Hydraulic Radius of Section Calculator

Hydraulic Radius of Trapezoidal Channel Formula:

\[ R_{H(Trap)} = \frac{(B_{trap} + z_{trap} \times d_{f(trap)}) \times d_{f(trap)}}{B_{trap} + 2 \times d_{f(trap)} \times \sqrt{z_{trap}^2 + 1}} \]

Width of Trap Channel (B_trap):

Side Slope of Trapezoidal Channel (z_trap):

(H:V)

Depth of Flow of Trapezoidal Channel (d_f(trap)):

Hydraulic Radius of Trapezoidal Channel (R_H(Trap)):

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1. What is Hydraulic Radius of Trapezoidal Channel?

The Hydraulic Radius of a Trapezoidal Channel is the ratio of the cross-sectional area of the channel to its wetted perimeter. It is a crucial parameter in open channel flow calculations as it influences flow velocity and discharge characteristics.

2. How Does the Calculator Work?

The calculator uses the hydraulic radius formula for trapezoidal channels:

\[ R_{H(Trap)} = \frac{(B_{trap} + z_{trap} \times d_{f(trap)}) \times d_{f(trap)}}{B_{trap} + 2 \times d_{f(trap)} \times \sqrt{z_{trap}^2 + 1}} \]

Where:

\( R_{H(Trap)} \) — Hydraulic Radius of Trapezoidal Channel (m)
\( B_{trap} \) — Width of Trap Channel (m)
\( z_{trap} \) — Side Slope of Trapezoidal Channel (H:V)
\( d_{f(trap)} \) — Depth of Flow of Trapezoidal Channel (m)

Explanation: The formula calculates the ratio of cross-sectional area to wetted perimeter, accounting for the trapezoidal shape and side slopes of the channel.

3. Importance of Hydraulic Radius Calculation

Details: Accurate hydraulic radius calculation is essential for determining flow characteristics, designing efficient drainage systems, calculating flow velocities, and ensuring proper channel capacity for various hydraulic engineering applications.

4. Using the Calculator

Tips: Enter the bottom width in meters, side slope as a ratio (horizontal to vertical), and flow depth in meters. All values must be positive numbers with appropriate units.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of hydraulic radius in fluid mechanics?
A: Hydraulic radius is a fundamental parameter used in Manning's equation and other flow formulas to determine flow velocity and discharge in open channels.

Q2: How does side slope affect the hydraulic radius?
A: Steeper side slopes generally increase the hydraulic radius for the same flow depth, as they reduce the wetted perimeter relative to the cross-sectional area.

Q3: What are typical values for trapezoidal channel side slopes?
A: Common side slopes range from 1:1 to 2:1 (horizontal to vertical), depending on soil stability and construction requirements.

Q4: Can this calculator be used for partially filled trapezoidal channels?
A: Yes, the formula applies to any flow depth within the trapezoidal channel, as long as the input values are correctly specified.

Q5: How accurate is this calculation for real-world applications?
A: The calculation provides theoretical values based on perfect geometry. In practice, factors like channel roughness, sediment transport, and irregular shapes may require additional considerations.