Question

Water flows through a horiztonal pipe at a rate of 98 ft³/min. A pressure gauge placed on a 3 inch diameter section of the pipe reads 16 psi. What is the gauge pressure in a section of pipe where the diameter is 5.2 inches?

(in psi)

Answer 1

P1 = 16 psi = 110316 Pa

d1 =3.0 inch = 0.0762 m

d2 = 5.2 inch =0.13208 m

Volume flow rate = 98 ft^3/min = 0.0462508 m^3/s

From equation of continuity V/t = A1v1 = A2v2

where A = pi*d^2/4

(3.14* 0.0762^2/4)*v1 = 0.0462508

v1 = 10.141 m/s

(3.14* 0.13208^2/4)*v2 = 0.0462508

v2 = 3.375 m/s

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

from Bernoulis principle

P1 +(1/2)pv1^2 =P2+(1/2)pv2^2

110316 +(0.5*1000*10.141^2) = P2 +(0.5*1000*3.375^2)

P2 =156047.642 Pa

P2 = 22.63 psi