Hydraulic Radius Calculator
Calculate hydraulic radius for channels and pipes using cross-sectional area and wetted perimeter
Calculate Hydraulic Radius
Width of the channel opening
Depth of water in the channel
Hydraulic Radius Results
Formula: R = A / P (Hydraulic Radius = Cross-sectional Area / Wetted Perimeter)
Wetted Perimeter: Length of channel boundary in contact with flowing liquid
Applications: Open channel flow, Manning's equation, flow analysis
Calculation Notes
Example: Rectangular Channel
Given Parameters
Channel width (b): 3.0 m
Flow depth (y): 1.5 m
Channel type: Rectangular open channel
Solution
Cross-sectional area: A = b × y = 3.0 × 1.5 = 4.5 m²
Wetted perimeter: P = b + 2y = 3.0 + 2(1.5) = 6.0 m
Hydraulic radius: R = A/P = 4.5/6.0 = 0.75 m
Channel Shapes
Rectangular
R = by / (b + 2y)
Most common in engineered channels
Trapezoidal
R = (by + y²z) / [b + 2y√(1+z²)]
Common in earth channels and canals
Triangular
R = yz / [2√(1+z²)]
V-shaped channels and ditches
Pipe
Full: R = r/2
Circular conduits and sewers
Applications
Manning's roughness equation
Open channel flow analysis
Pipe flow calculations
Hydraulic design optimization
Irrigation and drainage systems
Design Tips
Larger hydraulic radius = more efficient flow
Circular sections have maximum R for given area
Wide shallow channels have smaller R
Consider maintenance access in design
Understanding Hydraulic Radius
What is Hydraulic Radius?
The hydraulic radius is a geometric property of open channels and closed conduits that represents the efficiency of the cross-section for conveying flow. It is defined as the ratio of the cross-sectional area of flow to the wetted perimeter.
Why is it Important?
- •Essential parameter in Manning's equation for flow velocity
- •Indicates flow efficiency - larger R means better flow
- •Used in channel design and optimization
- •Critical for flood analysis and water management
Key Formulas
R = A / P
Rectangular: R = by/(b+2y)
Full Pipe: R = r/2
Triangle: R = yz/[2√(1+z²)]
- R: Hydraulic radius
- A: Cross-sectional area of flow
- P: Wetted perimeter
- b: Channel width
- y: Flow depth
- z: Side slope ratio
- r: Pipe radius
Note: The hydraulic radius is always less than or equal to the hydraulic diameter, which equals 4R for open channels.