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: 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.
Formula and source
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.
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