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Volume in container after flow

  1. Sep 27, 2012 #1
    1. The problem statement, all variables and given/known data
    Technically not homework, but could still qualify as one.
    Let's say we have container being filled (with an incompressible fluid for completeness sake) by a pipe of radius r. We have the initial present volume(expressed as x0 seems best in light of the latter parts of the expression), we have a certain flow rate and the rate at which this flow increases. At a certain point tdivert a specific amount DivertAmount of this flow is diverted away.
    How can I find the total volume in the container at the end t?

    2. Relevant equations
    x = x0 + v0t + 1/2*at2


    3. The attempt at a solution
    Voltotal = ((x0+v0*(tdivert)+1/2*a*POWER(tdivert,2))+((v0+a*(tdivert))*(t-tdivert)+(1/2*a*POWER(t-tdivert,2)))*DivertAmount)*π*r2

    Hopefully correct, but I'm not sure.
     
  2. jcsd
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