Specific Energy & Critical Depth — Reference
Specific energy is energy per unit weight relative to the channel bottom. It controls open-channel transitions, controls, and the sub/supercritical state of the flow.
Core Equations
Flow State by Depth
| Condition | State | Character |
|---|---|---|
| y > yc (Fr < 1) | Subcritical | Tranquil, deep/slow; controls act from downstream |
| y = yc (Fr = 1) | Critical | Minimum E; unstable, used as a flow-measurement control |
| y < yc (Fr > 1) | Supercritical | Rapid, shallow/fast; controls act from upstream |
Alternate Depths
For any E > Emin, two alternate depths pass the same Q at the same specific energy — one subcritical, one supercritical. They are equal in specific energy. Do not confuse them with the conjugate (sequent) depths of a hydraulic jump, which are equal in specific force (momentum) and dissipate energy between them.
Source: Chow, V.T. (1959), Open-Channel Hydraulics, Ch. 3. Henderson, F.M., Open Channel Flow.
Related cheat sheets and tools
Compare critical depth against the normal depth from Manning's using the channel geometry card; if normal < critical the channel is steep (supercritical) and a hydraulic jump may form on a slope break. For full water-surface-profile and routing analysis, see HydroComplete.