DrainageCalculators

Open Channel Flow Calculator for Rectangular, Trapezoidal & Triangular Channels

Calculate discharge, velocity, hydraulic radius, wetted perimeter, or normal depth with Manning's equation for rectangular, trapezoidal, triangular, parabolic, and surveyed open channels.

Try a Common Scenario

Click to pre-fill the calculator with realistic values.

Roadside DitchTrapezoidal Concrete ChannelWide Earth Channel

Open-channel capacity from geometry, roughness, and slope

Manning’s equation gives mean velocity as V = (k/n)R2/3S1/2 and discharge as Q = A·V. This calculator derives the flow area A, wetted perimeter P, and hydraulic radius R = A/P for the selected cross-section, or solves the normal depth for a known discharge.

Input Parameters

Channel Shape

Flow Parameters

ft

Known water depth; discharge will be computed

ft/ft

Longitudinal slope of channel bed

Roughness coefficient for channel material

View Manning's n Reference Table

Channel Geometry

ft

Width of the channel bottom

Ready to Calculate

Enter your channel parameters and click Calculate to see results.

For educational purposes only. Not a substitute for professional engineering judgment.

Interactive model

Manning open-channel prism

Compare rectangular, trapezoidal, and triangular cross-sections while flow area and wetted perimeter drive Manning discharge.

Open full model (opens in a new tab)

About Manning's Equation for Open Channels

Manning's equation is an empirical formula used to calculate the velocity of flow in open channels. It relates the flow velocity to the channel's hydraulic radius, slope, and roughness coefficient.

The Manning Equation

V = (k/n) * R2/3 * S1/2

Where:

  • V = Mean velocity (ft/s or m/s)
  • k = Conversion factor (1.486 for US units, 1.0 for SI)
  • n = Manning's roughness coefficient
  • R = Hydraulic radius = A/P (ft or m)
  • S = Channel slope (ft/ft or m/m)

Supported Channel Shapes and Solve Modes

Enter a known depth to compute discharge, or enter a known discharge to solve normal depth. The same numerical engine drives the Compute Curves table for depth, flow, slope, and roughness sweeps.

  • Rectangular - Common for lined channels, flumes, and box culverts
  • Trapezoidal - Most efficient for earthen channels and roadside ditches
  • Triangular - Used for gutters, V-ditches, and small swales
  • Parabolic - Natural channel shape, grass-lined swales
  • User-defined - Surveyed station/elevation vertices with a separate Manning’s n on each boundary zone

For varying roughness, contiguous equal-n segments are combined into hydraulic subareas. Their conveyances are summed and the equivalent composite n is reported using the Lotter method, matching the FHWA Hydraulic Toolbox workflow. Circular sections are already covered by the Manning’s Pipe Flow calculator.

Key Parameters

  • Hydraulic Radius (R) - Ratio of flow area to wetted perimeter
  • Wetted Perimeter (P) - Length of channel boundary in contact with water
  • Froude Number (Fr) - Ratio of inertial to gravitational forces; indicates flow regime
  • Specific Energy - Sum of flow depth and velocity head
  • Critical Hydraulics - Critical depth, velocity, and slope for the computed flow
  • Boundary Shear - Average γRS and FHWA maximum approximation γyS

Worked open-channel shape examples

These examples use the same calculation engine as the tool above. Compare A/P and R to see why cross-section geometry changes capacity even when depth, slope, and roughness are similar.

Rectangular concrete channel

6 ft bottom width, 2 ft flow depth, n = 0.013, and S = 0.010 ft/ft.

Area, A
12.00 ft²
Wetted perimeter, P
10.00 ft
Hydraulic radius, R
1.200 ft
Velocity, V
12.91 fps
Discharge, Q
154.90 cfs

Trapezoidal earthen ditch

4 ft bottom, 2 ft deep, 2H:1V side slopes, n = 0.025, and S = 0.005.

Area, A
16.00 ft²
Wetted perimeter, P
12.94 ft
Hydraulic radius, R
1.236 ft
Velocity, V
4.84 fps
Discharge, Q
77.45 cfs

Triangular metric V-ditch

0.6 m deep, 3H:1V side slopes, n = 0.030, and S = 0.010 m/m.

Area, A
1.08 m²
Wetted perimeter, P
3.79 m
Hydraulic radius, R
0.285 m
Velocity, V
1.44 mps
Discharge, Q
1.56 cms

Need to find depth instead of discharge? Select Enter flow (solve depth) in the calculator to solve the Manning normal depth for any supported shape, then compare it with the critical depth.

Reference & standards

Manning's n Reference Table

Look up Manning's n values for various channel materials and conditions.

Open Channel Hydraulics Guide

Learn the fundamentals of open channel flow and hydraulic design.

Channel Design Tutorial

Step-by-step guide to designing efficient open channels.

Professional Review: For projects requiring regulatory approval or where public safety is involved, have your calculations reviewed and stamped by a licensed Professional Engineer (PE).

Was this calculator helpful?

Last verified: August 2026