Hydraulic Radius Of Channel Section Given Discharge Calculator

Hydraulic Radius Formula:

\[ R_H = \frac{\left(\frac{Q}{C \times A_{cs}}\right)^2}{S} \]

Discharge of Channel (Q):

m³/s

Chezy's Constant (C):

Cross-Sectional Area of Channel (A_cs):

m²

Bed Slope (S):

Hydraulic Radius of Channel (R_H):

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1. What is Hydraulic Radius?

The Hydraulic Radius of Channel 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 open channel flow calculations.

2. How Does the Calculator Work?

The calculator uses the hydraulic radius formula:

\[ R_H = \frac{\left(\frac{Q}{C \times A_{cs}}\right)^2}{S} \]

Where:

\( R_H \) — Hydraulic Radius of Channel (m)
\( Q \) — Discharge of Channel (m³/s)
\( C \) — Chezy's Constant (dimensionless)
\( A_{cs} \) — Cross-Sectional Area of Channel (m²)
\( S \) — Bed Slope (dimensionless)

Explanation: The formula calculates the hydraulic radius based on discharge, Chezy's constant, cross-sectional area, and bed slope of the channel.

3. Importance of Hydraulic Radius Calculation

Details: Hydraulic radius is crucial for determining flow characteristics in open channels, including velocity distribution, flow resistance, and energy loss calculations. It's essential for hydraulic engineering and water resource management.

4. Using the Calculator

Tips: Enter discharge in m³/s, Chezy's constant (dimensionless), cross-sectional area in m², and bed slope (dimensionless). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for hydraulic radius values?
A: Hydraulic radius values vary widely depending on channel geometry, but typically range from 0.1m to 5m for most natural and artificial channels.

Q2: How does Chezy's constant affect the hydraulic radius?
A: Chezy's constant represents flow resistance. Higher values indicate smoother channels and result in different hydraulic radius calculations for the same discharge.

Q3: What is bed slope and how is it measured?
A: Bed slope is the inclination of the channel bottom, usually expressed as a dimensionless ratio (vertical drop/horizontal distance) or in percentage.

Q4: Can this formula be used for pressurized pipe flow?
A: While the concept of hydraulic radius applies to both open channel and pipe flow, this specific formula is designed for open channel flow calculations.

Q5: What are the limitations of this calculation?
A: The formula assumes steady, uniform flow and may not be accurate for rapidly varying flow conditions or complex channel geometries.