question_answer

For two-dimensionaly fluid element in x-y plane the rotational component is given by:

A) \[{{\omega }_{z}}=\frac{1}{2}\,\,\left( \frac{\partial u}{\partial x}-\frac{\partial v}{\partial y} \right)\]

B) \[{{\omega }_{z}}=\frac{1}{2}\,\,\left( \frac{\partial u}{\partial x}+\frac{\partial v}{\partial y} \right)\]

C) \[{{\omega }_{z}}=\frac{1}{2}\,\,\left( \frac{\partial v}{\partial x}-\frac{\partial u}{\partial y} \right)\]

D) \[{{\omega }_{z}}=\frac{1}{2}\,\,\left( \frac{\partial v}{\partial x}-\frac{\partial u}{\partial y} \right)\]