Hydraulic Radius of Entire Cross-Section Calculator

Hydraulic Radius Formula:

\[ r_H = D \times \left( \frac{V_{avg}}{V_{meas}} \right)^{3/2} \]

Depth of Water at Current Meter Location:

Max Velocity Averaged Over Inlet Cross Section:

m/s

Point Measurement of Maximum Velocity:

m/s

Hydraulic Radius:

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1. What is Hydraulic Radius?

The Hydraulic Radius is the ratio of the cross-sectional area of a channel or pipe in which a fluid flows to the conduit's wet perimeter. It is a fundamental parameter in open channel flow calculations and hydraulic engineering.

2. How Does the Calculator Work?

The calculator uses the hydraulic radius formula:

\[ r_H = D \times \left( \frac{V_{avg}}{V_{meas}} \right)^{3/2} \]

Where:

\( r_H \) — Hydraulic Radius (m)
\( D \) — Depth of Water at Current Meter Location (m)
\( V_{avg} \) — Max Velocity Averaged Over Inlet Cross Section (m/s)
\( V_{meas} \) — Point Measurement of Maximum Velocity (m/s)

Explanation: This formula calculates the hydraulic radius based on depth measurements and velocity ratios observed at specific points in the cross-section.

3. Importance of Hydraulic Radius Calculation

Details: Accurate hydraulic radius calculation is crucial for determining flow characteristics, designing efficient hydraulic systems, and analyzing open channel flow behavior in rivers, canals, and pipelines.

4. Using the Calculator

Tips: Enter depth in meters, velocities in m/s. All values must be positive numbers. Ensure measurements are taken at appropriate locations for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between hydraulic radius and hydraulic diameter?
A: Hydraulic radius is the cross-sectional area divided by wetted perimeter, while hydraulic diameter is four times the hydraulic radius, commonly used in pipe flow calculations.

Q2: Why is hydraulic radius important in open channel flow?
A: Hydraulic radius directly influences flow resistance, velocity distribution, and energy loss in open channels, making it essential for hydraulic design and analysis.

Q3: How does velocity ratio affect hydraulic radius?
A: The ratio of average to maximum velocity reflects the velocity distribution profile, which correlates with the cross-sectional shape and thus affects the hydraulic radius.

Q4: When should this calculation method be used?
A: This method is particularly useful when direct measurement of cross-sectional area and wetted perimeter is challenging, but velocity and depth measurements are available.

Q5: Are there limitations to this equation?
A: This approach assumes specific velocity distribution patterns and may be less accurate for irregular cross-sections or under extreme flow conditions.