Rectangular Channel Normal Depth (Manning)
The Manning normal (uniform-flow) depth of a rectangular channel.
Example
You enter
- Channel width b (ft) 10
- Discharge Q (cfs) 200
- Manning roughness n 0.015
- Channel slope S (ft/ft) 0.001
You get
- Normal depth yn 3.816 ft
- V (fps) 5.241
- Froude number Fr 0.473
- Yc (ft) 2.316
Checked against published worked examples from: FHWA.
Details, formula, and sources
ScopeSolved by bisection of Q = (1.486/n) A R^(2/3) sqrt(S) with A = b y, R = A/(b + 2y). A 10 ft channel carrying 200 cfs on a 0.1% slope at n 0.015 runs 3.82 ft deep at 5.24 ft/s, Fr 0.47; because that normal depth exceeds the 2.32 ft critical depth, the reach is a mild slope (subcritical). Prismatic rectangular section, uniform flow; trapezoidal sections and backwater profiles are separate. A design aid; the engineer of record governs.
Formula or tableQ = (1.486/n) A R^(2/3) S^(1/2), rectangular A = b y, R = A/(b + 2y); solve for the normal depth y by bisection; slope class from yc = (q^2/g)^(1/3).
Source and editionThe Manning normal (uniform-flow) depth of a rectangular channel and its slope class against the critical depth, as compiled in Chow's Open-Channel Hydraulics, by name.
Free accessManning's equation and the rectangular critical-depth relation are public results in the standard open-channel-hydraulics references.
What governsEstimate. AHJ and licensed professional govern.
API field namesb_ft, q_cfs, n, s_slope, yn_ft, v_fps, fr, yc_ft
- Manning normal depth Q = (1.486/n) A R^(2/3) sqrt(S), rectangular A = b y, R = A/(b + 2y), solved for yChow open-channel hydraulics
- Slope class yc = (q^2/g)^(1/3); yn > yc mild (subcritical), yn < yc steep (supercritical)Chow open-channel hydraulics
- Scope prismatic rectangular channel, uniform flow; trapezoidal sections and backwater profiles are separatescope of this tile