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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, 10:24 AM.


    Mathematics is to physics as masturbation is to sex.

    #2
    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, 1:31 PM.
    "If you think it's expensive to hire a professional to do the job, wait until you hire an amateur." - Red Adair.
    "Nothing is to high for the daring of mortals. We storm heaven it self in our folly." - Horace.

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      #3
      Use magnets for proper calculation.

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        #4
        Originally posted by Pedrocas View Post
        Use magnets for proper calculation.


        They exist

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          #5
          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.


          Mathematics is to physics as masturbation is to sex.

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            #6
            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.....
            "If you think it's expensive to hire a professional to do the job, wait until you hire an amateur." - Red Adair.
            "Nothing is to high for the daring of mortals. We storm heaven it self in our folly." - Horace.

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              #7


              Troll of a troll of a troll.

              /Inception

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                #8

                ? p - pressure drop due to friction in the pipe
                ? - 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
                "If you think it's expensive to hire a professional to do the job, wait until you hire an amateur." - Red Adair.
                "Nothing is to high for the daring of mortals. We storm heaven it self in our folly." - Horace.

                Signature by Ford GT

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                  #9
                  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
                  "It's not long enough to use in bed." -rickhamilton620

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                    #10
                    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, 2:01 PM.
                    "If you think it's expensive to hire a professional to do the job, wait until you hire an amateur." - Red Adair.
                    "Nothing is to high for the daring of mortals. We storm heaven it self in our folly." - Horace.

                    Signature by Ford GT

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                      #11
                      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.


                      Mathematics is to physics as masturbation is to sex.

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                        #12
                        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.
                        "It's not long enough to use in bed." -rickhamilton620

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                          #13
                          Call the maintenance guys, they will know.
                          "I don't care who does the electing, so long as I get to do the nominating" -Boss Tweed

                          "No man's life, liberty or happiness are safe while Congress is in session,"- Mark Twain

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                            #14
                            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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                              #15
                              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.


                              Mathematics is to physics as masturbation is to sex.

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                                #16
                                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, 10:26 AM.


                                Mathematics is to physics as masturbation is to sex.

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                                  #17
                                  You need counterweights in a bad weigh.
                                  "I don't care who does the electing, so long as I get to do the nominating" -Boss Tweed

                                  "No man's life, liberty or happiness are safe while Congress is in session,"- Mark Twain

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                                    #18
                                    Yeah we have figure out how to calculate the imbalances in it and try and resolve it.


                                    Mathematics is to physics as masturbation is to sex.

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