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Math Help - Air pressure over a diaphragm

  1. #1
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    Air pressure over a diaphragm

    Hi folks, I have a ‘kinda’-mathematical/physics problem here which im hoping somebody can help shed some light on.

    Basically, I have a pressurized lid, with a diaphragm inside it (green), and a ‘pin’ attached to the underside of the diaphragm (red). As the pressure in the lid increases (light blue), the diaphragm stretches down, and the pin moves down with it, and a dowel (pink) marks the pin. When the pressure is relieved, a spring (brown) under the red pin pushes the diaphragm back into its natural position. The pressure in the system is having to force down against the pressure of the spring.



    I want to work out how far down the pin will travel, for any given psi (realistically 0 – 30 psi), so for example if 5 psi is applied, the pin will move down 3mm, if 10psi is applied the pin will move down 7mm, etc etc.

    My question is, does the size of the diaphragm make a difference to the distance the pin will travel, for a given pressure? E.g, if 15psi is applied to a diaphragm 10cm in diameter, will the pin move down more/less/the same as if the diaphragm was 20cm in diameter?

    Any questions just ask, I know it’s a bit of an odd/confusing one!

    Thanks, Dan.
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  2. #2
    A Plied Mathematician
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    Re: Air pressure over a diaphragm

    My gut reaction would be to say that the diaphragm diameter makes no difference, because you're controlling the pressure (force per unit area). You've already sort of factored out the area, precisely because you're talking about pressure.

    Now, if you were controlling the volume of gas in-between the diaphragm and the lid, then the area of the diaphragm would matter.

    Those are my thoughts.
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  3. #3
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    e^(i*pi)'s Avatar
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    Re: Air pressure over a diaphragm

    I'd be inclined to say that the diaphragm will be negligible since you're using pressure to generate the downward force. The diaphragm will exert a small amount of force due to it's gravity but it should be small compared to the pressure.

    Pressure is, as Ackbeet stated, force per unit area and since you are tweaking pressure you're talking about force per unit area, if you increase the area you'll have to increase the force to get the same pressure.
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  4. #4
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    Re: Air pressure over a diaphragm

    Hi Dandandan.
    The movement of the pin depends on the characteristics of the spring.The force to compress the spring is psi x area (sqin) = pounds
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