Navier Stokes: Spherical form

[sam2]

Hi,

I'm trying to understand how to convert the cartesian form of the N-S equation to cylinderical/spherical form. Rather than re-derive the equation for spherical/cylindrical systems, I am trying to directly convert the cartesian PDE.

I'm ok with converting the d/dx and d2/dx2 terms. What I am struggling with a little, is the v_x, v_y and v_z terms which represent velocity in the x, y and z directions respectively.

Start simple with cylindrical...

Any idea on how to represent v_x and v_y in terms of v_r and v_theta?

I make v_r to be v_x / cos(theta). But can't see how to find v_theta. Any help is much appreciated.

Regards,

Sam

[sam2]

Any ideas at all?

Thanks,

Sam