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Bernoulli Equation - fluid mechanics question

  1. Mar 25, 2013 #1
    Hi, I am a first year studying mechanical engineering and I am having trouble understanding bernoulli equation. This is the first question in the tutorial and I can't seem to get the right answer.

    Water flows through the pipe contraction shown
    in the figure below. For the given 0.2 m
    difference in manometer level, determine the
    flowrate as a function of the diameter of the small
    pipe, D.
    (Ans: 1.56D2 m3/s)



    From the solution given by my lecturer, it says that z1 = z2 .. this will probably sound really stupid but what height does z actually represent?
    I know that there is a stagnation point at the pitot tube coming from the manometre so this means that v1 = 0 .. is that correct? The solutions also say that p1 = [itex]\gamma[/itex]h1 .. how can this be? I thought that pressure = Force x Area?

    If someone could explain the answer to me it would really help a lot.

    Thanks!
     

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    Last edited: Mar 25, 2013
  2. jcsd
  3. Mar 25, 2013 #2

    SteamKing

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    For fluids, pressure = rho * g * h, where
    rho - mass density of fluid (kg/m^3)
    g - acceleration due to gravity (9.81 m/s^2)
    h - depth of fluid at point where pressure is measured (m)
    rho*g = gamma - this is the weight density of the fluid, (N / m^2)

    Pressure has units of kg-m^2/(m^3s^2), which by rearranging becomes:
    (kg-m/s^2)*(m/m^3) = N/m^2, which is units of force / area.

    This is known as Pascal's Law.
     
  4. Mar 25, 2013 #3
    Thank you! That helps quite a bit!
     
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