Open Channel Hydraulics: Manning, Critical Flow, and Jumps
Core ideas
Open channel flow is driven by gravity and bounded by a free surface. Manning's equation in US customary units is Q = (1.486/n) A R^(2/3) S^(1/2), where R = A/P is the hydraulic radius, not the depth. Normal depth is the depth satisfying Manning for a given discharge and bed slope; it exists only for a fixed slope and roughness.
Critical flow occurs at Froude number Fr = V/√(gD) = 1, where D is hydraulic depth (A/T). Critical depth gives minimum specific energy for a given discharge. In a rectangular channel, yc = (q²/g)^(1/3), with q = Q/b. Specific energy is E = y + V²/2g. Flow is subcritical when Fr < 1 and supercritical when Fr > 1; disturbances travel upstream only in subcritical flow.
A hydraulic jump converts supercritical to subcritical flow, with energy loss. Sequent (conjugate) depths are not critical depth. Gradually varied flow profiles (M, S, C curves) are classified by bed slope and zone relative to normal and critical depth.
Traps
Substituting depth for hydraulic radius in narrow channels (R ≈ y only when the channel is very wide); omitting the 1.486 factor; using bed slope where the energy slope governs varied flow; and confusing sequent depth with critical depth.
Worked example
Rectangular channel, b = 10 ft, y = 3 ft, n = 0.015, S = 0.001. A = 30 ft², P = 16 ft, R = 1.875 ft. R^(2/3) ≈ 1.52. Q = (1.486/0.015)(30)(1.52)(0.0316) ≈ 99.1 × 30 × 1.52 × 0.0316 ≈ 143 cfs.