Question

Water is to be moved from a large, closed tank in which the air pressure is 20 psi into a large, open tank through 2000 ft of smooth pipe at the rate of 3 ft3/s. The fluid level in the open tank is 150 ft below that in the closed tank. Determine the required diameter of the pipe. Neglect minor losses.

Answer 1

diameter of the pipe required = 0.49 ft

Step-by-step explanation:

Thinking process:

The basic step requires a knowledge of the Bernoulli's equation for fluid motion. This is a continuity equation that has an energy balance and mass balance.

P1/p + z1 + v2/2g = P2/p + z2 + V2/2G + Minor losses

The minor losses are given as follows:

f(l/D) (V2/2g)

in addition:

V =
`(Q)/(A)`

=
`(3)/(0.25*22/7D2)`

= 3.82/D²

the equation becomes

D = 1.18 f(exp 1.5)

To find the pipe diameter, a trial and error method is applied using these properties:

Re = 5.87 × 10 ⁵

D = 0.540 H

f = 0.02

This gives

D = 0.491

using the Moody chart for correlations, the diameter can be evaluated as 0.492 ft