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.

Worldtech Asked on 29th October 2019 in Aerodynamics.
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    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.

    techAir Answered on 29th October 2019.
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