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Homework Help: Ideal fluids, bernouilli's law

  1. Oct 16, 2013 #1

    I do not understand why B is not true. There is much greater fluid molecules above point A, and given P = density x g x depth, pressure should be greater at point A.....making B true. But then again if u use poiseuilles' law for nonideal fluids you see that in order to keep flow rate Q constant, if radius is larger, then pressure must be smaller at point A....making B untrue. Could you pls explain how to recincile these cinflictinf cinclusions? Thank u so much !
    Last edited: Oct 16, 2013
  2. jcsd
  3. Oct 17, 2013 #2
    If you wanna get mathematical, pressure can be defined as force per unit area, so

    [tex]P = \frac{F}{A}[/tex]

    In the case of your picture, the cross sectional area of A is larger than B, so that would mean the pressure is less at A than at B
  4. Oct 17, 2013 #3
    Thank u for your reply :) but how come we can assume that force is equal at points A @nd B?
  5. Oct 17, 2013 #4
    The explanation is misleading. One should not analyze the situation from this perspective because doing so will cause you to hold F constant, which doesn't make sense.
  6. Oct 17, 2013 #5
    You are using an equation from fluid statics to analyze a dynamic situation.

    In dynamic fluid, pressure is never simply density x g x depth. You can study bernoulli's equation and realize that there are static pressure, dynamic pressure and pressure caused by gravity.
  7. Oct 17, 2013 #6
    Okay I guess it's a little more complicated than that, let's see:

    You have your continuity equation for fluids


    The problem says that this is an ideal fluid, so the fluid isn't compressible, so




    And since A = F/P


    From a simple thought experiment we can conclude that the velocities are different, think about putting your thumb over a running water hose. And we have already seen that the pressures are the same. This leaves us with


    Since the velocities are different, we can conclude that in fact, the forces must be different if both sides of the equation are to be equal.
  8. Oct 17, 2013 #7
    ##P_{1} = P_{2}## ? How is it possible?
  9. Oct 17, 2013 #8
    Oh wow I just realized I wrote that, allow me to slowly walk away, as I clearly don't know fluid mechanics :sly: I'll go ahead and blame the time of night
  10. Oct 17, 2013 #9
    Thank you both the disvussion was very helpful!!!!
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