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Mechanics question on equation of continuity

  1. Jan 19, 2012 #1
    1. The problem statement, all variables and given/known data
    A large vertical cylindrical rainwater collection tank of cross sectional area A is filled to a
    depth h. The top of the tank is open and in the centre of the bottom of the tank is a small hole
    of cross sectional area B (B<<A). Derive expressions for (i) the flow speed and (ii) the volume
    flow rate of the water flowing out of the small hole.

    It is mainly part i) I am struggling with, as once I have an expression for the flow speed, the volume flow rate should be easy enough(I hope!)

    2. Relevant equations
    I have come up with

    dV=Av1dT=Bv2dT
    h=vdT
    3. The attempt at a solution
    Av1dT=Bv2dT
    integrate both sides with respect to t
    ∫Av1dT=∫Bv2
    if I leave t as a constant ...
    Av1=Bv2
    v2=Av1/B
    However this doesn't seem right as there is no mention of a initial velocity in the question .. please give me some pointers :)
     
  2. jcsd
  3. Jan 19, 2012 #2
    Are you sure the relevant equations are correct? For one there is water coming frmo the top and flowing out at the bottom right so it might be a good idea to put a minus sign somewhere (although you could just put that in v). Also should it be dV= Av1dT + Bv2dT
    So the change in volume is what flows in minus (or that is in the v2) what flows out through the bottom.
     
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