Consider a velocity field where the radial and tangential components of velocity are Vr = 0 and Vθ = cr, respectively, where c is a constant. Is the flow field irrotational? Prove your answer.
Consider a velocity field where the radial and tangential components of velocity are V_{r} = 0 and V_{θ} = cr, respectively, where c is a constant. Is the flow field irrotational? Prove your answer.
Here V_{r} =0 and V_{\theta} = cr
\nabla \times \vec{V}=\vec{e_{z}}\left [ \frac{\partial }{\partial r}\left ( \frac{c}{r} \right )+\frac{cr}{r} -\frac{1}{r}\left ( \frac{\partial (0)}{\partial \theta} \right )\right ] \\=\vec{e_{z}}\left ( c+c-0 \right )=2c\vec{e_{z}}
Here vorticity is finite.Therefore the flow is rotational.
