Manning’s Equation Open Channel Flow Calculator

Understanding the Manning's equation open channel flow calculator — concept and principle

Manning's equation is the standard tool for estimating steady, uniform flow in open channels such as ditches, canals, part-full culverts and spillway chutes. Enter the channel shape, depth, slope and roughness, and the calculator returns the discharge, the mean velocity and the Froude number that tells you whether the flow is subcritical or supercritical.

The red wetted edge causes friction; a bigger A ÷ P lets water run faster.

How it is calculated

Area: A = (b + z·y)·y for a trapezoid with bottom width b, depth y and side slope z horizontal to 1 vertical (z = 0 gives a rectangle).
Wetted perimeter: P = b + 2y·√(1 + z²); hydraulic radius R = A/P.
Velocity: V = (1/n)·R^(2/3)·S^(1/2) in SI units (m, s).
Flow: Q = V·A.
Froude number: Fr = V/√(g·D), with hydraulic depth D = A/T and top width T = b + 2z·y.

The principle

In uniform flow the component of the water's weight acting down the slope is exactly balanced by friction on the wetted boundary. Robert Manning fitted measured channel data in 1889 and found velocity grows with R to the two-thirds power and with the square root of slope. The roughness coefficient n condenses boundary texture, vegetation and irregularity into one number: about 0.013–0.015 for finished concrete and 0.022–0.03 for clean earth channels. The hydraulic radius measures flow area per unit of rubbing boundary.

Worked example

Inputs: b = 2 m, y = 0.8 m, z = 1, S = 0.001, n = 0.015.
A = (2 + 0.8) × 0.8 = 2.24 m²; P = 2 + 2 × 0.8 × √2 = 4.2627 m; R = 0.5255 m.
R^(2/3) = 0.6512 and √S = 0.03162, so V = 0.6512 × 0.03162 / 0.015 = 1.373 m/s.
Q = 1.373 × 2.24 = 3.075 m³/s.
T = 2 + 2 × 0.8 = 3.6 m, D = 2.24/3.6 = 0.6222 m, so Fr = 1.373/√(9.81 × 0.6222) = 0.556.

Each point is the calculator re-run with only “Water depth (m)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Water depth (m)	Flow Q (m³/s)
0.2	0.2863260951
0.4	0.9201764759
0.6	1.850173107
0.8	3.0751249
1	4.60511392
1.2	6.454274703
1.6	11.17389074

How to read the result

Fr below 1 means subcritical, tranquil flow, which is typical and stable; Fr above 1 means fast, shallow supercritical flow, and values close to 1 give unstable, wavy surfaces that designers avoid. Velocity is checked against limits: too low and sediment settles, too high and an unlined channel erodes. Q is very sensitive to n, so a 10% change in roughness changes flow by about 10%.

Common mistakes

Entering slope in percent (0.1) instead of m/m (0.001).
Using the US customary form (with 1.49) together with metric inputs, or the SI form with feet.
Choosing an n for new concrete when the channel will be weedy or silted.
Applying uniform-flow results near gates, drops or bends where the flow is not uniform.

Keep in mind: Manning's equation assumes steady, uniform, fully turbulent flow. Real drainage design must also consider freeboard, backwater and local standards, and should be checked by a qualified engineer.

Frequently asked questions

How do I find the depth for a given flow?

Change the depth until the calculated Q matches the target; that depth is the normal depth.

Can I use it for a pipe flowing part full?

Yes, with the circular-segment area and perimeter, but a trapezoid input cannot represent a circular pipe.

What side slope is typical?

Earth channels often use 1.5 to 3 horizontal to 1 vertical depending on soil stability.

Sources: R. Manning, On the flow of water in open channels and pipes, Transactions of the Institution of Civil Engineers of Ireland, 1891 · V. T. Chow, Open-Channel Hydraulics, McGraw-Hill, 1959

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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