Hydraulic Radius Given Average Velocity In Channel Calculator

Hydraulic Radius Formula:

\[ R_H = \left( \frac{V_{avg}}{\sqrt{8 \cdot [g] \cdot \frac{S}{f}}} \right)^2 \]

Hydraulic Radius of Channel (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's a fundamental parameter in open channel flow calculations and pipe flow analysis.

2. How Does the Calculator Work?

The calculator uses the hydraulic radius formula:

\[ R_H = \left( \frac{V_{avg}}{\sqrt{8 \cdot [g] \cdot \frac{S}{f}}} \right)^2 \]

Where:

\( R_H \) — Hydraulic Radius of Channel (m)
\( V_{avg} \) — Average Velocity of Flow (m/s)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( S \) — Bed Slope
\( f \) — Darcy Friction Factor

Explanation: This formula calculates the hydraulic radius based on average flow velocity, bed slope, and Darcy friction factor, incorporating gravitational acceleration.

3. Importance of Hydraulic Radius Calculation

Details: Hydraulic radius is crucial for determining flow characteristics, calculating flow rates, designing hydraulic structures, and analyzing fluid behavior in open channels and pipes.

4. Using the Calculator

Tips: Enter average velocity in m/s, bed slope (dimensionless), and Darcy friction factor (dimensionless). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between hydraulic radius and hydraulic diameter?
A: Hydraulic radius is area divided by wetted perimeter, while hydraulic diameter is 4 times the hydraulic radius. Hydraulic diameter is more commonly used in pipe flow.

Q2: How does bed slope affect hydraulic radius?
A: Bed slope influences the flow velocity and shear stress, which in turn affects the hydraulic radius calculation through the flow dynamics.

Q3: What is the typical range for Darcy friction factor?
A: For smooth pipes, f ≈ 0.008-0.01; for rough pipes, f can be 0.03-0.06 or higher depending on surface roughness.

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

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