# Find the equation of streamlines.

Consider a velocity field where the $$x$$ and $$y$$ components of velocity are given by $$u = cy/(x^{2} + y^{2})$$ and $$v = −cx/(x^{2 }+ y^{2})$$, where $$c$$ is a constant.Obtain the equations of the streamlines.

Asked on 26th October 2019 in
Here $$x$$ and $$y$$ components of velocities are given.We need to find equation of streamlines. $vdx-udy=0 \\\frac{dy}{dx}=\frac{v}{u}=\frac{-cx}{x^{2}+y^{2}}\times \frac{x^{2}+y^{2}}{cy}=\frac{-x}{y} \\\Rightarrow \frac{dy}{dx}=\frac{-x}{y} \\\Rightarrow ydy=-xdx$
On integrating we get $\Rightarrow \frac{y^{2}}{2}=\frac{-x^{2}}{2}+C \\\Rightarrow x^{2}+y^{2}=4C \\\Rightarrow x^{2}+y^{2}=C_{1}$