CMS-Flow:Hydro Eqs

Governing Equation

The depth-averaged 2-D continuity and momentum equations are given by

        ${\frac {\partial h}{\partial t}}+{\frac {\partial (hU_{j})}{\partial x_{j}}}=S$

e=m c^2\,

(1)

for $j=1,2$

        ${\frac {\partial (hU_{i})}{\partial t}}+{\frac {\partial (hU_{i}U_{j})}{\partial x_{j}}}-\epsilon _{ij3}f_{c}U_{j}h=-gh{\frac {\partial \eta }{\partial x_{j}}}-{\frac {h}{\rho _{0}}}{\frac {\partial p_{a}}{\partial x_{j}}}+{\frac {\partial }{\partial x_{j}}}{\biggl (}\nu _{t}h{\frac {\partial U_{i}}{\partial x_{j}}}{\biggr )}+{\frac {\tau _{i}}{\rho }}$  

for $i=1,2$ and $j=1,2$

Symbol	Description	Units
$t$	Time	sec
$h$	Total water depth $h=\zeta +\eta$	m
$\zeta$	Still water depth	m
$\eta$	Water surface elevation with respect to the still water elevation	m
$U_{j}$	Current velocity in the jth direction	m/sec
$S$	Sum of Precipitation and evaporation per unit area	m/sec
$g$	Gravitational constant	m/sec2
$\rho$	Water density	kg/m3
$p_{a}$	Atmospheric pressure	Pa
$\nu _{t}$	Turbulent eddy viscosity	m2/sec

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