Question

A water pipe of diameter 10 inches constricts to a throat diameter of 5 inches. if the water pressure in the pipe is 8 pounds per square inch and in the throat is 6 pounds per square inch, determine the flow rate of the water in cubic feet/seconds.

Answer 1

`Q=12.59\ ft^3/s`

Step-by-step explanation:

Given that

Diameter of pipe = 10 in

diameter of throat = 5 in

Pressure in the pipe = 8 pounds per square inch

Pressure in the throat = 6 pounds per square inch

We know that discharge given as follows

`Q=A_1A_2((√(\Delta P))/(√(\rho)))/(√(A_1^2-A_2^2))`

For water

`\rho=0.036\ lb/in^3`

`A_1=(\pi)/(4)* 10^2\ in^2`

`A_1=78.53\ in^2`

`A_2=(\pi)/(4)* 5^2\ in^2`

`A_2=19.63\ in^2`

So

`Q=78.53* 19.63((√(2))/(√(0.036)))/(√(78.53^2-19.63^2))`

`Q=151.11\ in^3/s`

`Q=12.59\ ft^3/s`