A2 nominal schedule 40 pvc pipe is 75 ft long. it is to convey water. the available pump can provide a pressure drop of 1.84 psi. determine the expected flow rate of water in the pipe.

10.22 m^3/s

Explanation:

To estimate the pressure drop in a pipe we use the Darcy-Weisbach equation

(equation 1)

With:

= Darcy-Weisbach friction coefficient

L = length of duct or pipe

v = velocity of fluid

D= hydraulic diameter

Also flow rate is:

Where v is:

Area as a function of the diameter is:

So

(equation 2)

For a laminar regime the the Darcy-Weisbach friction coefficient is function of the Reynolds number (Re) as:

With: v =velocity, D= diameter if the pipe and u= viscosity.  

With this information alpha would be:

(equation 3)

Replacing equation 3 in equation 1 we have:

And finally replacing the value for v in this equation we have:

Clearing for Q we get an expression to estimate the expected flow rate in the pipe.

We know  

Delta P = 1.84 psi or

L= 75 ft or 900 in

D for a 2 nominal schedule 40 PVC is 2.047 in. In tables you find External diameter and internal diameter. For calculations you use internal diameter (ID)

U for water at 20°C is or

So the flow expected for this pipe is or

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