Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

B Curved Tube For Constant Pressure Increase?

Tags:
  1. Dec 13, 2016 #1
    My design concept stems from the fact that the pressure in a tube increases exponentially based on the length of the tube compressed. I would like to design a tube that increases pressure at a more constant rate. I would imagine that a tube curved inward toward the base would achieve this. As the air in the tube is being compressed by a greater distance, less air would be compressed since the size of the tube decreases. This would decrease the amount of pressure needed. However, I am not all sure if this would work, and I would be curious to hear your opinions on it.
     
  2. jcsd
  3. Dec 14, 2016 #2

    Nidum

    User Avatar
    Science Advisor
    Gold Member

    I don't understand . Draw some pictures .
     
  4. Dec 14, 2016 #3

    boneh3ad

    User Avatar
    Science Advisor
    Gold Member

    Also I am not sure where you are getting your exponential claim from. For an isothermal system, the pressure is inversely proportional to the volume.
     
  5. Dec 24, 2016 #4

    Redbelly98

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    True enough. Ignoring this misuse of the term "exponential", I've actually worked it out for the isothermal case.

    Disclaimer:
    the resulting shape is physically impossible to manufacture, so this all amounts to a purely theoretical exercise.

    I'll just set things up, without working through to the final solution. Setting aside the issue of designing a piston that must change in size to match the changing cross-sectional area of the tube during the piston's stroke...

    We want the pressure to increase linearly from its initial value P0 when the piston is at position x = 0, so:

    P = P0 + ax, where a is a constant.

    The volume V displaced by the piston, as a function of x, is

    Vdisp = [Integral]A dx,
    where A(x) is the cross-sectional area of the tube.

    The volume V of gas in the tube is then the initial volume V0, minus the displaced volume Vdisp.

    Setting PV = constant, you can then solve for the tube cross-sectional area A(x).
     
  6. Dec 24, 2016 #5

    CWatters

    User Avatar
    Science Advisor
    Homework Helper

    Use water or oil for the piston?
     
  7. Dec 28, 2016 #6

    Baluncore

    User Avatar
    Science Advisor

    A buoyant cylinder being pushed axially down into a liquid will present a force that rises linearly as the depth is increased. Changing the cross sectional area of the cylinder where it enters the liquid will change the rate of force increase.
     
  8. Dec 28, 2016 #7

    Redbelly98

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    What can keep a liquid piston like that contained, so that the increasing pressure within the cylinder doesn't blow it completely away?

    Ah, interesting idea. Provided that the piston does not move so fast that drag forces become appreciable. It would depend on the specific application, of course.
     
    Last edited: Dec 28, 2016
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Curved Tube For Constant Pressure Increase?
Loading...