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Open-channel flow

Intermediate Fluid Mechanics and Hydraulics Reviewed 24 Oct 2026 2 min read

In an open channel, such as a canal, river, drain or culvert running part-full, the water surface is free and gravity drives the flow. Design asks how deep the water will be for a given discharge, slope and channel shape.

For uniform flow, where depth stays constant along the channel, the Manning equation is the everyday tool. It relates velocity to the hydraulic radius (area divided by wetted perimeter), the bed slope and a roughness coefficient n that depends on the lining: smooth concrete is about 0.013 to 0.015, earth channels higher.

area A, perimeter P
Diagram: Indiacon original, not to scale.

Flow can be subcritical (deep and slow, Froude number below 1) or supercritical (shallow and fast, above 1). Where supercritical flow slows abruptly, as below a spillway, a hydraulic jump forms and dissipates energy; stilling basins are designed to hold it in place.

Efficient sections carry the most flow for the least area. For a rectangular channel the best hydraulic section has a width twice the depth.

Key formulas
  • Manning: V = (1/n) R^(2/3) S^(1/2) (SI units)
  • Q = A V; R = A / P
  • Froude number Fr = V / √(g D), D = hydraulic depth
  • Best rectangular section: b = 2y, R = y/2
Solved example

Problem. A concrete rectangular channel 2 m wide, depth 1 m, slope 0.001, n = 0.015. Find Q.

  1. A = 2 m², P = 2 + 2 × 1 = 4 m, R = 0.5 m.
  2. V = (1/0.015) × 0.5^(2/3) × 0.001^(1/2) = 66.67 × 0.630 × 0.0316 = 1.33 m/s.
  3. Q = 2 × 1.33 = 2.66 m³/s.

Answer. About 2.7 m³/s

Quick quiz

1What is hydraulic radius?

Flow area divided by wetted perimeter.

2Fr > 1 means?

Supercritical flow.

3Best rectangular section proportion?

Width twice the depth.

References and further reading

Standard texts, listed in no order of merit. We do not copy text, figures, tables or solved problems from any book; our explanations and examples are original.

  • P. N. Modi, S. M. Seth, Hydraulics and Fluid Mechanics including Hydraulic Machines, Standard Book House, latest edition.
  • V. T. Chow, Open-Channel Hydraulics, McGraw Hill, 1959.
  • K. Subramanya, Flow in Open Channels, McGraw Hill Education (India), latest edition.

Free and official sources

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