Shallow-water specific energy
= Shallow-water specific energy
{title2=$E=h+u^2/(2g)$}
For a steady rectangular-channel flow with discharge $Q=bhu$, the <shallow-water specific energy> relative to the bed is $E=h+Q^2/(2gb^2h^2)$. At fixed discharge and width, $E_h=1-F^2$, where the <Froude number> satisfies $F^2=Q^2/(gb^2h^3)$. The minimum is $E_c=3h_c/2$, with $h_c=(Q^2/(gb^2))^{1/3}$. Without dissipation, $E+H$ is the conserved <Bernoulli equation> head for bed elevation $H$.