Question

Consider a velocity field $\overrightarrow{V}=K(y\hat{i}+x\hat{k}$), where K is constant. The vorticity ,${\Omega }_z$, is

• A. -K
• B. K
• C. -K/2
• D. K/2

Answer 1

The correct option is A -K

Velocity vector,

$\overrightarrow{V}=K(y\hat{i}+x\hat{k})=Ky\hat{i}+Kx\hat{k}$

where, u=Ky, v=0 and w=Kx
Vorticity about z-axis,

${\Omega }_z=\frac{\partial v}{\partial x}-\frac{\partial u}{\partial y}$

$\frac{\partial v}{\partial x}=0,\frac{\partial u}{\partial y}=K$

$\therefore {\Omega }_z=0-K=-K$