id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ap-10175	Oyelade, Akintoye O.; Ehinmowo, Adegboyega B.; Oribayo, Oluwasola; Abiodun, Yetunde O.	Wave propagation in a pipe conveying two phase flow	2025	7	.pdf	application/pdf	4237	244	63	Keywords: Wave propagation, phase velocity, group velocity, two phase, natural frequency. − C2 p + 2CpvL √ βL ( 1 + KsvL αGρG ρL(1 − αG) ) − ( v2 L + v2 L ρG ρL K2 s αG (1 − αG) − T + P + θ ) = 0 (15) Then, the expressions for phase velocity and group velocity are defined as: Cp = 1 2 √ 4 ( vL √ βL + vL √ βL αGρG ρL(1 − αG) )2 + 4Γ + 2vL √ βL ( 1 + αGρG ρL(1 − αG) ) , (16)	cache/ap-10175.pdf	txt/ap-10175.txt