Hydraulic Radius Calculator

Hydraulic Radius Formula:

\[ r_H = \frac{A_{cs}}{P} \]

Hydraulic Radius (r_H):

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1. What is Hydraulic Radius?

Hydraulic Radius is the ratio of the cross-sectional area of a channel or pipe in which a fluid is flowing to the wet perimeter of the conduit. It is a fundamental parameter in hydraulic engineering for analyzing flow characteristics in open channels and pipes.

2. How Does the Calculator Work?

The calculator uses the Hydraulic Radius formula:

\[ r_H = \frac{A_{cs}}{P} \]

Where:

\( r_H \) — Hydraulic Radius (m)
\( A_{cs} \) — Cross Sectional Area of Flow (m²)
\( P \) — Wetted Perimeter (m)

Explanation: The hydraulic radius represents the efficiency of the channel cross-section in conveying flow. A larger hydraulic radius indicates a more efficient channel with less resistance to flow.

3. Importance of Hydraulic Radius Calculation

Details: Hydraulic radius is crucial for determining flow resistance, calculating flow rates using Manning's equation, designing efficient hydraulic structures, and analyzing sediment transport in channels.

4. Using the Calculator

Tips: Enter cross-sectional area in square meters (m²) and wetted perimeter in meters (m). Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between hydraulic radius and hydraulic diameter?
A: Hydraulic radius is the ratio of area to wetted perimeter, while hydraulic diameter is four times the hydraulic radius. Hydraulic diameter is primarily used for pipe flow calculations.

Q2: How does hydraulic radius affect flow efficiency?
A: Larger hydraulic radius values indicate more efficient flow conditions as there's less wetted perimeter per unit area, resulting in reduced frictional resistance.

Q3: Can hydraulic radius be used for partially filled pipes?
A: Yes, hydraulic radius calculations are particularly important for partially filled pipes and open channel flow where the wetted perimeter changes with flow depth.

Q4: What are typical hydraulic radius values for common channels?
A: Hydraulic radius values vary significantly based on channel geometry. For a wide rectangular channel, it approximates the flow depth, while for a full circular pipe, it's D/4.

Q5: How is hydraulic radius used in Manning's equation?
A: In Manning's equation (V = (1/n) * R^2/3 * S^1/2), the hydraulic radius (R) directly influences flow velocity, making it a critical parameter for flow rate calculations.