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

Integration of partials, specifically Euler to Bernoulli Equation

  1. Apr 13, 2014 #1

    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.


    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook