Hydraulic Radius Calculator
Free calculate hydraulic radius for open channel flow from cross-sectional area and wetted perimeter.
Input Parameters
Results
Enter area and perimeter to calculate
What is Hydraulic Radius?
The hydraulic radius (R) is a key parameter in open channel flow calculations. It represents the ratio of the cross-sectional area of flow to the wetted perimeter - the length of the channel boundary in contact with the fluid.
Unlike the geometric radius of a pipe, hydraulic radius is a measure of flow efficiency. A larger hydraulic radius indicates a more efficient channel shape, as it means more flow area relative to the wetted surface (which causes friction).
Hydraulic radius is essential in Manning's equation for calculating flow velocity and discharge in open channels, rivers, and drainage systems.
Hydraulic Radius Formula
Where:
- • R = Hydraulic radius (m)
- • A = Cross-sectional area of flow (m²)
- • P = Wetted perimeter (m)
Note: For a circular pipe flowing full, R = D/4, where D is the diameter.
How to Calculate Hydraulic Radius
-
1
Measure the cross-sectional area
Determine the area (A) of the flow cross-section perpendicular to the flow direction.
-
2
Measure the wetted perimeter
Calculate the length (P) of the channel boundary that is in contact with the flowing fluid.
-
3
Apply the formula
Divide the cross-sectional area by the wetted perimeter: R = A / P
Practical Examples
Example 1: Rectangular Channel
A rectangular channel is 2 m wide and has water flowing 1 m deep. Calculate the hydraulic radius.
Solution:
A = width × depth = 2 m × 1 m = 2 m²
P = width + 2×depth = 2 m + 2×1 m = 4 m
R = A / P = 2 m² / 4 m = 0.5 m
Example 2: Circular Pipe (Half Full)
A circular pipe with diameter 1 m is flowing half full. Calculate the hydraulic radius.
Solution:
A = (π × D²) / 8 = (π × 1²) / 8 = 0.393 m²
P = (π × D) / 2 = (π × 1) / 2 = 1.571 m
R = A / P = 0.393 m² / 1.571 m = 0.25 m
Applications
River Engineering
Used in Manning's equation to calculate flow velocity and discharge in rivers and streams.
Drainage Design
Essential for designing stormwater drainage systems and sewer networks.
Irrigation Channels
Used to optimize channel dimensions for efficient water delivery in agricultural systems.
Hydraulic Research
Fundamental parameter in open channel flow analysis and hydraulic modeling.
Frequently Asked Questions
What is the difference between hydraulic radius and hydraulic diameter?
Hydraulic radius (R) = A/P, while hydraulic diameter (D_h) = 4R = 4A/P. Hydraulic diameter is used in pipe flow, while hydraulic radius is used in open channel flow.
Why is hydraulic radius important?
It's a key parameter in Manning's equation for calculating flow velocity. A larger hydraulic radius means less friction per unit area, resulting in higher flow efficiency.
What is the wetted perimeter?
The wetted perimeter is the total length of the channel boundary that is in contact with the flowing fluid. It excludes the free surface (air-water interface).
How does channel shape affect hydraulic radius?
For the same cross-sectional area, a channel with a smaller wetted perimeter has a larger hydraulic radius and is more efficient. Circular channels flowing full have the maximum hydraulic radius.
Can hydraulic radius be greater than the geometric radius?
For a circular pipe flowing full, R = D/4 = r/2, so hydraulic radius is always less than the geometric radius. However, for other shapes, the relationship varies.