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Flowmetry: find height of fluid in cylinder

  1. Nov 9, 2017 #1
    1. The problem statement, all variables and given/known data
    A cylinder with varying diameters is being filled and emptied at the same time. The time is measured.
    I know Flow rate into cylinder. How do I find the height of fluid in the cylinder at a particular time?

    The diameter of the hole is 0.005m.
    The diameter of the bottom of the cylinder is 4cm.
    The diameter of the top of the cylinder is 6cm.

    I don't know Qout nor height, h.

    2. Relevant equations
    Qout= A. Cd. SQRT(2.g.h)

    3. The attempt at a solution
    At time=0 sec: change in height of fluid is 0
    At time=1 sec: change in height of fluid is (Qin-Qout)/Area of cylinder
  2. jcsd
  3. Nov 9, 2017 #2


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    You have a first-order differential equation to solve:
    ##d\over dt ## holdup = Qin - Qout
    holdup is a function of h(t)
    Qout is a function of h(t)

    Your initial condition (if what you write is correct) is ##d\over dt ## holdup = 0 at t=0

    Substitute the appropriate expressions for holdup(h) and Qout(h)
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