the rotational component for fluid element in x-y plane is

Question

For two- dimensional fluid element in x – y plane the rotational component is given by

$(a) \omega _{z} = \frac{1}{2}\left ( \frac{\partial u}{\partial x}-\frac{\partial v}{\partial y} \right )$

$(b) \omega _{z} = \frac{1}{2}\left ( \frac{\partial u}{\partial x}+\frac{\partial v}{\partial y} \right )$

$(c) \omega _{z} = \frac{1}{2}\left ( \frac{\partial v}{\partial x}+\frac{\partial u}{\partial y} \right )$

$(d) \omega _{z} = \frac{1}{2}\left ( \frac{\partial v}{\partial x}-\frac{\partial u}{\partial y} \right )$