question_answer

Which one of the following is the expression of the rotational component for a two-dimensional fluid element in \[x-y\]plane?   

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

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

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

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