Question

A 2 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.

Answer 1

10.22 m^3/s

Step-by-step explanation:

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

`((deltaP))/(L) =\alpha *((density)/(2))*((v^(2))/(D))` (equation 1)

With:

`\alpha` = Darcy-Weisbach friction coefficient

L = length of duct or pipe

v = velocity of fluid

D= hydraulic diameter

Also flow rate is:

`Q=v*A`

Where v is:

`v=(Q)/(A)`

Area as a function of the diameter is:

`A=\pi *(D^(2))/(4)`

So

`v=(4*Q)/(\pi*D^(2))` (equation 2)

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

`\alpha=(64)/(Re)`

`Re=(density*v*D)/(u)`

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

With this information alpha would be:

`\alpha=(64*u)/(density*v*D)` (equation 3)

Replacing equation 3 in equation 1 we have:

`((deltaP))/(L) =(32*u*v)/(D^(2))`

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

`((deltaP))/(L) =(128)/(\pi)*(u*Q)/(D^(4))`

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

`Q=(deltaP)/(L)*(\pi)/(128)*(D^(4))/(u)`

We know

Delta P = 1.84 psi or
`(lb)/(in^(2))`

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
`2.034*10^(-5)(lb*s)/(ft^(2))` or
`1.4113*10^(-7)(lb*s)/(in^(2))`

`Q=(1.84(lb)/(in^(2)))/(900in)*(\pi)/(128)*((2.047in)^(4))/(1.4113*10^(-7)(lb*s)/(in^(2))) = 6.24*10^(3)(in^(3))/(s)`

So the flow expected for this pipe is
`6.24*10^(3)(in^(3))/(s)` or
`10.22 (m^(3))/(s)`