Question

The velocity field is defined as $\overrightarrow{V}=(8x-6y)\hat{i}+(2y-x)\hat{j}$. The circulation around a closed curve defined by $y=1,x=3,y=3$ and $x=4$ is:

• A. 42
• B. -42
• C. 30
• D. -30

Answer 1

The correct option is C 30

Circulation $=$ Vorticity $\times$ Area
$=(\frac{\partial v}{\partial x}-\frac{\partial u}{\partial y})\times (2\times 3)$
$=(-1+6)\times 6$
$=30$
Note: Vorticity $=2{\omega }_z=\left(\frac{Circulation}{Area}\right)$