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	Dimensions
$t$	Time	T
$h$	Total water depth $h=\zeta +\eta$	L
$\zeta$	Still water depth	L
$\eta$	Water surface elevation with respect to the still water elevation	L
$u_j$	Current velocity in the jth direction	L / T
$S$	Sum of Precipitation and evaporation per unit area	L / T
$g$	Gravitational constant	L / T2
$\rho$	Water density	M / L3
$p_a$	Atmospheric pressure	M / (L T 2 )

---

Documentation Portal