Calculate Pipe Sized Based on Pressure Differential and Flow Rate

[SonnyBoy]

Hi, everyone. This is my first post so I figured I'd introduce myself very quickly before I get to the problem. My name is Matt and I'm a first year engineering student at Oregon State University. I've read quite a few topics here, but this is the first time I've really joined in on anything. I'm hoping to make that a more regular occurrence as my knowledge grows.

Homework Statement

With a given flow rate of 26 CFM of air and a pressure differential of 1.5 inches of Mercury between the start and end of the pipe, what is the inside diameter of pipe is necessary to maintain a flow velocity of 300 feet per second, assuming there are no losses along the length of the pipe.

Homework Equations

This is the part I need help with. I'm not sure where to start.

The Attempt at a Solution

I will attempt it as soon as I know which equation(s) to use.

 

[LawrenceC]

Problems states the volumetric flow rate is 26 CFM. What is the formula for volumetric flow rate?

 

[SonnyBoy]

I'm afraid I don't have a formula for the flow rate, it's a given value for the equation along with the pressure differential and air velocity.

 

[LawrenceC]

Volumetric flow rate is 26 ft^3/minute. What two common flow parameters must be multiplied together to arrive at ft^3/minute? That tells you the formula to use.

 

[SonnyBoy]

It's just Q = v * A? The pressure differential doesn't matter?

 

[LawrenceC]

I think it was a confusion factor. Volumetric flow rate is indeed velocity times area. You are given the velocity and the volumetric flow rate. Therefore you can compute the area once you make the units uniform.

Actually, I do not see how there is a pressure drop without friction unless the pipeline is going uphill or unless there is heat transfer or unless there is an area change.

 

[SonnyBoy]

The question was academic, so I suspect that you are correct in your friction statement. For the purposes of this problem, an air pump was "sucking" the air through the pipe and the low pressure generated by the pump was 1.5" of Hg.

 

[LawrenceC]

You'll be studying Fanno and Rayleigh flow in the future. Fanno flow is flow considering frictional effects while Rayleigh flow is flow considers heat transfer effects. In the real world, you have them simultaneously.

Good fortune with your studies.

 

[SonnyBoy]

Thanks very much for the help!