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Old   December 12, 2007, 01:12
Default navier-stokes equation
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Shuo
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The conservtion form in cartesian coordinates is

dU/dt + dF/dx + dG/dy + dH/dz = 0

U = [rho rho*u rho*v ...]

F = [rho*u rho*u*u + P - tau_xx rho*u*v - tau_xy ...]

G = [rho*v rho*u*v - tau_yx rho*v*v + P - tau_yy ... ]

How can I express these in cylindrical coordinates?

Shuo

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Old   December 12, 2007, 03:43
Default Re: navier-stokes equation
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Praveen. C
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You can derive it yourself. Take an elementary volume in cylindrical coordinates and apply the conservation principle to it.
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Old   December 12, 2007, 18:48
Default Re: navier-stokes equation
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Shuo
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Is there a reference I can compare my derivations to?
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Old   December 13, 2007, 04:27
Default Re: navier-stokes equation
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Praveen. C
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If you look at appendices of Batchelor's Fluid Dynamics, there are equations in all coordinate frames. But they are not given in conservation form. Also try the book of Aris, Vectors, Tensors and the equations of fluid dynamics.
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