How to use the Manning's Equation Open Channel Flow Calculator
- 1. Pick the channelRectangular, trapezoidal, triangular or a part-full circular pipe.
- 2. Enter size, n and slopeWidth, side slope or diameter, Manning's n and bed slope.
- 3. Get the flowDischarge or normal depth, velocity, R, Froude number and critical depth.
Manning's equation
In SI units: V = (1/n) R^(2/3) S^(1/2) and Q = A × V, where R = A/P is the hydraulic radius, S the bed slope and n Manning's roughness coefficient.
- Rectangular: A = by, P = b + 2y
- Trapezoidal: A = (b + zy)y, P = b + 2y√(1 + z²)
- Triangular: A = zy², P = 2y√(1 + z²)
- Circular: θ = 2cos⁻¹(1 − 2y/D), A = D²(θ − sinθ)/8, P = Dθ/2
Normal depth has no direct formula, so the tool finds it by trial (bisection) until Manning's Q matches the given discharge. Froude number Fr = V/√(gA/T) tells you whether the flow is subcritical (Fr < 1) or supercritical.
Worked example and exam tips
Rectangular channel 2 m wide, depth 1 m, n = 0.015, S = 0.001: A = 2 m², P = 4 m, R = 0.5 m. V = (1/0.015) × 0.63 × 0.0316 = 1.33 m/s and Q = 2.66 m³/s.
- In FPS units the equation uses 1.49/n instead of 1/n.
- A circular pipe carries its maximum discharge at about 0.94 D, not when running full.
- Use the n value given in the question. Textbook ranges are only a guide.
Frequently asked questions
What is Manning's n?
It is a roughness coefficient for the channel surface. Smooth concrete is about 0.012–0.015 and earth channels about 0.020–0.030. Higher n means slower flow.
What is normal depth?
It is the depth at which uniform flow occurs for a given discharge, slope and roughness. The tool finds it by trial because Manning's equation cannot be solved directly for depth.
What is hydraulic radius?
Flow area divided by wetted perimeter (A/P). It measures how efficiently the section carries water.
Is this calculator free?
Yes. You fill a short form once to see your result, and other Uncodemy tools then open without the form. Everything is calculated in your browser and nothing you type is uploaded.