Find the equation of the streamlines.

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.Obtain the equations of the streamlines.

Asked on 26th October 2019 in Aerodynamics.
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1 Answer(s)

Here \(V_{r}=0\) and  \(V_{\theta}=cr\) , \(x\) component of velocity is given as \[u=-V_{\theta}sin\theta=-cr\frac{y}{r}=-cy\] and \(y\) component of velocity is \[V=V_{\theta}cos\theta=cr\frac{x}{r}=cx\]

\[Vdx-udy=0
\\\Rightarrow \frac{dy}{dx}=\frac{V}{u}=\frac{-x}{y}\] On integrating

\[x^{2}+y^{2}=C\]

This equation represents a circle with centre at origin.

Answered on 26th October 2019.
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