Question

You are building a water supply system with rather cheap pipe that can only safely withstand a pressure of 34 PSI gauge. You deliver water through an output pipe of area 11 square feet from a reservoir of depth 330 feet. The bottom of the reservoir is at the same level as the output pipe. What is the maximum area of the pipe connecting the reservoir with the output pipe? Density= 2 slugs/cubic foot.

Answer 1

1 psi = 6894.76 pa

p = 34 psi = 2.344*10^5 pa

density = 1030.76 kg/m^3

depth = 330 ft = 100.584 m

area = 1.0219 m^2

p1-p2 = 1/2*rho(v2^2-v1^2)

v2^2-v1^2 = 2.344*10^5*2/1030.76 = 454.8

A1V1 = A2V2

A1 = V2/V1*1.0219 m^2

v1 = 1.74 m/s

v2 = 21.45 m/s

A1 = 12.6 m^2