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Deriving equation from 3D Euler Equations.

  1. Oct 11, 2012 #1
    1. The problem statement, all variables and given/known data
    I've got the 3D Euler equations
    [itex]\frac{\delta u}{\delta t} + (u\cdot \nabla)u = -\nabla p[/itex]
    [itex]\nabla \cdot u = 0 [/itex]

    I've been given that the impulse is
    [itex]\gamma = u + \nabla\phi[/itex]

    2. Relevant equations
    And I need to derive
    [itex] \frac{D\gamma}{Dt} = -(\nabla u)^T \gamma + \nabla \lambda [/itex]
    [itex] \frac{D\phi}{Dt} = p - \frac{\left|u\right|^2}{2} + \lambda [/itex]

    3. The attempt at a solution
    I've subbed the impulse equation into the first equation but don't really know where to go from there?
  2. jcsd
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