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Math Help - Fluid Mechanics

  1. #1
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    Fluid Mechanics

    I am stuck on this question:

    For the flow with velocity field u=(x+3z, 6x-2y-2z, -3x+z) calculate the vorticity, the principal rates of strain and the principal axis.

    Write down the rate of strain matrix corresponding to the principal axes and comment briefly on your results.

    Need help!
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  2. #2
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    Quote Originally Posted by flinted View Post
    I am stuck on this question:

    For the flow with velocity field u=(x+3z, 6x-2y-2z, -3x+z) calculate the vorticity, the principal rates of strain and the principal axis.

    Write down the rate of strain matrix corresponding to the principal axes and comment briefly on your results.

    Need help!
    Don't you just apply the definitions?

    eg. vorticity = \left(\frac{\partial \, u_3}{\partial \, y} - \frac{\partial \, u_2}{\partial \, z}\right){\bf i} + \left(\frac{\partial \, u_1}{\partial \, z} - \frac{\partial \, u_3}{\partial \, x}\right) {\bf j} + \left(\frac{\partial \, u_2}{\partial \, x} - \frac{\partial \, u_1}{\partial \, y}\right) {\bf k}.
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