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Integration of partials, specifically Euler to Bernoulli Equation

  1. Apr 13, 2014 #1
    Hi!

    I am having trouble following the derivation from Euler's Equation to Bernoulli's Equation. The trouble lies in the math, not the physics part. Especially the step when partial derivatives are being integrated.
    I have attached the relevant part as a screenshot.

    Euler.PNG

    How does the partial dp/dx change into dp? And where does gH come from?

    Any help will be much appreciated!
     
  2. jcsd
  3. Apr 13, 2014 #2
    You can simply note that, by the chain rule [itex] dp=\frac{\partial p}{\partial x}dx[/itex]. As far as gH is concerned, I think it should probably come from your boundary conditions. You need some information to determine the constant.
    However, I don't know what H is so I can't really answer your question.
     
  4. Apr 14, 2014 #3
    Thanks, that makes sense, I forgot about the chain rule for partials.
    Concerning gH I believe it is just another way of expressing the constant to give it a more physical meaning. With H being the "Head" measured in meters. They should have written ... = constant = g*H to make it more clear.
     
  5. Apr 14, 2014 #4
    Sounds reasonable.
     
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