Open-Channel Froude Number, Regime, and Critical Depth
Whether an open channel runs tranquil or rapid, which manning-slope and weir-flow never tell you.
Example
You enter
- Channel width b (ft) 4
- Discharge Q (cfs) 50
- Flow depth y (ft) 2
You get
- Mean velocity 6.25 ft/s
- Froude number Fr 0.78
- Critical depth yc 1.69
Details, formula, and sources
Fr = V/sqrt(g D) classifies the regime (Fr < 1 subcritical / downstream-controlled, Fr > 1 supercritical / upstream-controlled), and the rectangular critical depth yc = (q^2/g)^(1/3) confirms it. A 4 ft channel at 50 cfs and 2 ft deep runs Fr 0.78 subcritical (yc 1.69 < 2 ft); drop the depth to 1 ft and Fr 2.2 supercritical - the same channel, the setup for a hydraulic jump. Rectangular section; normal depth and the jump are separate. A design aid; the engineer of record governs.
V = Q/(b y); Fr = V/sqrt(g y) (g = 32.2, D = y rectangular); regime by Fr vs 1; q = Q/b; yc = (q^2/g)^(1/3).
The open-channel Froude-number regime classification Fr = V/sqrt(g D) and the rectangular critical depth yc = (q^2/g)^(1/3), as compiled in Chow's Open-Channel Hydraulics, by name.
The Froude-number classification and the rectangular critical-depth relation are public results in the standard open-channel-hydraulics references.
Estimate. AHJ and licensed professional govern.
Field names used by the API: b_ft, q_cfs, y_ft, v_fps, fr, yc_ft
- Froude number Fr = V/sqrt(g y) for a rectangular section; Fr < 1 subcritical, > 1 supercriticalChow open-channel hydraulics
- Critical depth yc = (q^2/g)^(1/3) with q = Q/b; flow is subcritical when y > ycChow open-channel hydraulics
- Scope prismatic rectangular channel; normal depth (Manning) and the hydraulic jump are separatescope of this tile