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Determine Force/pressure from air flow?

  1. Oct 13, 2004 #1
    I'm trying to determine the force or pressure applied to a surface based on mass air flow.

    I have a 4" pipe, that could also be 3" or 3.5", but for this example we'll stick with 4" OD. .065 wall thickness

    This pipe has air traveling through it at various speeds, pressures and temperatures. The information I have is only mass air flow.

    Min Flow: = .06 lbs/min or .79 SCFM
    Max Flow: =200 lbs/min or 2625 SCFM

    Pressure ranges from 25 in Hg (vacuum) to 35psi.

    Temp ranges from -20F to 250F.

    What I'm trying to determine is the range of force or pressure that would be exerted on some type of force/pressure sensor that I install inside this tube. I need to know this range before I can choose an appropriate sensor.

    I believe that the figures quoted above for mass air flow can be converted to velocities. Then those velocities, along with the area of the tube can be used to calculate the range of force exerted on a sensor. I don't yet have the dimensions of the sensor because I haven't selected one yet. I know this will have some bearing on the equation because you will probably need to know the surface area of the sensor that the air will be hitting. I am looking at one type of sensor right now that is actually a cable, 3.5mm in diameter. If I choose this form, I will probably lay several of these cables across the cross-section of the tube in a grid fashion, then take a measurement from the sensor that has the highest reading. I have to do this because there may be bends in this tube before or after the sensor, so the majority of the air flow may not necessarily be in the center.

    Let me know if you need more info. This area isn't my strong point, sorry, I'm just a redneck that knows how to do some metal fabrication, :wink: so put it in as much of laymans terms as possible. I believe that a formula is whats needed, so just give an example of the values/variables used.

    All help and input will be greatly apprecaited.
  2. jcsd
  3. Oct 14, 2004 #2


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    I think you and me need more figures of total pressure in order to solve your problem.

    Surely the pipe is breathing air from a vessel, pump or some device where the total pressure is specified.

    If you don't have the total pressure, then you will have to approximate this by the dynamic pressure:

    [tex] P_t \approx \rho \frac{v^2}{2} [/tex]

    in fact the force F exerted over the cable will be approximately:

    [tex]F=\rho \frac{v^2}{2} A[/tex]

    but this is only approximated. If you have a data of the total pressure (sure you have it, see the storage device upstream of the pipe) then, the force exerted on the cable will be approximately again:

    [tex]F=P_t A[/tex]

    but this time the total pressure is not equal to the dynamic pressure:

    [tex]P_t=P+\rho \frac{v^2}{2}[/tex]

    . I'm supposing the cable is transversal positioned to the main stream. Let me know what's your opinion about this.
    Last edited by a moderator: Oct 18, 2004
  4. Oct 14, 2004 #3
    The air flow will constantly vary between the two amounts I listed. Can total pressure not be calculated from those? I just need to know a min pressure/force and a max pressure/force.

    If you need more that what I've posted here, tell me specifically what data you need and I'll try to come up with it.
  5. Oct 14, 2004 #4


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    Mass flow and total pressure are two independent variables. You have to know "how much amount of force" is carrying the flow. That amount is measured by the total pressure, and that's a magnitude which is approximately conserved along the flow. You can obtain the total pressure seeing what happens upstream the pipe. First question: what is there just upstream the pipe? What device is the pipe connected to?

    I don't believe you only have mass flow available. Don't you really know where the air comes from?

    If you would know the total pressure you will obtain the <approximated> force exerted on the cable. To obtain the exact force you will have to integer the flow or know more variables. Why do you need the total pressure? Well, just at the front of the cable there will be an stagnation point (v=0). At that point the pressure of the air is just the total pressure. It will give you a good estimation of the force if you make F=Pt*A where A is the transverse area of the cable exposed to the stream. Also, knowing the total pressure you are capable of obtain the static pressure:

    [tex]P_t=P+\rho \frac{v^2}{2}[/tex]

    You know v and Pt, so that you will have P.

    Surely you have to employ a factor of correction because total pressure is not conserved totally along the stream.

    PD: if you only have the mass flow, why did you post a pressure range?
  6. Oct 14, 2004 #5


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    I'd assume this is for some boosted EFI application but 35psi and 200lbs/min sounds like a *REALLY* serious application for a 7 second car or for a big diesel. Why not run the MAF ahead of the compressor, shortens the temp range and then its only atmospheric to full vacum? Or is this for a dnyo setup to measure compressor efficiency or something like it?

    If I've guessed your application incorrectly apologies in advance.

  7. Oct 14, 2004 #6
    There is a pump upstream from this pipe, there is also a pump downstream. They both run at different flow rates. The pump upstream moves more air than the one downstream. It is possible that the pump downstream can create a vacuum when both pumps are running at their lowest settings. Neither of these pumps tell what their 'force' rating is.

    I posted the pressure range because I know what that will be from the upstream pump. I didn't think this pressure from the upstream pump was the force? I thought the force would be in newtons? I was just trying to provide all the information that I DO know.

    I thought that from the mass air flows, you could convert that to velocities and from velocities, make a calculation to determine force. But again, I know nothing about this conversion/calculation, thus why I am here for help.
  8. Oct 14, 2004 #7
    You are kind of close. I really can't discuss much about this application, nothing personal. The MAF can't be placed in front of the compressor for this application.
  9. Oct 15, 2004 #8


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    Ok. If you want to compute the force only with velocities take a look at my first post here. There I gave you a calculation of the force with the velocity.
    The velocity is obtained:

    [tex]m'=\rho v S[/tex]

    where S is the cross section of the flow, m' is the mass flow, and rho is the density. Surely your mass flow is referred to Normal Conditions or something like that. If so, take rho=1.24Kg/m^3. Anyway the density of the gas is not going to vary severely in spite of your mass flow measure is local.

    Good luck!
  10. Oct 16, 2004 #9
    I really appreciate your help on this, but can I get an example, with the info I've provided, so I can take that and be able to adjust it with varying values and see what I come up with? Sorry, like I said, I know VERY little about all of these formulas. I need a little more 'hand holding'.
  11. Oct 16, 2004 #10


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    Right, don't worry. But I'm going to have troubles with your sistem of unities. I'm not accustomed to work with lbs/min and SCFM. So the units conversion and calculation are left for you.

    We came up with the conclusion you want to estimate the force on the cable using only the velocity:

    [tex]F=\frac{m^2}{2\rho S^2}A[/tex]

    Here you have the force as a function of the mass flow(m). A range of mass flow will give you a range of forces.
    A=transverse area of the cable. If the cable has a lenght L and a diameter D, then A=LD;
    S=section of the pipe.
    \rho=density of the air.
    Last edited by a moderator: Oct 18, 2004
  12. Oct 19, 2004 #11


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    Nothing personal taken about discussing your application. Your username and questions just seemed to be a very different setup.

    You may want to include correction factors for changes in air density based on temperature which is complex since the temperature is affected by the compression before the sensor (and its efficiency and losses and ambient temperature).

    If you compare against a GM speed-density EFI setup it knows air temp and pressure from the IAT and MAP. For their MAF systems its the same as the above plus they use a heated wire in the MAF to measure flow as a function of heat extraction from the wire element (which is suppossed to be more accurate). But corrections for humidity (vapor pressure affects O2 density relative to air density) and other factors would likely be taken care of with the O2 sensor while in closed loop and help explain the reason the open-loop tables can easily be tweaked for better performance. Also, the MAF is used more for trimming back the fuel delivery at low-load than performance and its role in WOT seems unimportant as the speed density tables are suppossed to be in effect. Well, that's what I've read, I'm no expert in the area but thought this might very well be appropriate food for thought.

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