How to derive continuity eqn. in polar form?

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The continuity equation in polar form is derived by considering a small control volume with dimensions Theta * R and Theta * (R + dR). The equation states that the mass flow in minus the mass flow out plus the change in mass within the volume equals zero. This leads to the expression dRho/dt * R*dR*dTheta*dz representing the change in density over time. The flow enters from one side and exits from the other, highlighting the difference in mass flow rates. Understanding this derivation is crucial for applying the continuity equation in fluid dynamics.
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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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