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Hydraulic Radius Calculator

Calculate the efficiency ratio of a channel cross-section.

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Hydraulic Radius

Formula first

Overview

The hydraulic radius is a measure of a channel's flow efficiency, defined as the ratio of the cross-sectional area of flow to the wetted perimeter. It represents the relative amount of fluid in contact with the channel boundary, where a larger radius indicates lower frictional resistance.

Symbols

Variables

R = Hydraulic Radius, A = Cross-sectional Area, P = Wetted Perimeter

Hydraulic Radius
Cross-sectional Area
m²
Wetted Perimeter

Apply it well

When To Use

When to use: This formula is used when calculating flow velocity in open channels like rivers, canals, and sewers using the Manning or Chézy equations. It is applicable in scenarios involving steady, uniform flow where the relationship between channel shape and friction must be quantified.

Why it matters: It is a fundamental parameter in civil engineering and hydrology for designing drainage systems and flood control measures. Efficient channel design aims to maximize the hydraulic radius to reduce energy loss and increase the volume of water transported.

Avoid these traps

Common Mistakes

  • Including water surface in wetted perimeter.
  • Confusing with hydraulic depth.

One free problem

Practice Problem

A rectangular irrigation ditch has a cross-sectional area of 4.5 m² and a wetted perimeter of 6.0 m. What is its hydraulic radius?

Cross-sectional Area4.5 m²
Wetted Perimeter6 m

Solve for:

Hint: Divide the cross-sectional area by the wetted perimeter.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Chow, V. T., Maidment, D. R., & Mays, L. W. (1988). Applied Hydrology. McGraw-Hill.
  2. Wikipedia: Hydraulic radius
  3. Britannica: Hydraulic radius
  4. Bird, R. Byron, Stewart, Warren E., and Lightfoot, Edwin N. Transport Phenomena. 2nd ed. John Wiley & Sons, 2002.
  5. Chow, V. T. Open-Channel Hydraulics. McGraw-Hill, 1959.
  6. Bird, R. B., Stewart, W. E., & Lightfoot, E. N. Transport Phenomena. John Wiley & Sons, 2007.
  7. OCR A-Level Geography — Earth's Life Support Systems