1. What is Hydraulic Radius?

The hydraulic radius (R_h) is a measure of channel flow efficiency, defined as the cross-sectional area of flow divided by the wetted perimeter. For rectangular channels, it helps determine flow characteristics and resistance.

2. Formula Explanation

The hydraulic radius for a rectangular channel is calculated as:

Where:

• \( R_h \) — Hydraulic radius (meters)
• \( b \) — Channel width (meters)
• \( h \) — Water depth (meters)

Explanation: The numerator represents the cross-sectional area of flow (width × depth), while the denominator is the wetted perimeter (width + 2 × depth, since water contacts the bottom and two sides).

3. Importance in Hydraulics

Details: Hydraulic radius is crucial for calculating flow velocity (using Manning's equation), determining flow resistance, and designing efficient hydraulic structures like channels and culverts.

4. Using the Calculator

Tips: Enter channel width and water depth in meters. Both values must be positive numbers. The calculator will compute the hydraulic radius in meters.

5. Frequently Asked Questions (FAQ)

Q1: How does hydraulic radius differ from hydraulic diameter?
A: Hydraulic diameter is 4 × hydraulic radius. While diameter is used for pipes, radius is more common for open channel flow.

Q2: What's a typical hydraulic radius range?
A: For rectangular channels, values typically range from 0.1m (small channels) to several meters (large rivers), depending on dimensions.

Q3: Why is hydraulic radius important in Manning's equation?
A: Flow velocity is directly proportional to R_h^2/3, making it a key factor in determining flow characteristics.

Q4: Does hydraulic radius change with flow depth?
A: Yes, it increases with depth but at a decreasing rate, as the wetted perimeter increases faster than the cross-sectional area.

Q5: How is this different for non-rectangular channels?
A: The formula changes based on cross-section shape - circular pipes use diameter, trapezoidal channels include side slopes, etc.