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Manning's Equation Calculator

Calculate river flow velocity from channel characteristics.

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Velocity

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Overview

Manning's Equation is an empirical relationship used to estimate the mean velocity of water flowing in open channels or conduits. It correlates flow speed with the channel's physical dimensions, its longitudinal slope, and the frictional resistance caused by the lining material.

Symbols

Variables

v = Velocity, R = Hydraulic Radius, S = Channel Slope, n = Manning's n

Velocity
m/s
Hydraulic Radius
Channel Slope
Variable
Manning's n
Variable

Apply it well

When To Use

When to use: This formula is applied to steady, uniform open-channel flows where the water surface is parallel to the channel bed. It is commonly used by hydrologists and engineers to model rivers, canals, and culverts where the flow is driven by gravity.

Why it matters: It is fundamental for flood risk management and the design of urban drainage systems. By predicting flow velocity, planners can determine if a channel can handle specific discharge volumes or if the speed will cause significant bank erosion.

Avoid these traps

Common Mistakes

  • Using wrong Manning's n value.
  • Confusing hydraulic radius with depth.

One free problem

Practice Problem

A smooth concrete irrigation canal is constructed with a hydraulic radius of 1 meter and a longitudinal slope of 0.01 (1%). If the Manning's roughness coefficient for smooth concrete is 0.02, what is the average flow velocity in meters per second?

Hydraulic Radius1 m
Channel Slope0.01
Manning's n0.02

Solve for:

Hint: Plug the values into the formula v = (1/n) ×R^(2/3) ×S^(0.5) and remember that 1 raised to any power is 1.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Wikipedia: Manning formula
  2. Bird, R. Byron; Stewart, Warren E.; Lightfoot, Edwin N. Transport Phenomena
  3. Chow, V. T. (1959). Open-Channel Hydraulics. McGraw-Hill.
  4. Munson, B. R., Young, D. F., Okiishi, T. H., & Huebsch, W. W. (2013). Fundamentals of Fluid Mechanics (7th ed.). John Wiley & Sons.
  5. Chow, Ven Te. Open-Channel Hydraulics. McGraw-Hill, 1959.
  6. Bird, R. Byron, Stewart, Warren E., Lightfoot, Edwin N. Transport Phenomena. 2nd ed. John Wiley & Sons, 2002.
  7. Wikipedia: Manning formula (article title)
  8. Edexcel A-Level Geography — Water Insecurity and Hydrology