Question

A pump is filling a cylindrical water tank 30 feet in diameter and 30 feet high. The pump flow rate is 500 GPM, after 2 hours of operation, the pressure exerted from the water on the bottom of the tank is _____ psi. (Assume that the tank was empty prior to the pumping process)

Answer 1

given H = 30 feet = 30*0.3048 = 9.144 m

d = 30 feet = 30*0.3048 = 9.144 m

r = d/2 = 9.144/2 = 4.572 m

volume flow rate = 500 gallon/minute

dV/dt = 500*3.785*10^-3 = 1.8925 m^3/minute

volume of water in the tank after 2 hours,

dV = volume flowrate*time

dV= 1.8925*2*60 = 227.1 m^3

Now let h is the of water column in the tank.

using volume = V = pi*r^2*h

height h = V/(pi*r^2) =227.1/(pi*4.572^2)

h = 3.46 m

the pressure exerted from the water on the bottom of the tank,

P = Po + rho*g*h

P= 1.013*10^5 + 1000*9.8*3.46

P = 1.352*10^5 pa

P = 1.352*10^5/6894.76

P = 19.6 psi