# Find the equation of streamlines.

Consider a velocity field where the $$x$$ and $$y$$ components of velocity are given by $$u = cx$$ and $$v = −cy$$, where $$c$$ is a constant. Obtain the equations of the streamlines.

Asked on 27th October 2019 in

Here $$u=cx$$ and $$v=-cy$$.Since $vdx – udy=0$

Therefore $\frac{dy}{dx}=\frac{v}{u}=\frac{-y}{x} \\\Rightarrow \frac{dy}{y}=\frac{-dx}{x}$

On integrating $ln(y)=xln(x)+C_{1} \\\Rightarrow y=\frac{C_{2}}{x}$

These streamlines are in hyperbola shape.

Figure