Question

Water flows through a horiztonal pipe at a rate of 90 ft³/min. A pressure gauge placed on a 3.3 inch diameter section of the pipe reads 17 psi. What is the gauge pressure in a section of pipe where the diameter is 5.4 inches?

Pressure = __________psi

Answer 1

Answer:

Given:

P1 = 17 psi = 117211 Pa

d1 =3.3 inch = 0.08382 m

d2 = 5.4 inch = 0.13716 m

Volume flow rate = 90 ft^3/min = 0.042475 m^3/s

solution:

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From equation of continuity V/t = A1v1 = A2v2

A = pi*d^2/4

(3.14* 0.08382*0.08382/4)*v1 = 0.042475

v1 = 7.713 m/s

(3.14* 0.13716*0.13716/4)*v2 = 0.042475

v2 = 2.876 m/s

density of water rho p =1000 kg/m^3

from Bernoulis principle

P1 +(1/2)pv1^2 =P2+(1/2)dv2^2

117211 +(0.5*1000*7.713*7.713) = P2 +(0.5*1000*2.876*2.876)

P2 =142820.497 Pa

P2 = 20.714 psi

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