All tools
Open Manning's calculator →

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

Specific energy:   E = y + V²/(2g) = y + Q²/(2gA²)
Critical condition (general):   Q²T / (gA³) = 1  ⇔  Fr = 1
Rectangular:   yc = (q²/g)1/3,   q = Q/b,   Emin = 1.5·yc,   Vc = √(g·yc)

Flow State by Depth

ConditionStateCharacter
y > yc  (Fr < 1)SubcriticalTranquil, deep/slow; controls act from downstream
y = yc  (Fr = 1)CriticalMinimum E; unstable, used as a flow-measurement control
y < yc  (Fr > 1)SupercriticalRapid, 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.

Why it matters. Critical depth is a control section — at a free overfall, a broad-crested weir, or the crest of a bump, flow passes through yc and the stage-discharge relation is fixed. Knowing whether your channel runs sub- or supercritical determines where backwater/drawdown profiles start and whether a hydraulic jump can form.

Source: Chow, V.T. (1959), Open-Channel Hydraulics, Ch. 3. Henderson, F.M., Open Channel Flow.

Computing normal depth too? Open the Manning's calculator → · Will a jump form? Hydraulic jump reference.

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.

Get future cheat sheets in your inbox

One reference card or worked-example case study per month, delivered the moment it's published. Free.

Free. Unsubscribe anytime. Privacy.