Chézy friction law ($u=C\sqrt{R_{h}I}$)

The Chézy law relates mean open-channel speed to hydraulic radius and energy slope through a friction coefficient. Equivalently one can use bed shear ${\tau }_b=\rho fu|u|$; for positive uniform flow, balance $\rho gAI={\tau }_b{P}_b$ gives $u=\sqrt{gI/f}\sqrt{A/P_b}$. The absolute value makes drag oppose motion if reverse flows are admitted.