Calculation
v = (1/n)·R^(2/3)·I^(1/2)
A smoother channel (smaller n), a larger hydraulic radius or a steeper slope each increase flow velocity.
Gauckler-Manning-Strickler-Fließformel v = kSt·R^(2/3)·I^(1/2), kSt = 1/n (Dubbel B 6.2.6 beschreibt den gleichförmigen Gerinneabfluss über die Rohrreibungsform)
Flow velocity in an open channel (Manning equation)
A smoother channel (smaller n), a larger hydraulic radius or a steeper slope each increase flow velocity.
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Result
Select a target and calculate.
Understand the inputs
- Flow velocity v — Cross-section-averaged flow velocity under normal flow.
- Manning roughness coefficient n — Channel-wall roughness value; smooth concrete about 0.012 to 0.014, natural earth channels considerably higher.
- Hydraulic radius R — Ratio of the flow cross-sectional area to the wetted perimeter.
- Bed slope I — Longitudinal bed slope as a ratio (0.001 corresponds to 0.1%).
Example
n=0.013, R=0.5 m and I=0.001 give v=(1/0.013)·0.5^(2/3)·0.001^0.5≈1.53 m/s.
Assumptions and limits
Steady, uniform normal flow in a prismatic channel with constant cross-section, roughness and slope; unsteady flow, non-uniform cross-sections and blockages are excluded.
Understand Flow velocity in an open channel (Manning equation)
This calculator determines the average flow velocity in an open channel, such as a drainage channel, ditch or partially filled pipe, using the widely used Manning equation.
What does this quantity describe?
For steady normal flow in an open channel, v=(1/n)·R^(2/3)·I^(1/2), where n is the channel wall's roughness, R the hydraulic radius (flow area over wetted perimeter), and I the bed slope.
Formula and variables
v = (1/n)·R^(2/3)·I^(1/2)
v = (1/n)·R^(2/3)·I^(1/2)
| Symbol / input | Meaning |
|---|---|
| Flow velocity v | Cross-section-averaged flow velocity under normal flow. |
| Manning roughness coefficient n | Channel-wall roughness value; smooth concrete about 0.012 to 0.014, natural earth channels considerably higher. |
| Hydraulic radius R | Ratio of the flow cross-sectional area to the wetted perimeter. |
| Bed slope I | Longitudinal bed slope as a ratio (0.001 corresponds to 0.1%). |
Choose the inputs correctly
n is the Manning roughness coefficient of the channel wall, R the hydraulic radius of the flow cross-section, I the longitudinal bed slope of the channel.
How to use the calculator
Take n from reference tables for the wall material, compute R from the flow cross-section's geometry, and determine I from the height difference per length of flow path.
Worked example
n=0.013, R=0.5 m and I=0.001 give v=(1/0.013)·0.5^(2/3)·0.001^0.5≈1.53 m/s.
Understand the result and units
Flow velocity is most sensitive to roughness coefficient n, since it enters the equation as a reciprocal directly; a vegetated channel instead of a smooth one can substantially reduce velocity.
n and I are dimensionless, R a length. v is output as a speed.
Typical applications
Preliminary sizing of drainage ditches, gravity sewers and natural channels in water management.
Assumptions, limits and common mistakes
Steady, uniform normal flow in a prismatic channel with constant cross-section, roughness and slope; unsteady flow, non-uniform flow states, blockages and strongly varying cross-sections are excluded.
Common mistake: Do not confuse R with water depth; hydraulic radius additionally accounts for channel width via the wetted perimeter.
Frequently asked questions
What is “Flow velocity in an open channel (Manning equation)” used for?
Preliminary sizing of drainage ditches, gravity sewers and natural channels in water management.
Where do the input values come from?
n is the Manning roughness coefficient of the channel wall, R the hydraulic radius of the flow cross-section, I the longitudinal bed slope of the channel.
What does the result not cover?
Steady, uniform normal flow in a prismatic channel with constant cross-section, roughness and slope; unsteady flow, non-uniform flow states, blockages and strongly varying cross-sections are excluded.