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Velocity of efflux and pressure

  1. Oct 21, 2009 #1
    Is given by

    v2 = 2P/ρ

    Where P is the pressure and ρ is the density of water.

    What exactly do you mean by P?...the pressure at the point of the orifice while fluid is flowing or pressure at the same point when the fluid is not flowing?

    Assume constant pressure throughout the flow of the fluid.
  2. jcsd
  3. Oct 23, 2009 #2
    You know what...I was offline for 2 days, so I thought this thread would be CRAWLING with answers, but after opening this page...I was like -

  4. Oct 24, 2009 #3
    I really need the answers.
  5. Oct 24, 2009 #4
    P is both the pressure and the liquid internal energy per volume.
    Energy conservation before and after the injection ;
    kinetic energy + internal energy = 0 + P = 1/2 ρv2 + 0.
  6. Oct 25, 2009 #5
    Yes, it is pressure but at what state?...that's the issue.

    Anyway, I still do not have a derivation as to how P = energy.
  7. Oct 25, 2009 #6
    And yes, welcome to PF!
  8. Oct 25, 2009 #7

    The fluid would be incompressible and with no viscosity. Along a stream line 1/2 ρv^2 + p = const. by Bernouilli's theorem.
    At the starting point of the stream line where fluid is still, const = P the initial pressure with no injection holes and thus the pressure at anywhere by Pascal's principle. At the end point after injected out const. = 1/2 ρV^2 where p=0 in vacuum.

    I called p internal energy in error. Let us consider a small volume of stream tube of cross section A and length vΔt. Work done to fluid in time interval Δt is ( upstream side pressure - downstream side pressure )*A*vΔt = Δp*A. This causes the increase of kinetic energy along the stream line. p is not an energy fluid hold, but a potential ability to increase energy in downstream.
    Last edited: Oct 25, 2009
  9. Oct 25, 2009 #8


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    Staff: Mentor

    de_logistics, the question probably got few answers because your attempted answer makes little sense, so people probably didn't feel like trying to interpret it.

    P is velocity pressure at the point where you are trying to measure velocity.
  10. Oct 26, 2009 #9
    Apparently, you're right, so I'll re-explain the question.

    Consider a piston cylinder arrangement with absolutely no orifice...in a situation where there's no field involved, the pressure at every point is P.

    If an orifice is made in the cylinder, the volume of the fluid contained in it will decrease over time, i.e the fluid in the cylinder is flowing, at this state I think the pressure at every point in the cylinder will not by P, lets call this new pressure P1 -

    1) Will P1 and P be equal?

    I even do not know if the pressure P1 will be same thought the cylinder or not -

    2) In a piston cylinder arrangement which's getting emptied through an orifice will the pressure which is denoted by P1 will be the same throughout the cylinder? (including the place at which the orifice has been made but in the cylinder). Anyway, let's call the pressure at the orifice (in the cylinder) as P2

    3) What will be the p (either one of P, P1 and P2) in the formula v2 = 2p/ρ which relates the density of the fluid, pressure and velocity of efflux.
  11. Oct 26, 2009 #10
    We have a conflict of answers...I really hope the first 1 in the actual answer.
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