Table of Contents
What Is Hydraulic Radius?
The hydraulic radius (R) is the ratio of the cross-sectional area of flow to the wetted perimeter of the channel. It is a measure of the channel's flow efficiency and is a key parameter in open channel flow equations such as Manning's equation and the Chezy formula.
A larger hydraulic radius indicates a more efficient cross-section for conveying water. A circular pipe flowing full has the maximum hydraulic radius for a given area, which is why circular pipes are commonly used in sewer and drainage systems. For open channels, a semicircular shape is the most efficient, but trapezoidal and rectangular shapes are more practical to construct.
Formulas by Shape
Common Channel Shapes
| Shape | Area (A) | Wetted Perimeter (P) |
|---|---|---|
| Rectangular | b × y | b + 2y |
| Trapezoidal | (b + zy)y | b + 2y√(1+z²) |
| Triangular | zy² | 2y√(1+z²) |
| Circular (full) | πD²/4 | πD |
Manning's Equation
The hydraulic radius is most commonly used in Manning's equation for open channel flow velocity:
Where V is velocity (m/s), n is Manning's roughness coefficient, R is hydraulic radius (m), and S is the channel slope (m/m). The flow rate Q is then V times the cross-sectional area A.
Frequently Asked Questions
What is the most efficient channel cross-section?
The most hydraulically efficient cross-section is a semicircle, as it provides the maximum hydraulic radius for a given area. Among practical shapes, a half-hexagon trapezoidal section (with 60-degree side slopes) is the most efficient trapezoidal shape, and a section where depth equals half the width is optimal for rectangular channels.
What is the difference between hydraulic radius and hydraulic depth?
Hydraulic radius is the flow area divided by the wetted perimeter (R = A/P), while hydraulic depth is the flow area divided by the top width (D = A/T). Hydraulic depth is used to calculate the Froude number, while hydraulic radius is used in friction and flow resistance calculations.