Question

The velocity field has the component u = ay, u = bx, w = 0 what would be the conditions on constants a and b for obtaining an exact solution of the continuity and Navier-Stokes equations for incompressible flow?

          The velocity field has the component u = ay, u = bx, w = 0 what would be the conditions on constants a and b for obtaining an exact solution of the continuity and Navier-Stokes equations for incompressible flow?
        
The velocity field has the component u = ay, u = bx, w = 0 what would be the conditions on constants a and b for obtaining an exact solution of the continuity and Navier-Stokes equations for incompressible flow?

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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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The velocity field has the component u = ay, u = bx, w = 0. What would be the conditions on constants a and b for obtaining an exact solution of the continuity and Navier-Stokes equations for incompressible flow?
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Transcript

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00:01 Here in this question we are given the velocity component of a steeddy two dimensional space, that is u is equal to 3a x raised to the power 2 minus 2b x y.
00:13 So here we need to calculate the function of x using the equation, that is u is equal to 3a x raised to the power to minus 2b of x y.
00:22 So here we can say that a and b are constants.
00:27 So on differentiating this with t, du divided by dt will be equals to dx.
00:35 We can say that 6 of ax minus 2 of by...
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