How does knowing the 'specific energy' of water flowing in a channel help you tell if the flow is 'critical,' 'subcritical,' or 'supercritical'?

Knowing the 'specific energy' of water flowing in a channel helps classify the flow as 'critical,' 'subcritical,' or 'supercritical' by providing a direct comparison point based on the flow's energy state relative to its depth and velocity. Specific energy (E) is defined as the total energy per unit weight of water relative to the channel bottom. It is the sum of the flow depth (y) and the velocity head (V^2 / 2g), where 'V' is the average flow velocity and 'g' is the acceleration due to gravity. So, E = y + V^2 / 2g. For a given discharge (Q), there is a unique relationship between specific energy and flow depth. This relationship shows that there is a minimum specific energy possible for that discharge, which occurs at a specific depth called the 'critical depth' (y_c). This state of flow is known as 'critical flow.' 'Critical flow' occurs when the Froude number (Fr) is exactly 1. The Froude number is a dimensionless quantity that compares inertial forces to gravitational forces, and it is calculated as V / sqrt(g*D), where 'D' is the hydraulic depth. At critical ....