User:George100/sandbox



\begin{align} \frac{\partial \eta }{\partial t} + \frac{\partial (\eta u)}{\partial x} + \frac{\partial (\eta v)}{\partial y} & = 0\\[3pt] \frac{\partial (\eta u)}{\partial t}+ \frac{\partial}{\partial x}\left( \eta u^2 + \frac{1}{2}g \eta^2 \right) + \frac{\partial (\eta u v)}{\partial y} & = 0\\[3pt] \frac{\partial (\eta v)}{\partial t} + \frac{\partial (\eta uv)}{\partial x} + \frac{\partial}{\partial y}\left(\eta v^2 + \frac{1}{2}g \eta ^2\right) & = 0. \end{align} $$



\begin{align}

\frac{\partial \eta }{\partial t} + \frac{\partial (\eta u)}{\partial x} + \frac{\partial (\eta v)}{\partial y} & = 0\\[3pt] \frac{\partial (\eta u)}{\partial t}+ \frac{\partial}{\partial x}\left( \eta u^2 + \frac{1}{2}g \eta^2 \right) + \frac{\partial (\eta u v)}{\partial y} & = 0\\[3pt] \frac{\partial (\eta v)}{\partial t} + \frac{\partial (\eta uv)}{\partial x} + \frac{\partial}{\partial y}\left(\eta v^2 + \frac{1}{2}g \eta ^2\right) & = 0.

\end{align} $$