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Bernoulli equation

  1. Oct 8, 2005 #1
    can someone explain how to solve the bernoulli equation? i'm having a hard time understanding...
  2. jcsd
  3. Oct 8, 2005 #2


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    The Bernoulli equation is an energy conservation equation for fluid kinetics. In what way are you having difficulty solving it? o_O
  4. Oct 8, 2005 #3


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    You mean:


    The key to solving this is to recognize the differential form:


    and what, when differentiated, gives this. Well that would be:


    Hey, I know it's not easy. They catch me in here all the time with differential forms.

    Ok then so we'll divide by [itex]y^n[/itex] up there in the first equation and take the differential form:


    Alright then,so that's what we have right, the differential [itex]y^{-n}dy[/itex].

    So, let:


    and then substitute the differential form of this into the original equation. Here's the first part:

    We got:


    So the [itex]y^{-n}dy[/itex] part would just be:


    Do the rest and then get a first-order ODE in terms of z and x.
    Last edited: Oct 8, 2005
  5. Oct 8, 2005 #4
    hmm... so the key is to try to get the non-linear equation into a linear equation...
    saltydog, thank you very much for explaining it to me!!! :)
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