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Homework Help: Need MORE Hmwk help . Fluid mechanics, Fluids in motion, pressure

  1. Dec 11, 2009 #1
    College Physics

    1. The problem statement, all variables and given/known data

    The figure shows a section of a long tube that narrows near its open end to a diameter of 1.0mm. Water at 20celsius flows out of the open end at 0.020 L/s

    What is the gauge pressure at point P, where the diameter is 4.0mm?

    http://session.masteringphysics.com/problemAsset/1014234/7/jfk.Figure.P13.62.jpg

    2. Relevant equations

    Bernoulli's equation

    3. The attempt at a solution

    Same as my last post, no solution found yet. Please help me start and work through this problem.
     
  2. jcsd
  3. Dec 11, 2009 #2
    Bernoullis here is quite simple and the basis for a venturi tube. In the initial frame you have lower kinetic energy and some potential energy from pressure, P. Some of that potential energy is traded for kinetic energy;

    P1+1/2 rho(v^2)= P2 + 1/2 rho(v'^2). V' is the final velocity. From continuity of flow, the two velocities can be expressed as a ratio. That help?
     
  4. Dec 11, 2009 #3
    Thank you so much for replying!!
    So I plugged in everything that I calculated so far and ended up with:
    P1 = P2 +49805

    I can't figure out how to find the pressure in the smaller diameter tube so I can plug that in. I know it should be easy...I have the flow rate and the diameter, but I'm stuck.

    Variables I've used:
    rho=1000kg/m^3
    Velocity1 = 0.623 m/s
    Area of Larger section: 0.0126m
    Velocity2= 10m/s
    Area of Smaller section: 0.00785m
     
  5. Dec 11, 2009 #4
    So you need a numerical answer not expressed in terms of p?

    Edit: I reread the question it is asking for guage pressure.
     
  6. Dec 11, 2009 #5
    Correct, a numerical value in Pascals. I think I need to incorporate the length of each section as well, not sure how though.
     
  7. Dec 11, 2009 #6
    Well gauge pressure is relative to P. No length doesn't enter it unless you have frictional losses and data to compute these. More info would be given if it were needed.
     
  8. Dec 11, 2009 #7
    What do you mean by guage pressure is relative to P?

    Do you think that I am on the right track with the progress I've made? P1=P2+49806
     
  9. Dec 11, 2009 #8

    google gauge pressure. And yes.
     
  10. Dec 11, 2009 #9
    I was not able to get the answer before my assignment was due, the answer was 8.2E5 Pa.

    But thank you, I really appreciate your help.
     
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