Question

The incompressible continuity equation in polar coordinates is written as

• A. \(\dfrac{\partial \rho}{\partial r} + \dfrac{1}{r} \dfrac{\partial \rho}{\partial \theta} = 0\)
• B. \(\dfrac{\partial v_r}{\partial r} + \dfrac{\partial v_\theta}{\partial \theta} = 0\)
• C. \(\dfrac{\partial v_r}{\partial r} + \dfrac{1}{r} \dfrac{\partial v_\theta}{\partial \theta} = 0\)
• D. \(\dfrac{1}{r} \dfrac{\partial (r v_r)}{\partial r} + \dfrac{1}{r} \dfrac{\partial v_\theta}{\partial \theta} = 0\)

Hint:

Incompressibility means divergence of velocity is zero even in polar coordinates.

Answer 1

The Correct Option is D

The general continuity equation in polar coordinates for incompressible flow accounts for radial and tangential velocity components.