1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.


    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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Yes, you got it. :smile:
  4. Oct 19, 2009 #3
    Thank you! :smile:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Integral QuestionFluids
  1. Fluid Questions (Replies: 22)

  2. Fluids Question (Replies: 0)

  3. Fluids Question (Replies: 3)

  4. Fluid Question (Replies: 11)

  5. Fluid Question (Replies: 21)