How to derive continuity eqn. in polar form?

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loveblade
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You know that the continuity equation states out - in + change = 0
Therefore draw a small control colume with dimensions Theta * R, Theta * (R + dR). dR, dZ (looks like piece of pie with the point taken out.
The simply see flow going in on on side out on the other and the difference is the change, dRho/dt * R*dR*dTheta*dz
just to help you out:
 

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