Hydraulic Radius of Trapezoidal Channel Section Calculator

Hydraulic Radius Formula:

\[ R_H = \frac{d_f \times (B + d_f \times (\theta + \cot(\theta)))}{B + 2 \times d_f \times (\theta + \cot(\theta))} \]

Hydraulic Radius (R_H):

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1. What is Hydraulic Radius?

The hydraulic radius is a fundamental parameter in open channel flow calculations. It represents the ratio of the cross-sectional area of flow to the wetted perimeter, providing a measure of the efficiency of a channel section in conveying water.

2. How Does the Calculator Work?

The calculator uses the hydraulic radius formula for trapezoidal channels:

\[ R_H = \frac{d_f \times (B + d_f \times (\theta + \cot(\theta)))}{B + 2 \times d_f \times (\theta + \cot(\theta))} \]

Where:

\( R_H \) — Hydraulic radius (m)
\( d_f \) — Depth of flow (m)
\( B \) — Bottom width of trapezoidal channel (m)
\( \theta \) — Side slope angle (radians)
\( \cot(\theta) \) — Cotangent of the side slope angle

Explanation: This formula accounts for the geometry of trapezoidal channels, where the side slopes are defined by the angle θ and its cotangent.

3. Importance of Hydraulic Radius

Details: Hydraulic radius is crucial for calculating flow velocity, discharge, and energy losses in open channels. It's used in various hydraulic equations including Manning's equation for uniform flow calculations.

4. Using the Calculator

Tips: Enter depth of flow in meters, channel width in meters, and side slope angle in radians. 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 used in open channel flow calculations, while hydraulic diameter is typically used in closed conduit flow. Hydraulic diameter is four times the hydraulic radius.

Q2: Why is hydraulic radius important in Manning's equation?
A: In Manning's equation, flow velocity is proportional to the hydraulic radius raised to the 2/3 power, making it a critical parameter for flow rate calculations.

Q3: How does side slope angle affect hydraulic radius?
A: Steeper side slopes (larger θ values) generally increase the hydraulic radius for a given flow depth, making the channel more efficient in conveying water.

Q4: Can this calculator be used for other channel shapes?
A: No, this specific formula is designed for trapezoidal channels. Other channel shapes (rectangular, triangular, circular) have different hydraulic radius formulas.

Q5: What are typical values for hydraulic radius in engineering applications?
A: Hydraulic radius values vary widely depending on channel size and shape, but typically range from 0.1 m for small channels to several meters for large rivers and canals.