Energy equation [closed]

Question

The energy equation for an ideal inviscid fluid is $$\frac{d}{{dt}}\int_V {kdV = - \int_S {\left({\frac{p}{\rho } + gz + k} \right)\vec u \cdot \hat ndS}}$$ where $k = \frac{1}{2}\vec u \cdot \vec u$. Extend this energy equation to the two-dimensional viscous flow in the container V with rigid walls S using $$\vec u \cdot {\nabla ^2}\vec u = {\nabla ^2}k - \left( {\frac{{{\partial ^2}u}}{{\partial {x^2}}} + \frac{{{\partial ^2}u}}{{\partial {y^2}}} + \frac{{{\partial ^2}v}}{{\partial {x^2}}} + \frac{{{\partial ^2}v}}{{\partial {y^2}}}} \right).$$