	PROPN
ap-10175	160	31	e	e	NOUN
ap-10175	160	32	r	r	NOUN
ap-10175	160	33	�	�	PROPN
ap-10175	160	34	=	=	SYM
ap-10175	160	35	0	0	NUM
ap-10175	160	36	�	�	PROPN
ap-10175	160	37	=	=	SYM
ap-10175	160	38	2	2	NUM
ap-10175	160	39	�	�	NOUN
ap-10175	160	40	=	=	SYM
ap-10175	160	41	4	4	NUM
ap-10175	160	42	figure	figure	NOUN
ap-10175	160	43	6	6	NUM
ap-10175	160	44	.	.	PUNCT
ap-10175	160	45	group	group	NOUN
ap-10175	160	46	velocity	velocity	NOUN
ap-10175	160	47	versus	versus	ADP
ap-10175	160	48	wavenumber	wavenumber	NOUN
ap-10175	160	49	for	for	ADP
ap-10175	160	50	different	different	ADJ
ap-10175	160	51	vapour	vapour	NOUN
ap-10175	160	52	quality	quality	NOUN
ap-10175	160	53	values	value	NOUN
ap-10175	160	54	,	,	PUNCT
ap-10175	160	55	xg	xg	PROPN
ap-10175	160	56	=	=	NOUN
ap-10175	160	57	0.1	0.1	NUM
ap-10175	160	58	,	,	PUNCT
ap-10175	160	59	v	v	NOUN
ap-10175	160	60	=	=	SYM
ap-10175	160	61	3	3	NUM
ap-10175	160	62	.	.	NOUN
ap-10175	160	63	0	0	NUM
ap-10175	160	64	2	2	NUM
ap-10175	160	65	4	4	NUM
ap-10175	160	66	6	6	NUM
ap-10175	160	67	8	8	NUM
ap-10175	160	68	1	1	NUM
ap-10175	160	69	0	0	NUM
ap-10175	160	70	0	0	NUM
ap-10175	160	71	4	4	NUM
ap-10175	160	72	8	8	NUM
ap-10175	160	73	1	1	NUM
ap-10175	160	74	2	2	NUM
ap-10175	160	75	ph	ph	NOUN
ap-10175	160	76	as	as	ADP
ap-10175	160	77	e	e	NOUN
ap-10175	160	78	v	v	NOUN
ap-10175	160	79	elo	elo	NOUN
ap-10175	160	80	cit	cit	PROPN
ap-10175	160	81	y	y	PROPN
ap-10175	160	82	v	v	PROPN
ap-10175	160	83	e	e	X
ap-10175	160	84	l	l	NOUN
ap-10175	160	85	o	o	X
ap-10175	161	1	c	c	NOUN
ap-10175	162	1	i	i	PRON
ap-10175	162	2	t	t	VERB
ap-10175	163	1	y	y	NOUN
ap-10175	164	1	o	o	X
ap-10175	165	1	f	f	X
ap-10175	166	1	l	l	NOUN
ap-10175	167	1	i	i	PRON
ap-10175	167	2	q	q	NOUN
ap-10175	167	3	u	u	NOUN
ap-10175	167	4	i	i	NOUN
ap-10175	167	5	d	d	PROPN
ap-10175	167	6	�	�	PROPN
ap-10175	167	7	=	=	SYM
ap-10175	167	8	0	0	NUM
ap-10175	167	9	�	�	PROPN
ap-10175	167	10	=	=	SYM
ap-10175	167	11	2	2	NUM
ap-10175	167	12	�	�	NOUN
ap-10175	167	13	=	=	SYM
ap-10175	167	14	4	4	NUM
ap-10175	167	15	�	�	NOUN
ap-10175	167	16	=	=	SYM
ap-10175	167	17	6	6	NUM
ap-10175	167	18	figure	figure	NOUN
ap-10175	167	19	7	7	NUM
ap-10175	167	20	.	.	NOUN
ap-10175	167	21	phase	phase	NOUN
ap-10175	167	22	velocity	velocity	NOUN
ap-10175	167	23	versus	versus	ADP
ap-10175	167	24	wavenumber	wavenumber	NOUN
ap-10175	167	25	for	for	ADP
ap-10175	167	26	different	different	ADJ
ap-10175	167	27	wavenumber	wavenumber	NOUN
ap-10175	167	28	values	value	VERB
ap-10175	167	29	p	p	X
ap-10175	167	30	=	=	NOUN
ap-10175	167	31	0	0	NUM
ap-10175	167	32	,	,	PUNCT
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ap-10175	167	34	=	=	SYM
ap-10175	167	35	0	0	NUM
ap-10175	167	36	,	,	PUNCT
ap-10175	167	37	xg	xg	NOUN
ap-10175	167	38	=	=	SYM
ap-10175	167	39	0.0001	0.0001	NUM
ap-10175	167	40	,	,	PUNCT
ap-10175	167	41	β	β	X
ap-10175	167	42	=	=	SYM
ap-10175	167	43	0.5	0.5	NUM
ap-10175	167	44	.	.	NOUN
ap-10175	167	45	0	0	NUM
ap-10175	167	46	2	2	NUM
ap-10175	167	47	4	4	NUM
ap-10175	167	48	6	6	NUM
ap-10175	167	49	8	8	NUM
ap-10175	167	50	1	1	NUM
ap-10175	167	51	0	0	NUM
ap-10175	167	52	0	0	NUM
ap-10175	167	53	1	1	NUM
ap-10175	167	54	0	0	NUM
ap-10175	167	55	2	2	NUM
ap-10175	167	56	0	0	NUM
ap-10175	167	57	3	3	NUM
ap-10175	167	58	0	0	NUM
ap-10175	167	59	gr	gr	NUM
ap-10175	167	60	ou	ou	ADP
ap-10175	167	61	p	p	PROPN
ap-10175	167	62	v	v	PROPN
ap-10175	167	63	elo	elo	NOUN
ap-10175	167	64	cit	cit	PROPN
ap-10175	167	65	y	y	PROPN
ap-10175	167	66	v	v	PROPN
ap-10175	167	67	e	e	X
ap-10175	167	68	l	l	NOUN
ap-10175	167	69	o	o	X
ap-10175	168	1	c	c	NOUN
ap-10175	169	1	i	i	PRON
ap-10175	169	2	t	t	VERB
ap-10175	170	1	y	y	NOUN
ap-10175	171	1	o	o	X
ap-10175	172	1	f	f	X
ap-10175	173	1	l	l	NOUN
ap-10175	174	1	i	i	PRON
ap-10175	174	2	q	q	NOUN
ap-10175	174	3	u	u	NOUN
ap-10175	174	4	i	i	NOUN
ap-10175	174	5	d	d	PROPN
ap-10175	174	6	�	�	PROPN
ap-10175	174	7	=	=	SYM
ap-10175	174	8	0	0	NUM
ap-10175	174	9	�	�	PROPN
ap-10175	174	10	=	=	SYM
ap-10175	174	11	2	2	NUM
ap-10175	174	12	�	�	NOUN
ap-10175	174	13	=	=	SYM
ap-10175	174	14	4	4	NUM
ap-10175	174	15	�	�	NOUN
ap-10175	174	16	=	=	SYM
ap-10175	174	17	6	6	NUM
ap-10175	174	18	figure	figure	NOUN
ap-10175	174	19	8	8	NUM
ap-10175	174	20	.	.	PUNCT
ap-10175	175	1	group	group	NOUN
ap-10175	175	2	velocity	velocity	NOUN
ap-10175	175	3	versus	versus	ADP
ap-10175	175	4	wavenumber	wavenumber	NOUN
ap-10175	175	5	for	for	ADP
ap-10175	175	6	different	different	ADJ
ap-10175	175	7	wavenumber	wavenumber	NOUN
ap-10175	175	8	values	value	VERB
ap-10175	175	9	p	p	X
ap-10175	175	10	=	=	NOUN
ap-10175	175	11	0	0	NUM
ap-10175	175	12	,	,	PUNCT
ap-10175	175	13	t	t	NOUN
ap-10175	175	14	=	=	SYM
ap-10175	175	15	0	0	NUM
ap-10175	175	16	,	,	PUNCT
ap-10175	175	17	xg	xg	NOUN
ap-10175	175	18	=	=	SYM
ap-10175	175	19	0.0001	0.0001	NUM
ap-10175	175	20	,	,	PUNCT
ap-10175	175	21	β	β	X
ap-10175	175	22	=	=	SYM
ap-10175	175	23	0.5	0.5	NUM
ap-10175	175	24	.	.	PUNCT
ap-10175	176	1	decreases	decrease	NOUN
ap-10175	176	2	,	,	PUNCT
ap-10175	176	3	indicating	indicate	VERB
ap-10175	176	4	a	a	DET
ap-10175	176	5	dispersive	dispersive	ADJ
ap-10175	176	6	behaviour	behaviour	NOUN
ap-10175	176	7	.	.	PUNCT
ap-10175	177	1	for	for	ADP
ap-10175	177	2	illustration	illustration	NOUN
ap-10175	177	3	,	,	PUNCT
ap-10175	177	4	when	when	SCONJ
ap-10175	177	5	the	the	DET
ap-10175	177	6	wavenumber	wavenumber	NOUN
ap-10175	177	7	is	be	AUX
ap-10175	177	8	4	4	NUM
ap-10175	177	9	,	,	PUNCT
ap-10175	177	10	the	the	DET
ap-10175	177	11	wave	wave	NOUN
ap-10175	177	12	phase	phase	NOUN
ap-10175	177	13	velocity	velocity	NOUN
ap-10175	177	14	increases	increase	NOUN
ap-10175	177	15	from	from	ADP
ap-10175	177	16	zero	zero	NUM
ap-10175	177	17	to	to	ADP
ap-10175	177	18	5	5	NUM
ap-10175	177	19	as	as	ADP
ap-10175	177	20	the	the	DET
ap-10175	177	21	velocity	velocity	NOUN
ap-10175	177	22	of	of	ADP
ap-10175	177	23	the	the	DET
ap-10175	177	24	liquid	liquid	ADJ
ap-10175	177	25	increases	increase	NOUN
ap-10175	177	26	.	.	PUNCT
ap-10175	178	1	then	then	ADV
ap-10175	178	2	,	,	PUNCT
ap-10175	178	3	between	between	ADP
ap-10175	178	4	liquid	liquid	ADJ
ap-10175	178	5	velocities	velocity	NOUN
ap-10175	178	6	of	of	ADP
ap-10175	178	7	5	5	NUM
ap-10175	178	8	and	and	CCONJ
ap-10175	178	9	5.5	5.5	NUM
ap-10175	178	10	,	,	PUNCT
ap-10175	178	11	the	the	DET
ap-10175	178	12	phase	phase	NOUN
ap-10175	178	13	velocity	velocity	NOUN
ap-10175	178	14	decreases	decrease	VERB
ap-10175	178	15	with	with	ADP
ap-10175	178	16	increasing	increase	VERB
ap-10175	178	17	liquid	liquid	ADJ
ap-10175	178	18	velocity	velocity	NOUN
ap-10175	178	19	.	.	PUNCT
ap-10175	179	1	at	at	ADP
ap-10175	179	2	a	a	DET
ap-10175	179	3	liquid	liquid	ADJ
ap-10175	179	4	velocity	velocity	NOUN
ap-10175	179	5	of	of	ADP
ap-10175	179	6	5.5	5.5	NUM
ap-10175	179	7	,	,	PUNCT
ap-10175	179	8	the	the	DET
ap-10175	179	9	relationship	relationship	NOUN
ap-10175	179	10	between	between	ADP
ap-10175	179	11	the	the	DET
ap-10175	179	12	liquid	liquid	ADJ
ap-10175	179	13	velocity	velocity	NOUN
ap-10175	179	14	and	and	CCONJ
ap-10175	179	15	the	the	DET
ap-10175	179	16	phase	phase	NOUN
ap-10175	179	17	velocity	velocity	NOUN
ap-10175	179	18	becomes	become	VERB
ap-10175	179	19	linear	linear	ADJ
ap-10175	179	20	again	again	ADV
ap-10175	179	21	.	.	PUNCT
ap-10175	180	1	4.5	4.5	NUM
ap-10175	180	2	.	.	PUNCT
ap-10175	180	3	natural	natural	ADJ
ap-10175	180	4	frequency	frequency	NOUN
ap-10175	180	5	of	of	ADP
ap-10175	180	6	two	two	NUM
ap-10175	180	7	-	-	PUNCT
ap-10175	180	8	phase	phase	NOUN
ap-10175	180	9	flow	flow	NOUN
ap-10175	180	10	the	the	DET
ap-10175	180	11	relationships	relationship	NOUN
ap-10175	180	12	between	between	ADP
ap-10175	180	13	flow	flow	NOUN
ap-10175	180	14	velocity	velocity	NOUN
ap-10175	180	15	and	and	CCONJ
ap-10175	180	16	natural	natural	ADJ
ap-10175	180	17	frequency	frequency	NOUN
ap-10175	180	18	are	be	AUX
ap-10175	180	19	shown	show	VERB
ap-10175	180	20	in	in	ADP
ap-10175	180	21	figure	figure	NOUN
ap-10175	180	22	9	9	NUM
ap-10175	180	23	,	,	PUNCT
ap-10175	180	24	in	in	ADP
ap-10175	180	25	which	which	PRON
ap-10175	180	26	the	the	DET
ap-10175	180	27	number	number	NOUN
ap-10175	180	28	of	of	ADP
ap-10175	180	29	mode	mode	NOUN
ap-10175	180	30	is	be	AUX
ap-10175	180	31	fixed	fix	VERB
ap-10175	180	32	to	to	PART
ap-10175	180	33	be	be	AUX
ap-10175	180	34	n	n	PRON
ap-10175	180	35	=	=	SYM
ap-10175	180	36	1	1	X
ap-10175	180	37	.	.	X
ap-10175	181	1	for	for	ADP
ap-10175	181	2	a	a	DET
ap-10175	181	3	single	single	ADJ
ap-10175	181	4	phase	phase	NOUN
ap-10175	181	5	flow	flow	NOUN
ap-10175	181	6	(	(	PUNCT
ap-10175	181	7	xg	xg	NOUN
ap-10175	181	8	=	=	SYM
ap-10175	181	9	0.0001	0.0001	NUM
ap-10175	181	10	)	)	PUNCT
ap-10175	181	11	,	,	PUNCT
ap-10175	181	12	the	the	DET
ap-10175	181	13	critical	critical	ADJ
ap-10175	181	14	velocity	velocity	NOUN
ap-10175	181	15	is	be	AUX
ap-10175	181	16	3.14	3.14	NUM
ap-10175	181	17	.	.	PUNCT
ap-10175	182	1	as	as	SCONJ
ap-10175	182	2	the	the	DET
ap-10175	182	3	vapour	vapour	NOUN
ap-10175	182	4	quality	quality	NOUN
ap-10175	182	5	increases	increase	VERB
ap-10175	182	6	in	in	ADP
ap-10175	182	7	the	the	DET
ap-10175	182	8	flow	flow	NOUN
ap-10175	182	9	,	,	PUNCT
ap-10175	182	10	i.e.	i.e.	X
ap-10175	182	11	the	the	DET
ap-10175	182	12	flow	flow	NOUN
ap-10175	182	13	turns	turn	VERB
ap-10175	182	14	to	to	ADP
ap-10175	182	15	two	two	NUM
ap-10175	182	16	phase	phase	NOUN
ap-10175	182	17	flow	flow	NOUN
ap-10175	182	18	,	,	PUNCT
ap-10175	182	19	the	the	DET
ap-10175	182	20	critical	critical	ADJ
ap-10175	182	21	velocity	velocity	NOUN
ap-10175	182	22	reduces	reduce	VERB
ap-10175	182	23	.	.	PUNCT
ap-10175	183	1	when	when	SCONJ
ap-10175	183	2	xg	xg	PROPN
ap-10175	183	3	=	=	NOUN
ap-10175	183	4	0.3	0.3	NUM
ap-10175	183	5	,	,	PUNCT
ap-10175	183	6	the	the	DET
ap-10175	183	7	critical	critical	ADJ
ap-10175	183	8	velocity	velocity	NOUN
ap-10175	183	9	is	be	AUX
ap-10175	183	10	1.1	1.1	NUM
ap-10175	183	11	.	.	PUNCT
ap-10175	184	1	the	the	DET
ap-10175	184	2	imaginary	imaginary	ADJ
ap-10175	184	3	frequency	frequency	NOUN
ap-10175	184	4	plots	plot	NOUN
ap-10175	184	5	confirm	confirm	VERB
ap-10175	184	6	the	the	DET
ap-10175	184	7	critical	critical	ADJ
ap-10175	184	8	velocity	velocity	NOUN
ap-10175	184	9	point	point	NOUN
ap-10175	184	10	as	as	SCONJ
ap-10175	184	11	shown	show	VERB
ap-10175	184	12	in	in	ADP
ap-10175	184	13	the	the	DET
ap-10175	184	14	real	real	ADJ
ap-10175	184	15	part	part	NOUN
ap-10175	184	16	.	.	PUNCT
ap-10175	185	1	the	the	DET
ap-10175	185	2	influence	influence	NOUN
ap-10175	185	3	of	of	ADP
ap-10175	185	4	temperature	temperature	NOUN
ap-10175	185	5	on	on	ADP
ap-10175	185	6	the	the	DET
ap-10175	185	7	first	first	ADJ
ap-10175	185	8	three	three	NUM
ap-10175	185	9	modes	mode	NOUN
ap-10175	185	10	of	of	ADP
ap-10175	185	11	the	the	DET
ap-10175	185	12	natural	natural	ADJ
ap-10175	185	13	frequency	frequency	NOUN
ap-10175	185	14	is	be	AUX
ap-10175	185	15	shown	show	VERB
ap-10175	185	16	in	in	ADP
ap-10175	185	17	figure	figure	NOUN
ap-10175	185	18	10	10	NUM
ap-10175	185	19	.	.	PUNCT
ap-10175	186	1	temperature	temperature	NOUN
ap-10175	186	2	reduces	reduce	VERB
ap-10175	186	3	the	the	DET
ap-10175	186	4	critical	critical	ADJ
ap-10175	186	5	velocity	velocity	NOUN
ap-10175	186	6	of	of	ADP
ap-10175	186	7	the	the	DET
ap-10175	186	8	flow	flow	NOUN
ap-10175	186	9	,	,	PUNCT
ap-10175	186	10	as	as	SCONJ
ap-10175	186	11	can	can	AUX
ap-10175	186	12	be	be	AUX
ap-10175	186	13	observed	observe	VERB
ap-10175	186	14	for	for	ADP
ap-10175	186	15	both	both	CCONJ
ap-10175	186	16	the	the	DET
ap-10175	186	17	real	real	ADJ
ap-10175	186	18	and	and	CCONJ
ap-10175	186	19	imaginary	imaginary	ADJ
ap-10175	186	20	frequencies	frequency	NOUN
ap-10175	186	21	in	in	ADP
ap-10175	186	22	figure	figure	NOUN
ap-10175	186	23	10	10	NUM
ap-10175	186	24	.	.	PUNCT
ap-10175	187	1	5	5	NUM
ap-10175	187	2	.	.	X
ap-10175	187	3	conclusion	conclusion	VERB
ap-10175	187	4	the	the	DET
ap-10175	187	5	characteristics	characteristic	NOUN
ap-10175	187	6	of	of	ADP
ap-10175	187	7	wave	wave	NOUN
ap-10175	187	8	propagation	propagation	NOUN
ap-10175	187	9	in	in	ADP
ap-10175	187	10	a	a	DET
ap-10175	187	11	pipe	pipe	NOUN
ap-10175	187	12	conveying	convey	VERB
ap-10175	187	13	a	a	DET
ap-10175	187	14	two	two	NUM
ap-10175	187	15	phase	phase	NOUN
ap-10175	187	16	flow	flow	NOUN
ap-10175	187	17	is	be	AUX
ap-10175	187	18	studied	study	VERB
ap-10175	187	19	in	in	ADP
ap-10175	187	20	this	this	DET
ap-10175	187	21	paper	paper	NOUN
ap-10175	187	22	.	.	PUNCT
ap-10175	188	1	chisolm	chisolm	ADJ
ap-10175	188	2	correlation	correlation	NOUN
ap-10175	188	3	model	model	NOUN
ap-10175	188	4	was	be	AUX
ap-10175	188	5	used	use	VERB
ap-10175	188	6	to	to	PART
ap-10175	188	7	relate	relate	VERB
ap-10175	188	8	the	the	DET
ap-10175	188	9	twophase	twophase	NOUN
ap-10175	188	10	flow	flow	NOUN
ap-10175	188	11	in	in	ADP
ap-10175	188	12	the	the	DET
ap-10175	188	13	governing	govern	VERB
ap-10175	188	14	equation	equation	NOUN
ap-10175	188	15	.	.	PUNCT
ap-10175	189	1	a	a	DET
ap-10175	189	2	harmonic	harmonic	ADJ
ap-10175	189	3	solution	solution	NOUN
ap-10175	189	4	in	in	ADP
ap-10175	189	5	the	the	DET
ap-10175	189	6	form	form	NOUN
ap-10175	189	7	of	of	ADP
ap-10175	189	8	a	a	DET
ap-10175	189	9	traveling	travel	VERB
ap-10175	189	10	wave	wave	NOUN
ap-10175	189	11	was	be	AUX
ap-10175	189	12	used	use	VERB
ap-10175	189	13	to	to	PART
ap-10175	189	14	investigate	investigate	VERB
ap-10175	189	15	the	the	DET
ap-10175	189	16	phase	phase	NOUN
ap-10175	189	17	and	and	CCONJ
ap-10175	189	18	group	group	NOUN
ap-10175	189	19	velocities	velocity	NOUN
ap-10175	189	20	of	of	ADP
ap-10175	189	21	the	the	DET
ap-10175	189	22	two	two	NUM
ap-10175	189	23	-	-	PUNCT
ap-10175	189	24	phase	phase	NOUN
ap-10175	189	25	flow	flow	NOUN
ap-10175	189	26	dynamics	dynamic	NOUN
ap-10175	189	27	.	.	PUNCT
ap-10175	190	1	in	in	ADP
ap-10175	190	2	the	the	DET
ap-10175	190	3	numerical	numerical	ADJ
ap-10175	190	4	result	result	NOUN
ap-10175	190	5	,	,	PUNCT
ap-10175	190	6	the	the	DET
ap-10175	190	7	phase	phase	NOUN
ap-10175	190	8	velocity	velocity	NOUN
ap-10175	190	9	remains	remain	VERB
ap-10175	190	10	constant	constant	ADJ
ap-10175	190	11	over	over	ADP
ap-10175	190	12	a	a	DET
ap-10175	190	13	range	range	NOUN
ap-10175	190	14	of	of	ADP
ap-10175	190	15	wavenumbers	wavenumber	NOUN
ap-10175	190	16	for	for	ADP
ap-10175	190	17	the	the	DET
ap-10175	190	18	single	single	ADJ
ap-10175	190	19	-	-	PUNCT
ap-10175	190	20	phase	phase	NOUN
ap-10175	190	21	flow	flow	NOUN
ap-10175	190	22	,	,	PUNCT
ap-10175	190	23	while	while	SCONJ
ap-10175	190	24	for	for	ADP
ap-10175	190	25	the	the	DET
ap-10175	190	26	two	two	NUM
ap-10175	190	27	-	-	PUNCT
ap-10175	190	28	phase	phase	NOUN
ap-10175	190	29	flow	flow	NOUN
ap-10175	190	30	,	,	PUNCT
ap-10175	190	31	increased	increase	VERB
ap-10175	190	32	vapour	vapour	NOUN
ap-10175	190	33	quality	quality	NOUN
ap-10175	190	34	delays	delay	NOUN
ap-10175	190	35	the	the	DET
ap-10175	190	36	onset	onset	NOUN
ap-10175	190	37	of	of	ADP
ap-10175	190	38	dispersion	dispersion	NOUN
ap-10175	190	39	to	to	ADP
ap-10175	190	40	higher	high	ADJ
ap-10175	190	41	wavenumbers	wavenumber	NOUN
ap-10175	190	42	,	,	PUNCT
ap-10175	190	43	and	and	CCONJ
ap-10175	190	44	the	the	DET
ap-10175	190	45	group	group	NOUN
ap-10175	190	46	velocity	velocity	NOUN
ap-10175	190	47	exhibits	exhibit	VERB
ap-10175	190	48	critical	critical	ADJ
ap-10175	190	49	behaviour	behaviour	NOUN
ap-10175	190	50	,	,	PUNCT
ap-10175	190	51	indicative	indicative	ADJ
ap-10175	190	52	of	of	ADP
ap-10175	190	53	localised	localised	ADJ
ap-10175	190	54	energy	energy	NOUN
ap-10175	190	55	distribution	distribution	NOUN
ap-10175	190	56	.	.	PUNCT
ap-10175	191	1	temperature	temperature	NOUN
ap-10175	191	2	further	further	ADJ
ap-10175	191	3	modulates	modulate	NOUN
ap-10175	191	4	this	this	DET
ap-10175	191	5	behaviour	behaviour	NOUN
ap-10175	191	6	by	by	ADP
ap-10175	191	7	shifting	shift	VERB
ap-10175	191	8	the	the	DET
ap-10175	191	9	transition	transition	NOUN
ap-10175	191	10	between	between	ADP
ap-10175	191	11	non	non	ADJ
ap-10175	191	12	-	-	ADJ
ap-10175	191	13	dispersive	dispersive	ADJ
ap-10175	191	14	and	and	CCONJ
ap-10175	191	15	dispersive	dispersive	ADJ
ap-10175	191	16	regimes	regime	NOUN
ap-10175	191	17	to	to	ADP
ap-10175	191	18	higher	high	ADJ
ap-10175	191	19	wavenumbers	wavenumber	NOUN
ap-10175	191	20	,	,	PUNCT
ap-10175	191	21	and	and	CCONJ
ap-10175	191	22	variations	variation	NOUN
ap-10175	191	23	in	in	ADP
ap-10175	191	24	liquid	liquid	ADJ
ap-10175	191	25	velocity	velocity	NOUN
ap-10175	191	26	and	and	CCONJ
ap-10175	191	27	wavenumber	wavenumber	NOUN
ap-10175	191	28	reveal	reveal	VERB
ap-10175	191	29	complex	complex	ADJ
ap-10175	191	30	dispersive	dispersive	ADJ
ap-10175	191	31	effects	effect	NOUN
ap-10175	191	32	on	on	ADP
ap-10175	191	33	the	the	DET
ap-10175	191	34	phase	phase	NOUN
ap-10175	191	35	velocity	velocity	NOUN
ap-10175	191	36	.	.	PUNCT
ap-10175	192	1	additionally	additionally	ADV
ap-10175	192	2	,	,	PUNCT
ap-10175	192	3	the	the	DET
ap-10175	192	4	natural	natural	ADJ
ap-10175	192	5	frequency	frequency	NOUN
ap-10175	192	6	analysis	analysis	NOUN
ap-10175	192	7	shows	show	VERB
ap-10175	192	8	that	that	SCONJ
ap-10175	192	9	as	as	ADP
ap-10175	192	10	the	the	DET
ap-10175	192	11	flow	flow	NOUN
ap-10175	192	12	transitions	transition	NOUN
ap-10175	192	13	from	from	ADP
ap-10175	192	14	singlephase	singlephase	NOUN
ap-10175	192	15	to	to	ADP
ap-10175	192	16	two	two	NUM
ap-10175	192	17	-	-	PUNCT
ap-10175	192	18	phase	phase	NOUN
ap-10175	192	19	,	,	PUNCT
ap-10175	192	20	the	the	DET
ap-10175	192	21	critical	critical	ADJ
ap-10175	192	22	velocity	velocity	NOUN
ap-10175	192	23	decreases	decrease	VERB
ap-10175	192	24	,	,	PUNCT
ap-10175	192	25	with	with	ADP
ap-10175	192	26	temperature	temperature	NOUN
ap-10175	192	27	exerting	exert	VERB
ap-10175	192	28	a	a	DET
ap-10175	192	29	reducing	reduce	VERB
ap-10175	192	30	effect	effect	NOUN
ap-10175	192	31	on	on	ADP
ap-10175	192	32	the	the	DET
ap-10175	192	33	critical	critical	ADJ
ap-10175	192	34	velocity	velocity	NOUN
ap-10175	192	35	across	across	ADP
ap-10175	192	36	different	different	ADJ
ap-10175	192	37	modes	mode	NOUN
ap-10175	192	38	,	,	PUNCT
ap-10175	192	39	underscoring	underscore	VERB
ap-10175	192	40	the	the	DET
ap-10175	192	41	intricate	intricate	ADJ
ap-10175	192	42	interplay	interplay	NOUN
ap-10175	192	43	between	between	ADP
ap-10175	192	44	flow	flow	NOUN
ap-10175	192	45	parameters	parameter	NOUN
ap-10175	192	46	and	and	CCONJ
ap-10175	192	47	wave	wave	NOUN
ap-10175	192	48	dynamics	dynamic	NOUN
ap-10175	192	49	in	in	ADP
ap-10175	192	50	two	two	NUM
ap-10175	192	51	-	-	PUNCT
ap-10175	192	52	phase	phase	NOUN
ap-10175	192	53	systems	system	NOUN
ap-10175	192	54	.	.	PUNCT
ap-10175	193	1	list	list	NOUN
ap-10175	193	2	of	of	ADP
ap-10175	193	3	symbols	symbol	NOUN
ap-10175	193	4	l	l	PROPN
ap-10175	193	5	length	length	NOUN
ap-10175	193	6	of	of	ADP
ap-10175	193	7	the	the	DET
ap-10175	193	8	pipe	pipe	NOUN
ap-10175	193	9	e	e	NOUN
ap-10175	193	10	elastic	elastic	ADJ
ap-10175	193	11	modulus	modulus	NOUN
ap-10175	194	1	i	i	PRON
ap-10175	194	2	moment	moment	VERB
ap-10175	194	3	of	of	ADP
ap-10175	194	4	inertia	inertia	NOUN
ap-10175	194	5	a	a	DET
ap-10175	194	6	cross	cross	ADJ
ap-10175	194	7	-	-	ADJ
ap-10175	194	8	sectional	sectional	ADJ
ap-10175	194	9	area	area	NOUN
ap-10175	194	10	p̄	p̄	PROPN
ap-10175	194	11	pressure	pressure	VERB
ap-10175	194	12	t̄	t̄	PROPN
ap-10175	194	13	tension	tension	NOUN
ap-10175	194	14	338	338	NUM
ap-10175	194	15	vol	vol	NOUN
ap-10175	194	16	.	.	PUNCT
ap-10175	195	1	65	65	NUM
ap-10175	195	2	no	no	NOUN
ap-10175	195	3	.	.	PUNCT
ap-10175	196	1	3/2025	3/2025	NUM
ap-10175	196	2	wave	wave	NOUN
ap-10175	196	3	propagation	propagation	NOUN
ap-10175	196	4	in	in	ADP
ap-10175	196	5	a	a	DET
ap-10175	196	6	pipe	pipe	NOUN
ap-10175	196	7	conveying	convey	VERB
ap-10175	196	8	two	two	NUM
ap-10175	196	9	phase	phase	NOUN
ap-10175	196	10	flow	flow	NOUN
ap-10175	196	11	0	0	NUM
ap-10175	196	12	1	1	NUM
ap-10175	196	13	2	2	NUM
ap-10175	196	14	3	3	NUM
ap-10175	196	15	4	4	NUM
ap-10175	196	16	5	5	NUM
ap-10175	196	17	6	6	NUM
ap-10175	196	18	0	0	NUM
ap-10175	196	19	2	2	NUM
ap-10175	196	20	4	4	NUM
ap-10175	196	21	6	6	NUM
ap-10175	196	22	8	8	NUM
ap-10175	196	23	10	10	NUM
ap-10175	196	24	r	r	NOUN
ap-10175	196	25	e	e	NOUN
ap-10175	196	26	(	(	PUNCT
ap-10175	196	27	)	)	PUNCT
ap-10175	196	28	flow	flow	NOUN
ap-10175	196	29	velocity	velocity	NOUN
ap-10175	196	30	xg	xg	NOUN
ap-10175	197	1	=	=	SYM
ap-10175	197	2	0.0001	0.0001	NUM
ap-10175	197	3	xg	xg	NOUN
ap-10175	197	4	=	=	SYM
ap-10175	197	5	0.1	0.1	NUM
ap-10175	197	6	xg	xg	NOUN
ap-10175	197	7	=	=	NOUN
ap-10175	197	8	0.3	0.3	NUM
ap-10175	197	9	(	(	PUNCT
ap-10175	197	10	a	a	NOUN
ap-10175	197	11	)	)	PUNCT
ap-10175	197	12	.	.	PUNCT
ap-10175	198	1	real	real	ADJ
ap-10175	198	2	.	.	PUNCT
ap-10175	199	1	0	0	NUM
ap-10175	199	2	1	1	NUM
ap-10175	199	3	2	2	NUM
ap-10175	199	4	3	3	NUM
ap-10175	199	5	4	4	NUM
ap-10175	199	6	5	5	NUM
ap-10175	199	7	6	6	NUM
ap-10175	199	8	-60	-60	SYM
ap-10175	199	9	-40	-40	PROPN
ap-10175	199	10	-20	-20	NUM
ap-10175	199	11	0	0	NUM
ap-10175	199	12	20	20	NUM
ap-10175	199	13	40	40	NUM
ap-10175	199	14	60	60	NUM
ap-10175	199	15	i	i	PRON
ap-10175	199	16	m	m	VERB
ap-10175	199	17	ag	ag	PROPN
ap-10175	199	18	(	(	PUNCT
ap-10175	199	19	)	)	PUNCT
ap-10175	199	20	flow	flow	NOUN
ap-10175	199	21	velocity	velocity	NOUN
ap-10175	199	22	xg	xg	NOUN
ap-10175	199	23	=	=	SYM
ap-10175	200	1	0.0001	0.0001	NUM
ap-10175	200	2	xg	xg	NOUN
ap-10175	200	3	=	=	SYM
ap-10175	200	4	0.1	0.1	NUM
ap-10175	200	5	xg	xg	NOUN
ap-10175	200	6	=	=	NOUN
ap-10175	200	7	0.2	0.2	NUM
ap-10175	200	8	(	(	PUNCT
ap-10175	200	9	b	b	NOUN
ap-10175	200	10	)	)	PUNCT
ap-10175	200	11	.	.	PUNCT
ap-10175	201	1	imaginary	imaginary	ADJ
ap-10175	201	2	.	.	PUNCT
ap-10175	201	3	figure	figure	NOUN
ap-10175	201	4	9	9	NUM
ap-10175	201	5	.	.	PUNCT
ap-10175	202	1	the	the	DET
ap-10175	202	2	first	first	ADJ
ap-10175	202	3	-	-	PUNCT
ap-10175	202	4	order	order	NOUN
ap-10175	202	5	frequency	frequency	NOUN
ap-10175	202	6	diagrams	diagram	NOUN
ap-10175	202	7	for	for	ADP
ap-10175	202	8	the	the	DET
ap-10175	202	9	fluid	fluid	NOUN
ap-10175	202	10	conveying	convey	VERB
ap-10175	202	11	two	two	NUM
ap-10175	202	12	phase	phase	NOUN
ap-10175	202	13	flow	flow	NOUN
ap-10175	202	14	.	.	PUNCT
ap-10175	203	1	0	0	NUM
ap-10175	204	1	1	1	NUM
ap-10175	204	2	2	2	NUM
ap-10175	204	3	3	3	NUM
ap-10175	204	4	4	4	NUM
ap-10175	204	5	5	5	NUM
ap-10175	204	6	6	6	NUM
ap-10175	204	7	7	7	NUM
ap-10175	204	8	8	8	NUM
ap-10175	204	9	9	9	NUM
ap-10175	204	10	10	10	NUM
ap-10175	204	11	0	0	NUM
ap-10175	204	12	20	20	NUM
ap-10175	204	13	40	40	NUM
ap-10175	204	14	60	60	NUM
ap-10175	204	15	80	80	NUM
ap-10175	204	16	r	r	NOUN
ap-10175	204	17	e	e	NOUN
ap-10175	204	18	(	(	PUNCT
ap-10175	204	19	)	)	PUNCT
ap-10175	204	20	flow	flow	NOUN
ap-10175	204	21	velocity	velocity	NOUN
ap-10175	204	22	=	=	SYM
ap-10175	204	23	0	0	PUNCT
ap-10175	205	1	=	=	SYM
ap-10175	205	2	2	2	NUM
ap-10175	205	3	=	=	SYM
ap-10175	205	4	4	4	NUM
ap-10175	205	5	(	(	PUNCT
ap-10175	205	6	a	a	NOUN
ap-10175	205	7	)	)	PUNCT
ap-10175	205	8	.	.	PUNCT
ap-10175	206	1	real	real	ADJ
ap-10175	206	2	.	.	PUNCT
ap-10175	207	1	0	0	NUM
ap-10175	207	2	1	1	NUM
ap-10175	207	3	2	2	NUM
ap-10175	207	4	3	3	NUM
ap-10175	207	5	4	4	NUM
ap-10175	207	6	5	5	NUM
ap-10175	207	7	6	6	NUM
ap-10175	207	8	7	7	NUM
ap-10175	207	9	8	8	NUM
ap-10175	207	10	9	9	NUM
ap-10175	207	11	10	10	NUM
ap-10175	207	12	-60	-60	SYM
ap-10175	207	13	-40	-40	PROPN
ap-10175	207	14	-20	-20	NUM
ap-10175	207	15	0	0	NUM
ap-10175	207	16	20	20	NUM
ap-10175	207	17	40	40	NUM
ap-10175	207	18	60	60	NUM
ap-10175	207	19	i	i	PRON
ap-10175	207	20	m	m	VERB
ap-10175	207	21	ag	ag	PROPN
ap-10175	207	22	(	(	PUNCT
ap-10175	207	23	)	)	PUNCT
ap-10175	207	24	flow	flow	NOUN
ap-10175	207	25	velocity	velocity	NOUN
ap-10175	207	26	=	=	SYM
ap-10175	207	27	0	0	PUNCT
ap-10175	207	28	=	=	SYM
ap-10175	207	29	2	2	NUM
ap-10175	207	30	=	=	SYM
ap-10175	207	31	4	4	NUM
ap-10175	207	32	(	(	PUNCT
ap-10175	207	33	b	b	NOUN
ap-10175	207	34	)	)	PUNCT
ap-10175	207	35	.	.	PUNCT
ap-10175	208	1	imaginary	imaginary	ADJ
ap-10175	208	2	.	.	PUNCT
ap-10175	208	3	figure	figure	NOUN
ap-10175	208	4	10	10	NUM
ap-10175	208	5	.	.	PUNCT
ap-10175	209	1	the	the	DET
ap-10175	209	2	first	first	ADJ
ap-10175	209	3	three	three	NUM
ap-10175	209	4	order	order	NOUN
ap-10175	209	5	frequency	frequency	NOUN
ap-10175	209	6	diagrams	diagram	NOUN
ap-10175	209	7	for	for	ADP
ap-10175	209	8	the	the	DET
ap-10175	209	9	fluid	fluid	NOUN
ap-10175	209	10	conveying	convey	VERB
ap-10175	209	11	two	two	NUM
ap-10175	209	12	phase	phase	NOUN
ap-10175	209	13	flow	flow	NOUN
ap-10175	209	14	with	with	ADP
ap-10175	209	15	varying	vary	VERB
ap-10175	209	16	temperature	temperature	NOUN
ap-10175	209	17	parameters	parameter	NOUN
ap-10175	209	18	xg	xg	PROPN
ap-10175	209	19	=	=	SYM
ap-10175	209	20	0.0001	0.0001	NUM
ap-10175	209	21	.	.	PUNCT
ap-10175	210	1	mp	mp	PROPN
ap-10175	210	2	mass	mass	PROPN
ap-10175	210	3	of	of	ADP
ap-10175	210	4	the	the	DET
ap-10175	210	5	pipe	pipe	NOUN
ap-10175	210	6	mg	mg	PROPN
ap-10175	210	7	mass	mass	NOUN
ap-10175	210	8	of	of	ADP
ap-10175	210	9	the	the	DET
ap-10175	210	10	gas	gas	NOUN
ap-10175	210	11	mf	mf	PRON
ap-10175	210	12	mass	mass	NOUN
ap-10175	210	13	of	of	ADP
ap-10175	210	14	the	the	DET
ap-10175	210	15	fluid	fluid	ADJ
ap-10175	210	16	w̄	w̄	NOUN
ap-10175	210	17	transverse	transverse	NOUN
ap-10175	210	18	displacement	displacement	NOUN
ap-10175	210	19	ȳ0	ȳ0	NUM
ap-10175	210	20	initial	initial	ADJ
ap-10175	210	21	curvature	curvature	NOUN
ap-10175	210	22	θ	θ	PROPN
ap-10175	210	23	temperature	temperature	NOUN
ap-10175	210	24	v̄g	v̄g	ADJ
ap-10175	210	25	velocity	velocity	NOUN
ap-10175	210	26	of	of	ADP
ap-10175	210	27	the	the	DET
ap-10175	210	28	gas	gas	NOUN
ap-10175	210	29	v̄l	v̄l	ADJ
ap-10175	210	30	velocity	velocity	NOUN
ap-10175	210	31	of	of	ADP
ap-10175	210	32	the	the	DET
ap-10175	210	33	liquid	liquid	ADJ
ap-10175	210	34	xg	xg	NOUN
ap-10175	210	35	void	void	ADJ
ap-10175	210	36	quality	quality	NOUN
ap-10175	210	37	α	α	PROPN
ap-10175	210	38	thermal	thermal	ADJ
ap-10175	210	39	coefficient	coefficient	NOUN
ap-10175	210	40	ks	ks	NOUN
ap-10175	210	41	slip	slip	VERB
ap-10175	210	42	ratio	ratio	NOUN
ap-10175	210	43	acknowledgements	acknowledgement	NOUN
ap-10175	210	44	we	we	PRON
ap-10175	210	45	are	be	AUX
ap-10175	210	46	grateful	grateful	ADJ
ap-10175	210	47	for	for	ADP
ap-10175	210	48	the	the	DET
ap-10175	210	49	invaluable	invaluable	ADJ
ap-10175	210	50	support	support	NOUN
ap-10175	210	51	provided	provide	VERB
ap-10175	210	52	by	by	ADP
ap-10175	210	53	the	the	DET
ap-10175	210	54	university	university	PROPN
ap-10175	210	55	of	of	ADP
ap-10175	210	56	lagos	lago	NOUN
ap-10175	210	57	throughout	throughout	ADP
ap-10175	210	58	the	the	DET
ap-10175	210	59	research	research	NOUN
ap-10175	210	60	process	process	NOUN
ap-10175	210	61	.	.	PUNCT
ap-10175	211	1	references	reference	NOUN
ap-10175	211	2	[	[	X
ap-10175	211	3	1	1	NUM
ap-10175	211	4	]	]	PUNCT
ap-10175	211	5	k.	k.	PROPN
ap-10175	211	6	singh	singh	PROPN
ap-10175	211	7	,	,	PUNCT
ap-10175	212	1	a.	a.	PROPN
ap-10175	212	2	k.	k.	PROPN
ap-10175	212	3	mallik	mallik	PROPN
ap-10175	212	4	.	.	PROPN
ap-10175	212	5	wave	wave	PROPN
ap-10175	212	6	propagation	propagation	NOUN
ap-10175	212	7	and	and	CCONJ
ap-10175	212	8	vibration	vibration	NOUN
ap-10175	212	9	response	response	NOUN
ap-10175	212	10	of	of	ADP
ap-10175	212	11	a	a	DET
ap-10175	212	12	periodically	periodically	ADV
ap-10175	212	13	supported	support	VERB
ap-10175	212	14	pipe	pipe	NOUN
ap-10175	212	15	conveying	conveying	NOUN
ap-10175	212	16	fluid	fluid	NOUN
ap-10175	212	17	.	.	PUNCT
ap-10175	213	1	journal	journal	NOUN
ap-10175	213	2	of	of	ADP
ap-10175	213	3	sound	sound	NOUN
ap-10175	213	4	and	and	CCONJ
ap-10175	213	5	vibration	vibration	NOUN
ap-10175	213	6	54(1):55–66	54(1):55–66	NUM
ap-10175	213	7	,	,	PUNCT
ap-10175	213	8	1977	1977	NUM
ap-10175	213	9	.	.	PUNCT
ap-10175	214	1	https://doi.org/10.1016/0022-460x(77)90405-9	https://doi.org/10.1016/0022-460x(77)90405-9	PROPN
ap-10175	214	2	[	[	X
ap-10175	214	3	2	2	X
ap-10175	214	4	]	]	PUNCT
ap-10175	214	5	t.	t.	PROPN
ap-10175	214	6	ma	ma	PROPN
ap-10175	214	7	,	,	PUNCT
ap-10175	214	8	j.	j.	PROPN
ap-10175	214	9	gu	gu	PROPN
ap-10175	214	10	,	,	PUNCT
ap-10175	214	11	m.	m.	PROPN
ap-10175	214	12	duan	duan	PROPN
ap-10175	214	13	.	.	PUNCT
ap-10175	215	1	dynamic	dynamic	ADJ
ap-10175	215	2	response	response	NOUN
ap-10175	215	3	of	of	ADP
ap-10175	215	4	pipes	pipe	NOUN
ap-10175	215	5	conveying	convey	VERB
ap-10175	215	6	two	two	NUM
ap-10175	215	7	-	-	PUNCT
ap-10175	215	8	phase	phase	NOUN
ap-10175	215	9	flow	flow	NOUN
ap-10175	215	10	based	base	VERB
ap-10175	215	11	on	on	ADP
ap-10175	215	12	timoshenko	timoshenko	ADJ
ap-10175	215	13	beam	beam	NOUN
ap-10175	215	14	model	model	NOUN
ap-10175	215	15	.	.	PUNCT
ap-10175	216	1	marine	marine	PROPN
ap-10175	216	2	systems	system	NOUN
ap-10175	216	3	and	and	CCONJ
ap-10175	216	4	ocean	ocean	NOUN
ap-10175	216	5	technology	technology	NOUN
ap-10175	216	6	12(3):196–209	12(3):196–209	PROPN
ap-10175	216	7	,	,	PUNCT
ap-10175	216	8	2017	2017	NUM
ap-10175	216	9	.	.	PUNCT
ap-10175	217	1	https://doi.org/10.1007/s40868-017-0029-z	https://doi.org/10.1007/s40868-017-0029-z	PROPN
ap-10175	218	1	[	[	X
ap-10175	218	2	3	3	X
ap-10175	218	3	]	]	PUNCT
ap-10175	218	4	r.	r.	PROPN
ap-10175	218	5	a.	a.	PROPN
ap-10175	218	6	ibrahim	ibrahim	PROPN
ap-10175	218	7	.	.	PUNCT
ap-10175	219	1	overview	overview	NOUN
ap-10175	219	2	of	of	ADP
ap-10175	219	3	mechanics	mechanic	NOUN
ap-10175	219	4	of	of	ADP
ap-10175	219	5	pipes	pipe	NOUN
ap-10175	219	6	conveying	conveying	NOUN
ap-10175	219	7	fluids	fluid	NOUN
ap-10175	219	8	–	–	PUNCT
ap-10175	219	9	part	part	NOUN
ap-10175	220	1	i	i	NOUN
ap-10175	220	2	:	:	PUNCT
ap-10175	220	3	fundamental	fundamental	ADJ
ap-10175	220	4	studies	study	NOUN
ap-10175	220	5	.	.	PUNCT
ap-10175	221	1	journal	journal	NOUN
ap-10175	221	2	of	of	ADP
ap-10175	221	3	pressure	pressure	NOUN
ap-10175	221	4	vessel	vessel	NOUN
ap-10175	221	5	technology	technology	PROPN
ap-10175	221	6	132(3):034001	132(3):034001	PROPN
ap-10175	221	7	,	,	PUNCT
ap-10175	221	8	2010	2010	NUM
ap-10175	221	9	.	.	PUNCT
ap-10175	222	1	https://doi.org/10.1115/1.4001271	https://doi.org/10.1115/1.4001271	NOUN
ap-10175	223	1	[	[	X
ap-10175	223	2	4	4	NUM
ap-10175	223	3	]	]	X
ap-10175	223	4	c.	c.	NOUN
ap-10175	223	5	semler	semler	NOUN
ap-10175	223	6	,	,	PUNCT
ap-10175	223	7	g.	g.	PROPN
ap-10175	223	8	x.	x.	PROPN
ap-10175	223	9	li	li	PROPN
ap-10175	223	10	,	,	PUNCT
ap-10175	223	11	m.	m.	NOUN
ap-10175	224	1	p.	p.	PROPN
ap-10175	224	2	païdoussis	païdoussis	NOUN
ap-10175	224	3	.	.	PUNCT
ap-10175	225	1	the	the	DET
ap-10175	225	2	non	non	ADJ
ap-10175	225	3	-	-	ADJ
ap-10175	225	4	linear	linear	ADJ
ap-10175	225	5	equations	equation	NOUN
ap-10175	225	6	of	of	ADP
ap-10175	225	7	motion	motion	NOUN
ap-10175	225	8	of	of	ADP
ap-10175	225	9	pipes	pipe	NOUN
ap-10175	225	10	conveying	convey	VERB
ap-10175	225	11	fluid	fluid	NOUN
ap-10175	225	12	.	.	PUNCT
ap-10175	226	1	journal	journal	NOUN
ap-10175	226	2	of	of	ADP
ap-10175	226	3	sound	sound	NOUN
ap-10175	226	4	and	and	CCONJ
ap-10175	226	5	vibration	vibration	NOUN
ap-10175	226	6	169(5):577–599	169(5):577–599	NUM
ap-10175	226	7	,	,	PUNCT
ap-10175	226	8	1994	1994	NUM
ap-10175	226	9	.	.	PUNCT
ap-10175	227	1	https://doi.org/10.1006/jsvi.1994.1035	https://doi.org/10.1006/jsvi.1994.1035	PROPN
ap-10175	227	2	[	[	X
ap-10175	227	3	5	5	X
ap-10175	227	4	]	]	PUNCT
ap-10175	227	5	a.	a.	NOUN
ap-10175	227	6	ebrahimi	ebrahimi	PROPN
ap-10175	227	7	-	-	PUNCT
ap-10175	227	8	mamaghani	mamaghani	PROPN
ap-10175	227	9	,	,	PUNCT
ap-10175	227	10	r.	r.	PROPN
ap-10175	227	11	sotudeh	sotudeh	PROPN
ap-10175	227	12	-	-	PUNCT
ap-10175	227	13	gharebagh	gharebagh	PROPN
ap-10175	227	14	,	,	PUNCT
ap-10175	227	15	r.	r.	PROPN
ap-10175	227	16	zarghami	zarghami	PROPN
ap-10175	227	17	,	,	PUNCT
ap-10175	227	18	n.	n.	PROPN
ap-10175	227	19	mostoufi	mostoufi	PROPN
ap-10175	227	20	.	.	PUNCT
ap-10175	228	1	dynamics	dynamic	NOUN
ap-10175	228	2	of	of	ADP
ap-10175	228	3	two	two	NUM
ap-10175	228	4	-	-	PUNCT
ap-10175	228	5	phase	phase	NOUN
ap-10175	228	6	flow	flow	NOUN
ap-10175	228	7	in	in	ADP
ap-10175	228	8	vertical	vertical	ADJ
ap-10175	228	9	pipes	pipe	NOUN
ap-10175	228	10	.	.	PUNCT
ap-10175	229	1	journal	journal	NOUN
ap-10175	229	2	of	of	ADP
ap-10175	229	3	fluids	fluid	NOUN
ap-10175	229	4	and	and	CCONJ
ap-10175	229	5	structures	structure	NOUN
ap-10175	229	6	87:150–173	87:150–173	NUM
ap-10175	229	7	,	,	PUNCT
ap-10175	229	8	2019	2019	NUM
ap-10175	229	9	.	.	PUNCT
ap-10175	230	1	https	https	NOUN
ap-10175	230	2	:	:	PUNCT
ap-10175	231	1	//doi.org/10.1016	//doi.org/10.1016	PROPN
ap-10175	231	2	/	/	SYM
ap-10175	231	3	j.jfluidstructs.2019.03.010	j.jfluidstructs.2019.03.010	PROPN
ap-10175	232	1	[	[	X
ap-10175	232	2	6	6	NUM
ap-10175	232	3	]	]	PUNCT
ap-10175	232	4	a.	a.	NOUN
ap-10175	232	5	o.	o.	PROPN
ap-10175	232	6	oyelade	oyelade	PROPN
ap-10175	232	7	,	,	PUNCT
ap-10175	232	8	a.	a.	NOUN
ap-10175	232	9	a.	a.	NOUN
ap-10175	232	10	oyediran	oyediran	PROPN
ap-10175	232	11	.	.	PUNCT
ap-10175	233	1	nonlinear	nonlinear	ADJ
ap-10175	233	2	dynamics	dynamic	NOUN
ap-10175	233	3	of	of	ADP
ap-10175	233	4	horizontal	horizontal	ADJ
ap-10175	233	5	pipes	pipe	NOUN
ap-10175	233	6	conveying	convey	VERB
ap-10175	233	7	two	two	NUM
ap-10175	233	8	phase	phase	NOUN
ap-10175	233	9	flow	flow	NOUN
ap-10175	233	10	.	.	PUNCT
ap-10175	234	1	european	european	PROPN
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ap-10175	234	5	,	,	PUNCT
ap-10175	234	6	a	a	DET
ap-10175	234	7	/	/	SYM
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ap-10175	234	9	90:104367	90:104367	NUM
ap-10175	234	10	,	,	PUNCT
ap-10175	234	11	2021	2021	NUM
ap-10175	234	12	.	.	PUNCT
ap-10175	235	1	https	https	NOUN
ap-10175	235	2	:	:	PUNCT
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ap-10175	235	4	/	/	SYM
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ap-10175	235	6	339	339	NUM
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ap-10175	236	5	https://doi.org/10.1016/j.jfluidstructs.2019.03.010	https://doi.org/10.1016/j.jfluidstructs.2019.03.010	NOUN
ap-10175	236	6	https://doi.org/10.1016/j.jfluidstructs.2019.03.010	https://doi.org/10.1016/j.jfluidstructs.2019.03.010	PROPN
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ap-10175	236	8	https://doi.org/10.1016/j.euromechsol.2021.104367	https://doi.org/10.1016/j.euromechsol.2021.104367	PROPN
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ap-10175	236	10	o.	o.	PROPN
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ap-10175	236	14	b.	b.	PROPN
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ap-10175	236	16	,	,	PUNCT
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ap-10175	236	18	oribayo	oribayo	PROPN
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ap-10175	236	20	y.	y.	PROPN
ap-10175	236	21	o.	o.	PROPN
ap-10175	236	22	abiodun	abiodun	PROPN
ap-10175	236	23	acta	acta	PROPN
ap-10175	236	24	polytechnica	polytechnica	PROPN
ap-10175	237	1	[	[	X
ap-10175	237	2	7	7	X
ap-10175	237	3	]	]	PUNCT
ap-10175	237	4	p.	p.	NOUN
ap-10175	237	5	h.	h.	PROPN
ap-10175	237	6	de	de	PROPN
ap-10175	237	7	m.	m.	PROPN
ap-10175	237	8	c.	c.	PROPN
ap-10175	237	9	matos	matos	PROPN
ap-10175	237	10	,	,	PUNCT
ap-10175	237	11	d.	d.	PROPN
ap-10175	237	12	a.	a.	PROPN
ap-10175	237	13	das	das	PROPN
ap-10175	237	14	neves	neve	NOUN
ap-10175	237	15	,	,	PUNCT
ap-10175	237	16	s.	s.	PROPN
ap-10175	237	17	c.	c.	PROPN
ap-10175	237	18	vieira	vieira	PROPN
ap-10175	237	19	,	,	PUNCT
ap-10175	237	20	et	et	PROPN
ap-10175	237	21	al	al	PROPN
ap-10175	237	22	.	.	PUNCT
ap-10175	238	1	a	a	DET
ap-10175	238	2	wave	wave	NOUN
ap-10175	238	3	-	-	PUNCT
ap-10175	238	4	based	base	VERB
ap-10175	238	5	approach	approach	NOUN
ap-10175	238	6	for	for	ADP
ap-10175	238	7	estimating	estimate	VERB
ap-10175	238	8	void	void	ADJ
ap-10175	238	9	fraction	fraction	NOUN
ap-10175	238	10	in	in	ADP
ap-10175	238	11	horizontal	horizontal	ADJ
ap-10175	238	12	pipes	pipe	NOUN
ap-10175	238	13	conveying	convey	VERB
ap-10175	238	14	two	two	NUM
ap-10175	238	15	-	-	PUNCT
ap-10175	238	16	phase	phase	NOUN
ap-10175	238	17	flow	flow	NOUN
ap-10175	238	18	.	.	PUNCT
ap-10175	239	1	journal	journal	NOUN
ap-10175	239	2	of	of	ADP
ap-10175	239	3	petroleum	petroleum	NOUN
ap-10175	239	4	science	science	NOUN
ap-10175	239	5	and	and	CCONJ
ap-10175	239	6	engineering	engineering	NOUN
ap-10175	239	7	216:110766	216:110766	NUM
ap-10175	239	8	,	,	PUNCT
ap-10175	239	9	2022	2022	NUM
ap-10175	239	10	.	.	PUNCT
ap-10175	240	1	https://doi.org/10.1016/j.petrol.2022.110766	https://doi.org/10.1016/j.petrol.2022.110766	NOUN
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ap-10175	241	2	8	8	NUM
ap-10175	241	3	]	]	PUNCT
ap-10175	241	4	a.	a.	NOUN
ap-10175	241	5	o.	o.	PROPN
ap-10175	241	6	oyelade	oyelade	PROPN
ap-10175	241	7	,	,	PUNCT
ap-10175	242	1	p.	p.	PROPN
ap-10175	242	2	j.	j.	PROPN
ap-10175	243	1	v.	v.	PROPN
ap-10175	243	2	ponte	ponte	PROPN
ap-10175	243	3	,	,	PUNCT
ap-10175	243	4	a.	a.	NOUN
ap-10175	243	5	a.	a.	NOUN
ap-10175	243	6	oyediran	oyediran	PROPN
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ap-10175	244	1	dynamic	dynamic	ADJ
ap-10175	244	2	stability	stability	NOUN
ap-10175	244	3	of	of	ADP
ap-10175	244	4	slightly	slightly	ADV
ap-10175	244	5	curved	curved	ADJ
ap-10175	244	6	tensioned	tensione	VERB
ap-10175	244	7	pipe	pipe	NOUN
ap-10175	244	8	conveying	convey	VERB
ap-10175	244	9	pressurized	pressurize	VERB
ap-10175	244	10	hot	hot	ADJ
ap-10175	244	11	two	two	NUM
ap-10175	244	12	phase	phase	NOUN
ap-10175	244	13	fluid	fluid	NOUN
ap-10175	244	14	resting	rest	VERB
ap-10175	244	15	on	on	ADP
ap-10175	244	16	non	non	ADJ
ap-10175	244	17	uniform	uniform	PROPN
ap-10175	244	18	foundation	foundation	PROPN
ap-10175	244	19	.	.	PUNCT
ap-10175	245	1	engineering	engineering	NOUN
ap-10175	245	2	structures	structure	NOUN
ap-10175	245	3	286:116138	286:116138	NUM
ap-10175	245	4	,	,	PUNCT
ap-10175	245	5	2023	2023	NUM
ap-10175	245	6	.	.	PUNCT
ap-10175	246	1	https://doi.org/10.1016/j.engstruct.2023.116138	https://doi.org/10.1016/j.engstruct.2023.116138	PROPN
ap-10175	247	1	[	[	X
ap-10175	247	2	9	9	X
ap-10175	247	3	]	]	PUNCT
ap-10175	247	4	p.	p.	NOUN
ap-10175	247	5	j.	j.	PROPN
ap-10175	248	1	v.	v.	PROPN
ap-10175	248	2	ponte	ponte	PROPN
ap-10175	248	3	,	,	PUNCT
ap-10175	248	4	t.	t.	PROPN
ap-10175	248	5	g.	g.	PROPN
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ap-10175	248	7	,	,	PUNCT
ap-10175	248	8	j.	j.	PROPN
ap-10175	248	9	f.	f.	PROPN
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ap-10175	248	11	.	.	PUNCT
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ap-10175	249	2	analysis	analysis	NOUN
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ap-10175	249	4	a	a	DET
ap-10175	249	5	pipe	pipe	NOUN
ap-10175	249	6	conveying	convey	VERB
ap-10175	249	7	a	a	DET
ap-10175	249	8	two	two	NUM
ap-10175	249	9	–	–	PUNCT
ap-10175	249	10	phase	phase	NOUN
ap-10175	249	11	fluid	fluid	NOUN
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ap-10175	249	13	uncertainties	uncertainty	NOUN
ap-10175	249	14	in	in	ADP
ap-10175	249	15	the	the	DET
ap-10175	249	16	flow	flow	NOUN
ap-10175	249	17	parameters	parameter	NOUN
ap-10175	249	18	.	.	PUNCT
ap-10175	250	1	journal	journal	NOUN
ap-10175	250	2	of	of	ADP
ap-10175	250	3	the	the	DET
ap-10175	250	4	brazilian	brazilian	ADJ
ap-10175	250	5	society	society	NOUN
ap-10175	250	6	of	of	ADP
ap-10175	250	7	mechanical	mechanical	ADJ
ap-10175	250	8	sciences	science	NOUN
ap-10175	250	9	and	and	CCONJ
ap-10175	250	10	engineering	engineering	NOUN
ap-10175	250	11	42(12):626	42(12):626	NUM
ap-10175	250	12	,	,	PUNCT
ap-10175	250	13	2020	2020	NUM
ap-10175	250	14	.	.	PUNCT
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ap-10175	251	2	[	[	X
ap-10175	251	3	10	10	NUM
ap-10175	251	4	]	]	X
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ap-10175	251	6	y.	y.	PROPN
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ap-10175	251	9	v.	v.	PROPN
ap-10175	251	10	g.	g.	PROPN
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ap-10175	251	12	,	,	PUNCT
ap-10175	251	13	g.	g.	PROPN
ap-10175	251	14	s.	s.	PROPN
ap-10175	251	15	samuelsen	samuelsen	PROPN
ap-10175	251	16	.	.	PUNCT
ap-10175	252	1	the	the	DET
ap-10175	252	2	two	two	NUM
ap-10175	252	3	-	-	PUNCT
ap-10175	252	4	phase	phase	NOUN
ap-10175	252	5	flow	flow	NOUN
ap-10175	252	6	downstream	downstream	NOUN
ap-10175	252	7	of	of	ADP
ap-10175	252	8	a	a	DET
ap-10175	252	9	production	production	NOUN
ap-10175	252	10	engine	engine	NOUN
ap-10175	252	11	combustor	combustor	NOUN
ap-10175	252	12	swirl	swirl	NOUN
ap-10175	252	13	cup	cup	NOUN
ap-10175	252	14	.	.	PUNCT
ap-10175	253	1	symposium	symposium	NOUN
ap-10175	253	2	(	(	PUNCT
ap-10175	253	3	international	international	ADJ
ap-10175	253	4	)	)	PUNCT
ap-10175	253	5	on	on	ADP
ap-10175	253	6	combustion	combustion	NOUN
ap-10175	253	7	24(1):1457–1463	24(1):1457–1463	NUM
ap-10175	253	8	,	,	PUNCT
ap-10175	253	9	1992	1992	NUM
ap-10175	253	10	.	.	PUNCT
ap-10175	254	1	https://doi.org/10.1016/s0082-0784(06)80170-0	https://doi.org/10.1016/s0082-0784(06)80170-0	PROPN
ap-10175	255	1	[	[	X
ap-10175	255	2	11	11	NUM
ap-10175	255	3	]	]	PUNCT
ap-10175	255	4	a.	a.	PROPN
ap-10175	255	5	b.	b.	PROPN
ap-10175	255	6	ehinmowo	ehinmowo	PROPN
ap-10175	255	7	,	,	PUNCT
ap-10175	255	8	y.	y.	PROPN
ap-10175	255	9	cao	cao	PROPN
ap-10175	255	10	.	.	PUNCT
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ap-10175	256	2	analysis	analysis	NOUN
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ap-10175	256	4	slug	slug	NOUN
ap-10175	256	5	flow	flow	NOUN
ap-10175	256	6	control	control	NOUN
ap-10175	256	7	.	.	PUNCT
ap-10175	257	1	systems	system	NOUN
ap-10175	257	2	science	science	PROPN
ap-10175	257	3	&	&	CCONJ
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ap-10175	257	5	engineering	engineering	PROPN
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ap-10175	257	7	,	,	PUNCT
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ap-10175	257	9	.	.	PUNCT
ap-10175	258	1	https://doi.org/10.1080/21642583.2016.1213189	https://doi.org/10.1080/21642583.2016.1213189	PUNCT
ap-10175	259	1	[	[	X
ap-10175	259	2	12	12	NUM
ap-10175	259	3	]	]	PUNCT
ap-10175	259	4	a.	a.	PROPN
ap-10175	259	5	b.	b.	PROPN
ap-10175	259	6	ehinmowo	ehinmowo	PROPN
ap-10175	259	7	,	,	PUNCT
ap-10175	259	8	o.	o.	PROPN
ap-10175	259	9	d.	d.	PROPN
ap-10175	259	10	orodu	orodu	PROPN
ap-10175	259	11	,	,	PUNCT
ap-10175	259	12	p.	p.	NOUN
ap-10175	259	13	a.	a.	PROPN
ap-10175	259	14	l.	l.	PROPN
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ap-10175	259	16	,	,	PUNCT
ap-10175	259	17	o.	o.	PROPN
ap-10175	259	18	o.	o.	PROPN
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ap-10175	259	20	.	.	PUNCT
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ap-10175	260	3	slug	slug	NOUN
ap-10175	260	4	flow	flow	NOUN
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ap-10175	260	10	increased	increase	VERB
ap-10175	260	11	oil	oil	NOUN
ap-10175	260	12	production	production	NOUN
ap-10175	260	13	without	without	ADP
ap-10175	260	14	feedback	feedback	NOUN
ap-10175	260	15	control	control	NOUN
ap-10175	260	16	signal	signal	NOUN
ap-10175	260	17	.	.	PUNCT
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ap-10175	261	3	petroleum	petroleum	NOUN
ap-10175	261	4	science	science	NOUN
ap-10175	261	5	and	and	CCONJ
ap-10175	261	6	engineering	engineering	NOUN
ap-10175	261	7	146:1130–1141	146:1130–1141	NOUN
ap-10175	261	8	,	,	PUNCT
ap-10175	261	9	2016	2016	NUM
ap-10175	261	10	.	.	PUNCT
ap-10175	262	1	https://doi.org/10.1016/j.petrol.2016.08.019	https://doi.org/10.1016/j.petrol.2016.08.019	NUM
ap-10175	262	2	[	[	X
ap-10175	262	3	13	13	NUM
ap-10175	262	4	]	]	PUNCT
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ap-10175	263	3	g.-l	g.-l	NOUN
ap-10175	263	4	.	.	PUNCT
ap-10175	264	1	she	she	PRON
ap-10175	264	2	.	.	PUNCT
ap-10175	265	1	nonlinear	nonlinear	ADJ
ap-10175	265	2	vibration	vibration	NOUN
ap-10175	265	3	of	of	ADP
ap-10175	265	4	graphene	graphene	NOUN
ap-10175	265	5	platelets	platelet	NOUN
ap-10175	265	6	reinforced	reinforce	VERB
ap-10175	265	7	metal	metal	NOUN
ap-10175	265	8	foams	foam	NOUN
ap-10175	265	9	pipe	pipe	NOUN
ap-10175	265	10	conveying	convey	VERB
ap-10175	265	11	fluid	fluid	NOUN
ap-10175	265	12	under	under	ADP
ap-10175	265	13	combined	combine	VERB
ap-10175	265	14	resonance	resonance	NOUN
ap-10175	265	15	.	.	PUNCT
ap-10175	266	1	steel	steel	NOUN
ap-10175	266	2	and	and	CCONJ
ap-10175	266	3	composite	composite	ADJ
ap-10175	266	4	structures	structure	NOUN
ap-10175	266	5	,	,	PUNCT
ap-10175	266	6	53(3):363–376	53(3):363–376	PROPN
ap-10175	266	7	,	,	PUNCT
ap-10175	266	8	2024	2024	NUM
ap-10175	266	9	.	.	PUNCT
ap-10175	267	1	https://doi.org/10.12989/scs.2024.53.3.363	https://doi.org/10.12989/scs.2024.53.3.363	NOUN
ap-10175	268	1	[	[	X
ap-10175	268	2	14	14	NUM
ap-10175	268	3	]	]	PUNCT
ap-10175	268	4	y.-w	y.-w	PROPN
ap-10175	268	5	.	.	PUNCT
ap-10175	269	1	zhang	zhang	PROPN
ap-10175	269	2	,	,	PUNCT
ap-10175	269	3	g.-l	g.-l	NOUN
ap-10175	269	4	.	.	PUNCT
ap-10175	270	1	she	she	PRON
ap-10175	270	2	.	.	PUNCT
ap-10175	271	1	investigation	investigation	NOUN
ap-10175	271	2	on	on	ADP
ap-10175	271	3	internal	internal	ADJ
ap-10175	271	4	resonance	resonance	NOUN
ap-10175	271	5	of	of	ADP
ap-10175	271	6	fluid	fluid	NOUN
ap-10175	271	7	conveying	conveying	NOUN
ap-10175	271	8	pipes	pipe	NOUN
ap-10175	271	9	with	with	ADP
ap-10175	271	10	initial	initial	ADJ
ap-10175	271	11	geometric	geometric	ADJ
ap-10175	271	12	imperfection	imperfection	NOUN
ap-10175	271	13	.	.	PUNCT
ap-10175	272	1	applied	apply	VERB
ap-10175	272	2	ocean	ocean	PROPN
ap-10175	272	3	research	research	PROPN
ap-10175	272	4	146:103961	146:103961	NUM
ap-10175	272	5	,	,	PUNCT
ap-10175	272	6	2024	2024	NUM
ap-10175	272	7	.	.	PUNCT
ap-10175	273	1	https://doi.org/10.1016/j.apor.2024.103961	https://doi.org/10.1016/j.apor.2024.103961	NOUN
ap-10175	273	2	[	[	X
ap-10175	273	3	15	15	NUM
ap-10175	273	4	]	]	X
ap-10175	273	5	s.	s.	PROPN
ap-10175	273	6	gourari	gourari	PROPN
ap-10175	273	7	,	,	PUNCT
ap-10175	273	8	f.	f.	PROPN
ap-10175	273	9	mebarek	mebarek	PROPN
ap-10175	273	10	-	-	PUNCT
ap-10175	273	11	oudina	oudina	PROPN
ap-10175	273	12	,	,	PUNCT
ap-10175	273	13	o.	o.	PROPN
ap-10175	273	14	d.	d.	PROPN
ap-10175	273	15	makinde	makinde	PROPN
ap-10175	273	16	,	,	PUNCT
ap-10175	273	17	m.	m.	NOUN
ap-10175	273	18	rabhi	rabhi	PROPN
ap-10175	273	19	.	.	PUNCT
ap-10175	274	1	numerical	numerical	PROPN
ap-10175	274	2	investigation	investigation	NOUN
ap-10175	274	3	of	of	ADP
ap-10175	274	4	gas	gas	NOUN
ap-10175	274	5	-	-	PUNCT
ap-10175	274	6	liquid	liquid	ADJ
ap-10175	274	7	two	two	NUM
ap-10175	274	8	-	-	PUNCT
ap-10175	274	9	phase	phase	NOUN
ap-10175	274	10	flows	flow	NOUN
ap-10175	274	11	in	in	ADP
ap-10175	274	12	a	a	DET
ap-10175	274	13	cylindrical	cylindrical	ADJ
ap-10175	274	14	channel	channel	NOUN
ap-10175	274	15	.	.	PUNCT
ap-10175	275	1	defect	defect	VERB
ap-10175	275	2	and	and	CCONJ
ap-10175	275	3	diffusion	diffusion	NOUN
ap-10175	275	4	forum	forum	PROPN
ap-10175	275	5	409:39–48	409:39–48	PROPN
ap-10175	275	6	,	,	PUNCT
ap-10175	275	7	2021	2021	NUM
ap-10175	275	8	.	.	PUNCT
ap-10175	276	1	https	https	NOUN
ap-10175	276	2	:	:	PUNCT
ap-10175	276	3	//doi.org/10.4028	//doi.org/10.4028	ADJ
ap-10175	276	4	/	/	SYM
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ap-10175	277	2	/	/	SYM
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ap-10175	277	6	]	]	PUNCT
ap-10175	277	7	y.-w	y.-w	PROPN
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ap-10175	278	2	,	,	PUNCT
ap-10175	278	3	g.-l	g.-l	NOUN
ap-10175	278	4	.	.	PUNCT
ap-10175	279	1	she	she	PRON
ap-10175	279	2	.	.	PUNCT
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ap-10175	280	2	propagation	propagation	NOUN
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ap-10175	280	4	vibration	vibration	NOUN
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ap-10175	280	6	fg	fg	PROPN
ap-10175	280	7	pipes	pipe	NOUN
ap-10175	280	8	conveying	convey	VERB
ap-10175	280	9	hot	hot	ADJ
ap-10175	280	10	fluid	fluid	NOUN
ap-10175	280	11	.	.	PUNCT
ap-10175	281	1	steel	steel	NOUN
ap-10175	281	2	and	and	CCONJ
ap-10175	281	3	composite	composite	ADJ
ap-10175	281	4	structures	structure	NOUN
ap-10175	281	5	42(3):397–405	42(3):397–405	PROPN
ap-10175	281	6	,	,	PUNCT
ap-10175	281	7	2022	2022	NUM
ap-10175	281	8	.	.	PUNCT
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ap-10175	283	2	17	17	NUM
ap-10175	283	3	]	]	PUNCT
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ap-10175	283	6	,	,	PUNCT
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ap-10175	283	10	,	,	PUNCT
ap-10175	283	11	l.	l.	PROPN
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ap-10175	283	13	.	.	PUNCT
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ap-10175	284	2	of	of	ADP
ap-10175	284	3	the	the	DET
ap-10175	284	4	differential	differential	ADJ
ap-10175	284	5	transformation	transformation	NOUN
ap-10175	284	6	method	method	NOUN
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ap-10175	284	9	analysis	analysis	NOUN
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ap-10175	284	11	pipes	pipe	NOUN
ap-10175	284	12	conveying	convey	VERB
ap-10175	284	13	fluid	fluid	NOUN
ap-10175	284	14	.	.	PUNCT
ap-10175	285	1	applied	apply	VERB
ap-10175	285	2	mathematics	mathematic	NOUN
ap-10175	285	3	and	and	CCONJ
ap-10175	285	4	computation	computation	NOUN
ap-10175	285	5	217(16):7028–7038	217(16):7028–7038	NUM
ap-10175	285	6	,	,	PUNCT
ap-10175	285	7	2011	2011	NUM
ap-10175	285	8	.	.	PUNCT
ap-10175	286	1	https://doi.org/10.1016/j.amc.2011.01.116	https://doi.org/10.1016/j.amc.2011.01.116	PROPN
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ap-10175	287	2	18	18	NUM
ap-10175	287	3	]	]	X
ap-10175	287	4	h.	h.	PROPN
ap-10175	287	5	yu	yu	PROPN
ap-10175	287	6	,	,	PUNCT
ap-10175	287	7	f.	f.	PROPN
ap-10175	287	8	liang	liang	PROPN
ap-10175	287	9	,	,	PUNCT
ap-10175	287	10	y.	y.	PROPN
ap-10175	287	11	qian	qian	PROPN
ap-10175	287	12	,	,	PUNCT
ap-10175	287	13	et	et	PROPN
ap-10175	287	14	al	al	PROPN
ap-10175	287	15	.	.	PROPN
ap-10175	287	16	phononic	phononic	ADJ
ap-10175	287	17	band	band	NOUN
ap-10175	287	18	gap	gap	NOUN
ap-10175	287	19	and	and	CCONJ
ap-10175	287	20	free	free	ADJ
ap-10175	287	21	vibration	vibration	NOUN
ap-10175	287	22	analysis	analysis	NOUN
ap-10175	287	23	of	of	ADP
ap-10175	287	24	fluid	fluid	NOUN
ap-10175	287	25	-	-	PUNCT
ap-10175	287	26	conveying	convey	VERB
ap-10175	287	27	pipes	pipe	NOUN
ap-10175	287	28	with	with	ADP
ap-10175	287	29	periodically	periodically	ADV
ap-10175	287	30	varying	vary	VERB
ap-10175	287	31	cross	cross	NOUN
ap-10175	287	32	-	-	NOUN
ap-10175	287	33	section	section	NOUN
ap-10175	287	34	.	.	PUNCT
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ap-10175	288	2	sciences	science	NOUN
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ap-10175	288	4	,	,	PUNCT
ap-10175	288	5	2021	2021	NUM
ap-10175	288	6	.	.	PUNCT
ap-10175	289	1	https://doi.org/10.3390/app112110485	https://doi.org/10.3390/app112110485	VERB
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ap-10175	289	3	19	19	NUM
ap-10175	289	4	]	]	PUNCT
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ap-10175	289	6	.	.	PUNCT
ap-10175	290	1	li	li	PROPN
ap-10175	290	2	,	,	PUNCT
ap-10175	290	3	g.-m	g.-m	PROPN
ap-10175	290	4	.	.	PUNCT
ap-10175	291	1	liu	liu	PROPN
ap-10175	291	2	,	,	PUNCT
ap-10175	291	3	w.-t	w.-t	PROPN
ap-10175	291	4	.	.	PUNCT
ap-10175	292	1	kong	kong	PROPN
ap-10175	292	2	.	.	PUNCT
ap-10175	293	1	vibration	vibration	NOUN
ap-10175	293	2	analysis	analysis	NOUN
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ap-10175	293	4	pipes	pipe	NOUN
ap-10175	293	5	conveying	convey	VERB
ap-10175	293	6	fluid	fluid	NOUN
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ap-10175	293	8	transfer	transfer	NOUN
ap-10175	293	9	matrix	matrix	NOUN
ap-10175	293	10	method	method	NOUN
ap-10175	293	11	.	.	PUNCT
ap-10175	294	1	nuclear	nuclear	ADJ
ap-10175	294	2	engineering	engineering	NOUN
ap-10175	294	3	and	and	CCONJ
ap-10175	294	4	design	design	NOUN
ap-10175	294	5	266:78–88	266:78–88	NUM
ap-10175	294	6	,	,	PUNCT
ap-10175	294	7	2014	2014	NUM
ap-10175	294	8	.	.	PUNCT
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ap-10175	296	2	20	20	NUM
ap-10175	296	3	]	]	X
ap-10175	296	4	y.	y.	PROPN
ap-10175	296	5	ma	ma	PROPN
ap-10175	296	6	,	,	PUNCT
ap-10175	296	7	y.	y.	PROPN
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ap-10175	296	9	,	,	PUNCT
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ap-10175	296	11	chen	chen	PROPN
ap-10175	296	12	,	,	PUNCT
ap-10175	296	13	et	et	PROPN
ap-10175	296	14	al	al	PROPN
ap-10175	296	15	.	.	PUNCT
ap-10175	296	16	application	application	NOUN
ap-10175	296	17	of	of	ADP
ap-10175	296	18	harmonic	harmonic	ADJ
ap-10175	296	19	differential	differential	NOUN
ap-10175	296	20	quadrature	quadrature	NOUN
ap-10175	296	21	(	(	PUNCT
ap-10175	296	22	hdq	hdq	NOUN
ap-10175	296	23	)	)	PUNCT
ap-10175	296	24	method	method	NOUN
ap-10175	296	25	for	for	ADP
ap-10175	296	26	vibration	vibration	NOUN
ap-10175	296	27	analysis	analysis	NOUN
ap-10175	296	28	of	of	ADP
ap-10175	296	29	pipes	pipe	NOUN
ap-10175	296	30	conveying	convey	VERB
ap-10175	296	31	fluid	fluid	NOUN
ap-10175	296	32	.	.	PUNCT
ap-10175	297	1	applied	apply	VERB
ap-10175	297	2	mathematics	mathematic	NOUN
ap-10175	297	3	and	and	CCONJ
ap-10175	297	4	computation	computation	NOUN
ap-10175	297	5	439:127613	439:127613	NUM
ap-10175	297	6	.	.	PROPN
ap-10175	297	7	,	,	PUNCT
ap-10175	297	8	2023	2023	NUM
ap-10175	297	9	.	.	PUNCT
ap-10175	298	1	https://doi.org/10.1016/j.amc.2022.127613	https://doi.org/10.1016/j.amc.2022.127613	PUNCT
ap-10175	298	2	[	[	X
ap-10175	298	3	21	21	NUM
ap-10175	298	4	]	]	PUNCT
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ap-10175	298	6	m.	m.	PROPN
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ap-10175	298	8	.	.	PUNCT
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ap-10175	298	12	coupled	couple	VERB
ap-10175	298	13	vibration	vibration	NOUN
ap-10175	298	14	of	of	ADP
ap-10175	298	15	cylindrical	cylindrical	ADJ
ap-10175	298	16	pipes	pipe	NOUN
ap-10175	298	17	conveying	convey	VERB
ap-10175	298	18	fluid	fluid	NOUN
ap-10175	298	19	with	with	ADP
ap-10175	298	20	the	the	DET
ap-10175	298	21	wave	wave	NOUN
ap-10175	298	22	propagation	propagation	NOUN
ap-10175	298	23	approach	approach	NOUN
ap-10175	298	24	.	.	PUNCT
ap-10175	299	1	computers	computer	NOUN
ap-10175	299	2	&	&	CCONJ
ap-10175	299	3	structures	structure	NOUN
ap-10175	299	4	80(3–4):287–295	80(3–4):287–295	NOUN
ap-10175	299	5	,	,	PUNCT
ap-10175	299	6	2002	2002	NUM
ap-10175	299	7	.	.	PUNCT
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ap-10175	301	1	[	[	X
ap-10175	301	2	22	22	NUM
ap-10175	301	3	]	]	X
ap-10175	301	4	f.	f.	PROPN
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ap-10175	301	6	,	,	PUNCT
ap-10175	301	7	x.	x.	PROPN
ap-10175	301	8	d.	d.	PROPN
ap-10175	301	9	yang	yang	PROPN
ap-10175	301	10	.	.	PROPN
ap-10175	301	11	wave	wave	NOUN
ap-10175	301	12	properties	property	NOUN
ap-10175	301	13	and	and	CCONJ
ap-10175	301	14	band	band	NOUN
ap-10175	301	15	gap	gap	NOUN
ap-10175	301	16	analysis	analysis	NOUN
ap-10175	301	17	of	of	ADP
ap-10175	301	18	deploying	deploy	VERB
ap-10175	301	19	pipes	pipe	NOUN
ap-10175	301	20	conveying	convey	VERB
ap-10175	301	21	fluid	fluid	NOUN
ap-10175	301	22	with	with	ADP
ap-10175	301	23	periodic	periodic	ADJ
ap-10175	301	24	varying	vary	VERB
ap-10175	301	25	parameters	parameter	NOUN
ap-10175	301	26	.	.	PUNCT
ap-10175	302	1	applied	apply	VERB
ap-10175	302	2	mathematical	mathematical	ADJ
ap-10175	302	3	modelling	model	VERB
ap-10175	302	4	77:522–538	77:522–538	NUM
ap-10175	302	5	,	,	PUNCT
ap-10175	302	6	2020	2020	NUM
ap-10175	302	7	.	.	PUNCT
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ap-10175	304	1	[	[	X
ap-10175	304	2	23	23	NUM
ap-10175	304	3	]	]	PUNCT
ap-10175	304	4	a.	a.	NOUN
ap-10175	304	5	o.	o.	PROPN
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ap-10175	304	7	,	,	PUNCT
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ap-10175	304	9	o.	o.	PROPN
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ap-10175	304	11	,	,	PUNCT
ap-10175	304	12	k.	k.	PROPN
ap-10175	304	13	orolu	orolu	PROPN
ap-10175	304	14	,	,	PUNCT
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ap-10175	304	16	o.	o.	PROPN
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ap-10175	305	2	of	of	ADP
ap-10175	305	3	horizontal	horizontal	ADJ
ap-10175	305	4	pipes	pipe	NOUN
ap-10175	305	5	conveying	convey	VERB
ap-10175	305	6	two	two	NUM
ap-10175	305	7	phase	phase	NOUN
ap-10175	305	8	flow	flow	NOUN
ap-10175	305	9	with	with	ADP
ap-10175	305	10	nonlinear	nonlinear	ADJ
ap-10175	305	11	boundary	boundary	ADJ
ap-10175	305	12	conditions	condition	NOUN
ap-10175	305	13	.	.	PUNCT
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ap-10175	306	2	systems	system	NOUN
ap-10175	306	3	and	and	CCONJ
ap-10175	306	4	signal	signal	NOUN
ap-10175	306	5	processing	process	VERB
ap-10175	306	6	217:111520	217:111520	NUM
ap-10175	306	7	,	,	PUNCT
ap-10175	306	8	2024	2024	NUM
ap-10175	306	9	.	.	PUNCT
ap-10175	307	1	https://doi.org/10.1016/j.ymssp.2024.111520	https://doi.org/10.1016/j.ymssp.2024.111520	PROPN
ap-10175	308	1	[	[	X
ap-10175	308	2	24	24	NUM
ap-10175	308	3	]	]	PUNCT
ap-10175	308	4	j.	j.	PROPN
ap-10175	308	5	x.	x.	PROPN
ap-10175	308	6	f.	f.	PROPN
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ap-10175	308	9	r.	r.	PROPN
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ap-10175	309	3	of	of	ADP
ap-10175	309	4	gas	gas	NOUN
ap-10175	309	5	void	void	NOUN
ap-10175	309	6	fraction	fraction	NOUN
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ap-10175	309	10	highly	highly	ADV
ap-10175	309	11	viscous	viscous	ADJ
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ap-10175	309	13	and	and	CCONJ
ap-10175	309	14	gas	gas	NOUN
ap-10175	309	15	two	two	NUM
ap-10175	309	16	-	-	PUNCT
ap-10175	309	17	phase	phase	NOUN
ap-10175	309	18	vertical	vertical	ADJ
ap-10175	309	19	flows	flow	NOUN
ap-10175	309	20	.	.	PUNCT
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ap-10175	310	2	of	of	ADP
ap-10175	310	3	natural	natural	ADJ
ap-10175	310	4	gas	gas	NOUN
ap-10175	310	5	science	science	NOUN
ap-10175	310	6	and	and	CCONJ
ap-10175	310	7	engineering	engineering	NOUN
ap-10175	310	8	76:103107	76:103107	NOUN
ap-10175	310	9	,	,	PUNCT
ap-10175	310	10	2020	2020	NUM
ap-10175	310	11	.	.	PUNCT
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ap-10175	311	2	[	[	X
ap-10175	311	3	25	25	NUM
ap-10175	311	4	]	]	PUNCT
ap-10175	311	5	m.	m.	NOUN
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ap-10175	311	9	a.	a.	PROPN
ap-10175	311	10	j.	j.	PROPN
ap-10175	311	11	ghajar	ghajar	PROPN
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ap-10175	312	1	comparison	comparison	NOUN
ap-10175	312	2	of	of	ADP
ap-10175	312	3	void	void	ADJ
ap-10175	312	4	fraction	fraction	NOUN
ap-10175	312	5	correlations	correlation	NOUN
ap-10175	312	6	for	for	ADP
ap-10175	312	7	different	different	ADJ
ap-10175	312	8	flow	flow	NOUN
ap-10175	312	9	patterns	pattern	NOUN
ap-10175	312	10	in	in	ADP
ap-10175	312	11	horizontal	horizontal	ADJ
ap-10175	312	12	and	and	CCONJ
ap-10175	312	13	upward	upward	ADJ
ap-10175	312	14	inclined	inclined	ADJ
ap-10175	312	15	pipes	pipe	NOUN
ap-10175	312	16	.	.	PUNCT
ap-10175	313	1	international	international	ADJ
ap-10175	313	2	journal	journal	PROPN
ap-10175	313	3	of	of	ADP
ap-10175	313	4	multiphase	multiphase	PROPN
ap-10175	313	5	flow	flow	NOUN
ap-10175	313	6	33(4):347–370	33(4):347–370	PROPN
ap-10175	313	7	,	,	PUNCT
ap-10175	313	8	2007	2007	NUM
ap-10175	313	9	.	.	PUNCT
ap-10175	314	1	https://doi.org/10.1016/j.ijmultiphaseflow	https://doi.org/10.1016/j.ijmultiphaseflow	PROPN
ap-10175	314	2	.	.	PUNCT
ap-10175	315	1	2006.09.004	2006.09.004	PROPN
ap-10175	316	1	[	[	X
ap-10175	316	2	26	26	NUM
ap-10175	316	3	]	]	X
ap-10175	316	4	f.	f.	PROPN
ap-10175	316	5	liang	liang	PROPN
ap-10175	316	6	,	,	PUNCT
ap-10175	316	7	x.-d	x.-d	PROPN
ap-10175	316	8	.	.	PUNCT
ap-10175	316	9	yang	yang	PROPN
ap-10175	316	10	,	,	PUNCT
ap-10175	316	11	w.	w.	PROPN
ap-10175	316	12	zhang	zhang	PROPN
ap-10175	316	13	,	,	PUNCT
ap-10175	316	14	y.-j	y.-j	PROPN
ap-10175	316	15	.	.	PROPN
ap-10175	317	1	qian	qian	PROPN
ap-10175	317	2	.	.	PUNCT
ap-10175	318	1	dynamical	dynamical	ADJ
ap-10175	318	2	modeling	modeling	NOUN
ap-10175	318	3	and	and	CCONJ
ap-10175	318	4	free	free	ADJ
ap-10175	318	5	vibration	vibration	NOUN
ap-10175	318	6	analysis	analysis	NOUN
ap-10175	318	7	of	of	ADP
ap-10175	318	8	spinning	spin	VERB
ap-10175	318	9	pipes	pipe	NOUN
ap-10175	318	10	conveying	convey	VERB
ap-10175	318	11	fluid	fluid	NOUN
ap-10175	318	12	with	with	ADP
ap-10175	318	13	axial	axial	ADJ
ap-10175	318	14	deployment	deployment	NOUN
ap-10175	318	15	.	.	PUNCT
ap-10175	319	1	journal	journal	PROPN
ap-10175	319	2	of	of	ADP
ap-10175	319	3	sound	sound	NOUN
ap-10175	319	4	and	and	CCONJ
ap-10175	319	5	vibration	vibration	NOUN
ap-10175	319	6	417:65–79	417:65–79	ADV
ap-10175	319	7	,	,	PUNCT
ap-10175	319	8	2018	2018	NUM
ap-10175	319	9	.	.	PUNCT
ap-10175	320	1	https://doi.org/10.1016/j.jsv.2017.12.005	https://doi.org/10.1016/j.jsv.2017.12.005	PROPN
ap-10175	320	2	340	340	NUM
ap-10175	320	3	https://doi.org/10.1016/j.petrol.2022.110766	https://doi.org/10.1016/j.petrol.2022.110766	NOUN
ap-10175	320	4	https://doi.org/10.1016/j.engstruct.2023.116138	https://doi.org/10.1016/j.engstruct.2023.116138	PROPN
ap-10175	320	5	https://doi.org/10.1007/s40430-020-02710-x	https://doi.org/10.1007/s40430-020-02710-x	PROPN
ap-10175	320	6	https://doi.org/10.1016/s0082-0784(06)80170-0	https://doi.org/10.1016/s0082-0784(06)80170-0	NOUN
ap-10175	320	7	https://doi.org/10.1080/21642583.2016.1213189	https://doi.org/10.1080/21642583.2016.1213189	PROPN
ap-10175	320	8	https://doi.org/10.1016/j.petrol.2016.08.019	https://doi.org/10.1016/j.petrol.2016.08.019	NOUN
ap-10175	320	9	https://doi.org/10.12989/scs.2024.53.3.363	https://doi.org/10.12989/scs.2024.53.3.363	NOUN
ap-10175	320	10	https://doi.org/10.1016/j.apor.2024.103961	https://doi.org/10.1016/j.apor.2024.103961	ADJ
ap-10175	320	11	https://doi.org/10.4028/www.scientific.net/ddf.409.39	https://doi.org/10.4028/www.scientific.net/ddf.409.39	NOUN
ap-10175	320	12	https://doi.org/10.4028/www.scientific.net/ddf.409.39	https://doi.org/10.4028/www.scientific.net/ddf.409.39	VERB
ap-10175	320	13	https://doi.org/10.12989/scs.2022.42.3.397	https://doi.org/10.12989/scs.2022.42.3.397	PROPN
ap-10175	320	14	https://doi.org/10.1016/j.amc.2011.01.116	https://doi.org/10.1016/j.amc.2011.01.116	ADJ
ap-10175	320	15	https://doi.org/10.3390/app112110485	https://doi.org/10.3390/app112110485	PROPN
ap-10175	320	16	https://doi.org/10.1016/j.nucengdes.2013.10.028	https://doi.org/10.1016/j.nucengdes.2013.10.028	PROPN
ap-10175	320	17	https://doi.org/10.1016/j.amc.2022.127613	https://doi.org/10.1016/j.amc.2022.127613	PROPN
ap-10175	320	18	https://doi.org/10.1016/s0045-7949(02)00005-6	https://doi.org/10.1016/s0045-7949(02)00005-6	PROPN
ap-10175	320	19	https://doi.org/10.1016/j.apm.2019.07.064	https://doi.org/10.1016/j.apm.2019.07.064	PROPN
ap-10175	320	20	https://doi.org/10.1016/j.ymssp.2024.111520	https://doi.org/10.1016/j.ymssp.2024.111520	PROPN
ap-10175	320	21	https://doi.org/10.1016/j.jngse.2019.103107	https://doi.org/10.1016/j.jngse.2019.103107	ADP
ap-10175	320	22	https://doi.org/10.1016/j.ijmultiphaseflow.2006.09.004	https://doi.org/10.1016/j.ijmultiphaseflow.2006.09.004	PROPN
ap-10175	320	23	https://doi.org/10.1016/j.ijmultiphaseflow.2006.09.004	https://doi.org/10.1016/j.ijmultiphaseflow.2006.09.004	NOUN
ap-10175	320	24	https://doi.org/10.1016/j.jsv.2017.12.005	https://doi.org/10.1016/j.jsv.2017.12.005	VERB
ap-10175	320	25	acta	acta	PROPN
ap-10175	320	26	polytechnica	polytechnica	PROPN
ap-10175	320	27	65(3):334–340	65(3):334–340	PROPN
ap-10175	320	28	,	,	PUNCT
ap-10175	320	29	2025	2025	NUM
ap-10175	320	30	1	1	NUM
ap-10175	320	31	introduction	introduction	NOUN
ap-10175	320	32	2	2	NUM
ap-10175	320	33	derivation	derivation	NOUN
ap-10175	320	34	of	of	ADP
ap-10175	320	35	the	the	DET
ap-10175	320	36	equation	equation	NOUN
ap-10175	320	37	of	of	ADP
ap-10175	320	38	motion	motion	NOUN
ap-10175	320	39	2.1	2.1	NUM
ap-10175	320	40	dimensionless	dimensionless	NOUN
ap-10175	320	41	quantities	quantity	NOUN
ap-10175	320	42	3	3	NUM
ap-10175	320	43	wave	wave	NOUN
ap-10175	320	44	propagation	propagation	NOUN
ap-10175	320	45	approach	approach	NOUN
ap-10175	320	46	4	4	NUM
ap-10175	320	47	results	result	NOUN
ap-10175	320	48	and	and	CCONJ
ap-10175	320	49	discussion	discussion	NOUN
ap-10175	320	50	4.1	4.1	NUM
ap-10175	320	51	validation	validation	NOUN
ap-10175	320	52	of	of	ADP
ap-10175	320	53	the	the	DET
ap-10175	320	54	result	result	NOUN
ap-10175	320	55	4.2	4.2	NUM
ap-10175	320	56	effect	effect	NOUN
ap-10175	320	57	of	of	ADP
ap-10175	320	58	two	two	NUM
ap-10175	320	59	-	-	PUNCT
ap-10175	320	60	phase	phase	NOUN
ap-10175	320	61	flow	flow	NOUN
ap-10175	320	62	on	on	ADP
ap-10175	320	63	phase	phase	NOUN
ap-10175	320	64	and	and	CCONJ
ap-10175	320	65	group	group	NOUN
ap-10175	320	66	velocities	velocity	NOUN
ap-10175	320	67	4.3	4.3	NUM
ap-10175	320	68	effect	effect	NOUN
ap-10175	320	69	of	of	ADP
ap-10175	320	70	temperature	temperature	NOUN
ap-10175	320	71	on	on	ADP
ap-10175	320	72	phase	phase	NOUN
ap-10175	320	73	and	and	CCONJ
ap-10175	320	74	group	group	NOUN
ap-10175	320	75	velocities	velocity	NOUN
ap-10175	320	76	4.4	4.4	NUM
ap-10175	320	77	effect	effect	NOUN
ap-10175	320	78	of	of	ADP
ap-10175	320	79	wavenumber	wavenumber	NOUN
ap-10175	320	80	on	on	ADP
ap-10175	320	81	phase	phase	NOUN
ap-10175	320	82	velocity	velocity	NOUN
ap-10175	320	83	4.5	4.5	NUM
ap-10175	320	84	natural	natural	ADJ
ap-10175	320	85	frequency	frequency	NOUN
ap-10175	320	86	of	of	ADP
ap-10175	320	87	two	two	NUM
ap-10175	320	88	-	-	PUNCT
ap-10175	320	89	phase	phase	NOUN
ap-10175	320	90	flow	flow	NOUN
ap-10175	320	91	5	5	NUM
ap-10175	320	92	conclusion	conclusion	NOUN
ap-10175	320	93	list	list	NOUN
ap-10175	320	94	of	of	ADP
ap-10175	320	95	symbols	symbol	NOUN
ap-10175	320	96	acknowledgements	acknowledgement	NOUN
ap-10175	320	97	references	reference	NOUN