Specific Energy in an Open Channel

Specific energy is the total head measured from the channel bed rather than from a fixed datum, which is a deceptively small change that unlocks most of open-channel hydraulics. It is depth plus velocity head: two metres of water moving at 3 m/s carries $2 + 9/19.61 = 2.459$ m of specific energy. Because the datum moves with the bed, specific energy is exactly what stays constant across a smooth transition where friction is negligible, so it is the quantity to track through a contraction, an expansion or a step.

Plot depth against specific energy for a fixed discharge and you get the famous E-y curve, a hyperbola-like shape with a minimum. The unguessable part is that above that minimum there are always two depths carrying the same discharge at the same energy: a deep slow one and a shallow fast one. These are the alternate depths, and which one the channel actually chooses depends entirely on the control, not on the energy. The minimum itself is critical depth, and it is the reason a channel cannot pass a given flow with less energy than $1.5 y_c$ in a rectangular section.

The classic field mistake is confusing alternate depths with sequent depths. Alternate depths share the same specific energy and are what you get across a smooth transition. Sequent depths share the same momentum and are what you get across a hydraulic jump, which loses energy. They are different pairs of numbers for the same flow, and using one where the other belongs is how a stilling basin ends up the wrong length. Also watch the velocity head coefficient: in a compound section with a floodplain, the true kinetic energy is well above $V^2/2g$ computed on the mean velocity, and HEC-RAS carries an alpha of 1.5 or more for exactly that reason.