Conditions for critical flow in open channel

When flow in an open channel is critical, the following conditions are satisfied.

1. Froude number equals unity: $Fr=\dfrac{V}{\sqrt{gD_h}}=1$, where $D_h=A/T$ is the hydraulic depth. Velocity equals the celerity of a small gravity wave.
2. Specific energy is minimum for the given discharge: $\dfrac{dE}{dy}=0\Rightarrow\dfrac{Q^2T}{gA^3}=1$.
3. Discharge is maximum for a given specific energy.
4. Specific force (momentum function) is minimum for the given discharge.
5. Velocity head equals half the hydraulic depth: $\dfrac{V^2}{2g}=\dfrac{A}{2T}$. For rectangular channels, $\dfrac{V_c^2}{2g}=\dfrac{y_c}{2}$ and $E_{min}=\tfrac32y_c$.
6. Critical depth for a rectangular channel is $y_c=\sqrt[3]{q^2/g}$ and for other sections is found from $\dfrac{A^3}{T}=\dfrac{Q^2}{g}$ (section factor $Z=Q/\sqrt g$).
7. The slope of the channel equals the critical slope $S_c$ (for uniform flow at critical depth): $S_c=\dfrac{gn^2D_h}{R^{4/3}}$ or $\dfrac{g P_c}{C^2T_c}$.
8. The flow is unstable: the water surface is wavy and sensitive to small changes in energy or roughness, and the depth changes rapidly. The flow is at the boundary between subcritical and supercritical states.
9. Disturbances (small waves) cannot travel upstream.