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Integral QuestionFluids

  1. Oct 18, 2009 #1
    1. The problem statement, all variables and given/known data

    I have include the schematic for visual purposes only. My question is about an integral, so a knowledge of Fluids is not necessarily required to answer my question.

    Picture1-40.png


    2. Relevant equations

    This is the mass balance in a form that is suitable for this problem:

    [tex]\frac{d}{d\,t}(\int_{vol}\rho\,dV) + \int_{surf}\rho(\mathbf{v}\cdot\mathbf{n})d\,A = 0[/tex]

    Now the integral that I am concerned with is this next line of the above:

    [tex]\frac{d}{d\,t}(\int_{vol}\rho A_b\,dh) + \int{surf}\rho\sqrt{2gh}\,dA = 0 [/tex]

    Now, in the solution, in the 2nd term, they 'pulled' [itex]\sqrt{2gh}[/itex] through the integral.

    I know that 'h' varies with 't' but it does not vary with 'A.' This is why they did that right?

    I am just trying to see why that was legal, but I think that I get it. Just another case of
    me 'thinking out loud' again. :redface:
     
  2. jcsd
  3. Oct 18, 2009 #2

    Redbelly98

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    Yes, you got it. :smile:
     
  4. Oct 19, 2009 #3
    Thank you! :smile:
     
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