# Energy equation [closed]

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 $$\vec u \cdot {\nabla ^2}\vec u = {\nabla ^2}k - \left( {\frac{{{\partial ^2}u}}{{\partial {x^2}}} + \frac{{{\partial ^2}u}}{{\partial {y^2}}} + \frac{{{\partial ^2}v}}{{\partial {x^2}}} + \frac{{{\partial ^2}v}}{{\partial {y^2}}}} \right).$$

-

## closed as too localized by David Zaslavsky♦Oct 8 '12 at 3:48

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, see the FAQ.