RHCES Manning's Open Channel Flow Calculator

Inputs

Units

Solve For

Section

Manning's n

n value

Discharge Qm³/s

Slope S (m/m or ft/ft)e.g. 0.001 = 0.1%

Notes & assumptions

Manning's: V = (1/n)·R^(2/3)·S^(1/2). Imperial uses 1.486/n.
R = A/P (hydraulic radius). Normal depth solver uses bisection.
Circular: input diameter D and depth y (must be ≤ D).
Critical depth, Froude number and flow regime are reported.

Results

Discharge Q—

Velocity V—

Depth y—

Flow Area A—

Wetted Perimeter P—

Hydraulic Radius R—

Top Width T—

Slope S—

Froude Fr—

Flow Regimesubcritical

About this calculator

This tool sizes open-channel flow using Manning's equation for rectangular, trapezoidal, triangular and circular (partially full) sections. Given any two of discharge, normal depth and slope, it solves for the third, then reports velocity, hydraulic radius, top width and Froude number so you can judge whether flow is subcritical or supercritical. It's built for hydraulic and civil engineers, and students, sizing drains, canals and culverts at a preliminary level.

Method & Formulas

Manning's equation: V = (k/n)·R^2/3·S^1/2, where V is mean velocity, n is Manning's roughness coefficient, R = A/P is the hydraulic radius (flow area A over wetted perimeter P), S is the channel slope, and k is a unit constant (k = 1 in SI units, k = 1.486 in US customary units). Discharge Q = V·A.

Trapezoidal section (bottom width b, side slope m horizontal : 1 vertical, depth y): A = (b + m·y)·y, P = b + 2y√(1+m²), top width T = b + 2my. Rectangular and triangular sections are the m→0 and b→0 special cases.

Circular section, partially full (diameter D, depth y): wetted central angle θ from cos(θ/2) = 1 − 2y/D, giving A = (D²/8)(θ − sinθ) and P = Dθ/2.

Normal-depth solving: when solving for depth, the tool searches (bisection) for the y that makes Manning's-equation discharge match your target Q.

Flow regime: Froude number Fr = V/√(g·D_h), with hydraulic depth D_h = A/T. Fr < 1 subcritical, Fr > 1 supercritical.

Worked Example

Trapezoidal channel, b = 1.5 m, side slope m = 1.5 (H:V), normal depth y = 0.8 m, n = 0.013 (finished concrete), S = 0.001 (0.1%):

A = (1.5 + 1.5×0.8)×0.8 = 2.16 m².

P = 1.5 + 2(0.8)√(1+1.5²) = 1.5 + 1.6×1.803 ≈ 4.38 m → R = A/P ≈ 0.493 m.

V = (1/0.013)×0.493^2/3×√0.001 = 76.9 × 0.624 × 0.0316 ≈ 1.52 m/s.

Q = V×A ≈ 1.52 × 2.16 ≈ 3.28 m³/s.

Assumptions & Limitations

Uniform (normal) flow in a prismatic channel is assumed; the equation does not model gradually- or rapidly-varied flow profiles or backwater curves.

Manning's n is a single lumped roughness value — pick it carefully, since discharge scales linearly with 1/n; run a sensitivity check across a plausible n range.

Steady, single-phase, gravity flow is assumed. The circular-section model is for partially full pipe flow, not pressurized (surcharged) flow.

Freeboard, sediment transport, and structure losses (bends, transitions, culvert entrance/exit losses) are not evaluated — add them separately.

Verify results against the governing code and a licensed engineer's judgment before finalizing channel or culvert sizing.

FAQ

Which unit constant should I use — 1 or 1.486?

Use SI units (m, m³/s) and the tool applies k = 1 automatically; switch the Units toggle to Imperial (ft, cfs) and it applies k = 1.486 for you.

How does the tool solve for normal depth?

It runs a numerical bisection search between a very small depth and the channel's practical maximum (the pipe diameter for circular sections), converging on the depth where Manning's-equation discharge equals your target Q.

What does the Froude number tell me?

It indicates flow regime — Fr well below 1 is subcritical (calm, controlled from downstream), Fr well above 1 is supercritical (fast, controlled from upstream); values near 1 indicate flow close to critical depth, which can be unstable.

InputsReset