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DannyB01

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I'm trying to work out the flow rate of gas down a pipe. My setup is simply an air compressor with a pipe coming out of it, with a pressure gauge and flow control valve about 20cm from the end (for all intents and purposes, it actually leads to a circular reed and piezoelectric sounder circuit). I thought this would be a fairly simple thing to do after a bit of reading but I'm getting values way off. I'm not an engineer and have never dealt with fluid equations in the slightest everything here is completely new to me, so apologies for any rookie errors.

All in all pipe length is about 6.2m.

The pipe's diameter is 8mm.

I'm dealing with a few different pressure differentials - 1bar, 2bar, 3bar, 4bar and 5bar.

Using air at room temperature so about 25 celsius in an environment at atmospheric pressure.

I started off using Bernouilli's equation (P + 0.5ρ*v^2 + ρgh = constant), ignored the ρgh term for being negligible and rearranged etc. eventually finding an expression for the velocity of v=(2*(P1 - P2)/ρ)^0.5. But for 5bar as the pressure differential (ie what's read on the pressure gauge and relative to the room's atmosphere), converting gives 500000Pa and putting this in the equation gives a ridiculously high value of 917m/s for the flow speed, which can't be right.

I have also tried using the volumetric flow rate equation: Q=(Pi*(P1 - P2)*R^4)/8μL. I used μ=1.98E-5 kg/(m.s) for air at this temperature, and again for 5bar I got a pretty obscene value of Q=0.41m^3/s. As a 1m length of pipe only has 5.03E-5 m^3 volume this relates to a speed of 8151m/s. Again this seems silly, and I would hope that if I could use both equations I would get at least a very similar value for the speed of the air with each!

What I was expecting was to find that the gas speed was low enough to approximate the situation to laminar flow, ie Reynolds number, Re < 2320, which I worked out would be speeds of about 4.8m/s or lower. I would also then be able to say that these speeds are low enough to not have to factor in the compression of the air leading to an increased air density.

Could you tell me what I'm missing here and show me how you'd calculate it to get a more reasonable result? I'm getting the feeling that I'll have to model it as turbulent flow and perhaps even a choked gas velocity - I'd be intimidated by that if I'm honest but will try it if that's the only way. More likely to me it seems that my values for the pressure differentials are wrong, as I've seen it said that after a short distance down the pipe the pressure will have dropped down considerably. I wouldn't quite understand this because I designed the system so that the pressure gauge is very near the end and, when the flow control valve is fully open, it reads the same pressure as the air compressor when the gas control valve is open (at the end of the pipe attached to the compressor by a snap lock I think it's called) - so if the pressure's stayed the same the first 6m down the pipe I can't see how it would've changed so dramatically in the final 20cm.

If anyone can help me with this they'll be a lifesaver. Hopefully it will be possible to work it out with what I've given you, but seeing the equations and knowing how you did it is what I'd love to know most as I'd like to actually understand where I'm going wrong. I can't stress enough how much I appreciate the help!Dan.Edit: Also, as much as I don't like to rush people, if I'm going to have to take physical measurements (which I hope I don't have to) I only really have until the end of friday for that, so it'd be nice to have an answer by then. I'm going to head to bed because 6 hours of failing fluid dynamics like this has done me in! :)