In potential function, rotational component is:

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Question

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JKSSB JE CE 2021 Official Paper Shift 2 (Held on 27 Oct 2021)

Answer 1

Concept:

Vorticity(ξ):

It is defined as the ratio of limiting value of circulation and area of a closed contour. it measures the local rotation of a fluid parcel.

\({\bf{vorticity}} = \frac{{{\bf{Circulation}}}}{{{\bf{Area}}}}\)

Vorticity is defined as the twice of the rotational component.

ξ = 2ω,

But, \(\vec{\omega }=\frac{1}{2}\left( \nabla \times \vec{V} \right)\)

\(\Rightarrow \vec{\xi }=2~\vec{\omega }=2.\frac{1}{2}\left( \nabla \times \vec{V} \right)\)

\(\Rightarrow \vec{\xi }=\nabla \times \vec{V}\)

Where \(\vec{V}\) represents velocity field

\(\vec{V}=u\hat{i}+v\hat{j}+w\hat{k}\)

So vorticity is also equal to the curl of the velocity factor.