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Thread: Calculating air flow rate from pressure and area.

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    Calculating air flow rate from pressure and area.

    The basic jist of the problem is that we're building a single cylinder engine that runs off an air compressor (this is at uni, and is hidden so I can't check to see if has a flow rate written on it), and it goes through a 4mm diameter opening into a closed cylinder when a valve is opened. I asked my professor for the flow rate of the air-compressor, and all he told me was that the air is at 80 psi, and it flows through a 4mm circular opening. So I'm assuming that it is possible to attain a very rough estimate of flow velocity knowing just these two pieces of information (that is assuming no pressure drop, friction etc).

    Now I haven't studied thermodynamics comprehensively or have done a fluids unit, so I don't have all that much background knowledge to rely on to calculate. I've tried applying Bernoulli's equation to find the flow velocity (both the incompressible method by assuming an isentropic flow and the compressible flow variant on wikipedia) but they are both giving me velocities in the realm of 1000 m/s which is ridiculous.

    If there is any way I can calculate it that would be helpful, because it would mean I could apply it to the flow of once the exhaust valve is opened (which I can't measure because it wont be built in time for the report next week). Otherwise I'll have to measure it roughly and guess the exhaust flow for the report.

    Thanks in advanced.
    Last edited by Cold Fussion; October 5th, 2011 at 10:24 AM.
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    280 m/s or there abouts, assuming 300 kelvin or so, and a pipe roughness of 0.1mm, pipe length of 100mm.

    I have been known to be wrong however
    Last edited by warden; August 11th, 2011 at 1:31 PM.
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    9gag reposting troll Pedrocas's Avatar
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    Use magnets for proper calculation.
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    Resident Callboy RaptorJesus's Avatar
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    Quote Originally Posted by Pedrocas View Post
    Use magnets for proper calculation.


    They exist


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    Cold Fussion's Avatar
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    Quote Originally Posted by warden View Post
    280 m/s or there abouts, assuming 300 kelvin or so, and a pipe roughness of 0.1mm, pipe length of 100mm.

    I have been known to be wrong however
    Can I ask how you went about calculating it? My air compressor at home has a "free air delivery" rating of 117L/min, however I'm still googling as to what sort aperture size this at.
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    Quote Originally Posted by RaptorJesus View Post


    They exist

    See, those flow meters are the bane of my existance They're always installed on pipelines under cathodic protection incorrectly. They require earthing rings to be installed at either end which are electrically isolated from the pipe under CP, but they never are. This causes major earthing problems and accelerated corrosion on the buried asset...

    However that model doesn't work with air.....
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    Resident Callboy RaptorJesus's Avatar
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    Troll of a troll of a troll.

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    warden's Avatar
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    Δ p - pressure drop due to friction in the pipe
    ρ - density
    f - friction coefficient
    L - pipe length
    v - velocity
    D - internal pipe diameter
    Q - volumetric flow rate

    Using that equation, bookmarked from http://www.pipeflowcalculations.com/...-of-fluids.php
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    .sa = bad driver!
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    What you've described is very similar to an orifice plate inside a pipe, for which there are many correlations. Here are some links to get you started:

    Wikipedia - Flow of gases through an orifice
    Orifice plate flowrate calculator 1
    Orifice plate flowrate calculator 2
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    warden's Avatar
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    Hrm, didn't even occur to me to look at an Orifice flow. I get very low flow rates though, 8 m/s if assuming a 10mm hose.
    Last edited by warden; August 11th, 2011 at 2:01 PM.
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    Cold Fussion's Avatar
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    Quote Originally Posted by chaos386 View Post
    What you've described is very similar to an orifice plate inside a pipe, for which there are many correlations. Here are some links to get you started:

    Wikipedia - Flow of gases through an orifice
    Orifice plate flowrate calculator 1
    Orifice plate flowrate calculator 2
    Thank you very much, this looks like it could be the go. However I'm a little unsure on the pressure on the downstream. In my case that would be the pressure in the cylinder, which I could calculate using PV=mRT, however as I don't know how much air has entered the cylinder I'm not sure how I could calculate pressure in this way.
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    .sa = bad driver!
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    Quote Originally Posted by Cold Fussion View Post
    Thank you very much, this looks like it could be the go. However I'm a little unsure on the pressure on the downstream. In my case that would be the pressure in the cylinder, which I could calculate using PV=mRT, however as I don't know how much air has entered the cylinder I'm not sure how I could calculate pressure in this way.
    I'd do an iterative approach.

    First, assume it's at 0 PSIG (I'm assuming here that your 80 PSI air supply is 80 PSIG, not PSIA), then, using the information for how much air is flowing into the cylinder, integrate over time to see how much total air goes inside. Then, integrate again for the exhaust portion of the cycle, and find out what pressure you get at the end (right before the inlet port opens up and everything starts over), and use this as your starting pressure for the next iteration of the cycle. Once your pressures at the start and end of the cycle are reasonably close, you're done.
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    Call the maintenance guys, they will know.
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    Whoa, whoa, whoa?

    Science, maths and mechanics? In its own dedicated thread? Get this shit back in the Funny pictures thread where it belongs!
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    Cold Fussion's Avatar
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    Quote Originally Posted by chaos386 View Post
    I'd do an iterative approach.

    First, assume it's at 0 PSIG (I'm assuming here that your 80 PSI air supply is 80 PSIG, not PSIA), then, using the information for how much air is flowing into the cylinder, integrate over time to see how much total air goes inside. Then, integrate again for the exhaust portion of the cycle, and find out what pressure you get at the end (right before the inlet port opens up and everything starts over), and use this as your starting pressure for the next iteration of the cycle. Once your pressures at the start and end of the cycle are reasonably close, you're done.
    Thanks for that, I'll have a go at integrating it.
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    Cold Fussion's Avatar
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    If anyone is interested we recently had the engine up and running and it works pretty well apart from some pretty bad harmonics issues:



    It injects into an open cylinder with a double ended piston (think this is called a spool valve?) which forms a chamber, when then in turns sends the air into the cylinder. Depending on the position it sends it to either the top or bottom side, creating a double action system.
    Last edited by Cold Fussion; October 5th, 2011 at 10:26 AM.
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    Cold Fussion's Avatar
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    Yeah we have figure out how to calculate the imbalances in it and try and resolve it.
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