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Math Help - kinetic energy PDE

  1. #1
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    kinetic energy PDE

    How can I show that the kinetic energy for an incompressible, irrotational fluid with no sources or sinks is equal to
    (delta/2)*(double integral of u*(du/dn))dS where delta is the density, u is the velocity potential, and S is a closed surface bounding the volume V. Assume that the density is constant. du/dn is a partial derivative

    I know that kinetic energy = (1/2) triple integral((v^2*delta)dt).
    I'm sorry for the typing; can anyone help me? I'm a little lost.
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  2. #2
    Super Member Rebesques's Avatar
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    Since the fluid is incompressible without singularities, we have p=const, and since it is irrational, we have v=\nabla u for the velocity v. Now, apply Gauss's theorem on the triple integral representing the kinetic energy.
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