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Toricelli’s Principle

  1. May 10, 2007 #1
    OK - I'm working on Toricelli's Principle at the moment. That is, a tank where theres a small hole at the bottom and we're supposed to plot h (height) vs. t (time), V_jet vs. t, mass flow rate vs. t, and change in height vs. t.

    Now - I get a linear graph for V_jet and mass flow rate vs. time, but a non-linear curve for h and mass in the tank vs time. And I can't prove it.

    We're neglecting any internal energy transfers, etc. just plain old V = Sqrt(2.g.h)

    Any help muchly appreciated.
     
  2. jcsd
  3. May 10, 2007 #2

    HallsofIvy

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    If "mass flow rate" vs time is linear, rate= kt, then mass moved out of the tank will be quadratice in time: (1/2)kt2; so of course, the mass in the tank will be quadratic.
     
  4. May 10, 2007 #3
    Let mass vs t is v(kg/min) so : h' =-A*v( A is a constant)
    And we can see that v is linearly propotional to h or v=B*h
    then combine the two we have:
    h'=-C*h
    Solve this differential equation, we have the function h=D*exp(-k.t). So h=f(t) is not a quadratic, it's an exponential.
     
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