CMS-Flow:Hydro Eqs

Governing Equation

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

        $\frac{\partial h}{\partial t}+\frac{\partial (h{u}_j)}{\partial x_j}=S$

for $j=1,2$

        $\frac{\partial (h{u}_i)}{\partial t}+\frac{\partial (h{u}_i{u}_j)}{\partial x_j}-{ϵ}_{ij3}{f}_c{u}_{j}h=g\frac{\partial \eta }{\partial x_j}+\frac{1}{{\rho }_0}\frac{\partial p_a}{\partial x_j}+\frac{\partial }{\partial x_j}\left[{\nu }_{t}h\frac{\partial u_i}{\partial x_j}\right]+\frac{{\tau }_i}{\rho }$  

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
$u_j$	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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