Question

Oil is flowing through a horizontal pipe constriction. In the large section, the pipe has a diameter of 1.6 meters and a pressure of 600 kPa. If the pipe constricts to a diameter of 0.5 meters, what is the pressure in the constricted pipe section. (Assume the oil flow rate is 65 m3/min and oil density is 900 kg/m3)

Multiple choice answers

		a) 49,431.174 kPa
		b) 586.432016 kPa
		c) 12.967984 kPa
		d) 613.829264 kPa

Answer 1

here,

the volume flow rate , V = 65 m^3 /min = 1.083 m^3 /s

the diameter in larger section , d1 = 1.6 m

radius , r1 = d1 /2 = 0.8 m

the speed of oil in larger section , v1 = V /(pi * r1^2)

v1 = 1.083 /( pi * 0.8^2) = 0.54 m/s

the pressure in larger section , P1 = 600 KPa = 6 * 10^5 Pa

the diameter of smaller section , d2 = 0.5 m

the radius of smaller section , r2 = d2/2 = 0.25 m

the speed of oil in smaller section , v2 = V /(pi * r2^2)

v2 = 1.083 /( pi * 0.25^2) = 5.52 m/s

using Bernauli's theorm

for same horizontal level

P1 + 0.5 * p * v1^2 = P2 + 0.5 * p * v2^2

6 * 10^6 + 0.5 * 900 * 0.54^2 = P2 + 0.5 * 900 * 5.52^2

P2 = 586432 Pa = 586.432 KPa

the pressure in the constricted pipe is b) 586.432 KPa