Determine air flow rate from pressure drop and hose diameter

[jsg94]

Good evening everyone,

I have a pressure meter from where we determined a pressure drop of 5.5 psi (Initial pressure 45.5 psi, final pressure 40 psi). The working fluid is air. The diameter of one of the hoses that is connected to the pressure meter is 1/4". I wasn't able to take a picture of the setup but I attached a quick drawing I made. The other diameter (i.e. D2) is still unknown but can be easily measured if necessary. We need to calculate the flow rate based on this information.

I know that with incompressible fluids it's easier to determine the Flow rate, since it can be approximated as the square root of the pressure difference across the pressure meter. But I suppose this wouldn't be a good assumption for compressible fluids. I was trying to use the Bernoulli equation but then again, in my Fluids book it is specified that "We assume the flow is horizontal (z1 = z2), steady, inviscid, and incompressible between points (1) and (2)". The following equations are shown:

EQUATION 1.

EQUATION 2.

EQUATION 3.

Would it be possible to use these equations and use air as an incompressible fluid? I tried going over the chapter on my book that covered compressible fluids but it was no help. I couldn't find what I was looking for. Any ideas? I would really appreciate your help!

 

[JBA]

It is not possible to calculate the flow rate based upon pressure drop without knowing the inside diameter/length/material of all of the hose(s) and any fittings that are installed between the 45. psig point the 40 psig point.

 

[jsg94]

It is not possible to calculate the flow rate based upon pressure drop without knowing the inside diameter/length/material of all of the hose(s) and any fittings that are installed between the 45. psig point the 40 psig point.

I guess those dimensions would be internal to the pressure meter, which would be a little difficult to take apart.
Would you recommend maybe looking at the data sheet of either the pressure meter or the compressor that is being used? That's the only thing I can think of. I guess they can provide a flow rate rated at a specific pressure.

Also, what do you think about this graph shown on this website? http://www.engineeringtoolbox.com/air-flow-compressed-air-pipe-line-d_1280.html

Thank you for your time

 

[russ_watters]

Let me state that a different way: What, exactly, is the pressure meter measuring a drop from/to? Because the way the picture is drawn, it sort of looks like the pressure meter is installed at a single point.

What you need is the pressure drop across a known orifice or other known obstruction. Pressure drop from one section of pipe to another is too unpredictable to be a useful flow meter.