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.
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.
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.
