Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    3. The attempt at a solution
    integrate both sides with respect to t
    if I leave t as a constant ...
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook