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Math Help - Fluid Dynamics

  1. #1
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    Fluid Dynamics

    Hello, guys. I hope that you can help me with this problem. Here it is below. Thanks for the help.

    Show that the voricity (w) for the isentropic flow satisfies

    Dw/Dt = u(w . del)u.

    vorticity =
    u is a vector , and del operator is the upside down triangle. the dot represents the dot product between the two.

    I know that
    Dw/Dt = dw/dt + (u . del)w partial of w with respect to t, dw/dt but how do i get the rest?
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  2. #2
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    Quote Originally Posted by Dream View Post
    Hello, guys. I hope that you can help me with this problem. Here it is below. Thanks for the help.

    Show that the voricity (w) for the isentropic flow satisfies

    Dw/Dt = u(w . del)u.

    vorticity =
    u is a vector , and del operator is the upside down triangle. the dot represents the dot product between the two.

    I know that
    Dw/Dt = dw/dt + (u . del)w partial of w with respect to t, dw/dt but how do i get the rest?
    What equations are you starting with? Are they

    (\rho u)_x + (\rho v)_y = 0
    u u_x + v u_y = -\frac{p_x}{\rho}
    u v_x + v v_y = - \frac{p_y}{\rho}

    and p = k \rho^\gamma for isentropic flows?
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