# 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

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.