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Manning's equation calculator

Open-channel flow from depth, or normal depth from flow — rectangular, trapezoidal and partly full pipes.

Free, right in your browser. Every result shows its work.

ft
ft

Concrete ≈ 0.013 · earth ≈ 0.025

ft/ft

Result

Discharge, Q
91.7ft³/s
Velocity, V
4.585ft/s
Flow area, A
20ft²
Wetted perimeter, P
14ft
Hydraulic radius, R_h
1.429ft
Top width, T
10ft
Froude number
0.572 — subcritical
  1. 1.A = b·y = 10 × 2 = 20; P = b + 2y = 14
  2. 2.R_h = A/P = 1.429 ft
  3. 3.V = (1.486/n) R_h^(2/3) S^(1/2) = (1.486/0.013) × 1.429^(2/3) × 0.001^(1/2) = 4.585 ft/s
  4. 4.Q = VA = 4.585 × 20 = 91.7 ft³/s
  5. 5.Fr = V / √(gA/T) = 0.572

How it's tested on the exam

Shows up on: PE Civil (Water Resources & Environmental)

  • 1.486 in US units, 1.0 in SI. The constant carries the units; forgetting it in US units under-predicts flow by a third.
  • Hydraulic radius is A/P, the wetted perimeter only — never include the free surface.
  • Normal depth needs trial and error. Q depends on depth through both A and R_h, so solving for depth is iterative (this calculator solves it exactly).
  • A circular pipe carries its maximum flow slightly below full (about 0.94 D), not when full.
  • Froude number tells you the regime: below 1 is subcritical, above 1 supercritical — it decides where a hydraulic jump can form.

Worked example

A 10-ft-wide rectangular concrete channel (n = 0.013) on a 0.001 slope flows 2 ft deep. Find the discharge.

  1. 1.A = 10 × 2 = 20 ft²; P = 10 + 2(2) = 14 ft; R_h = 20/14 = 1.429 ft
  2. 2.V = (1.486/0.013) × 1.429^(2/3) × 0.001^(1/2) = 4.59 ft/s
  3. 3.Q = VA = 4.59 × 20 = 91.7 ft³/s; Fr = 0.57 (subcritical)

Q ≈ 91.7 cfs, subcritical.

Where it is in the Handbook

  • Open-Channel Flow — Manning's Equation — PE Civil Reference Handbook
  • Open-Channel Flow — Flow in Channels (Geometric Elements of Channel Sections) — PE Civil Reference Handbook

Section names as printed in the current NCEES PE Reference Handbooks (Mechanical 2.1, Civil 2.2); numbering can shift between versions. On exam day you'll use your own approved calculator — here's which models NCEES allows.