Width Of Sections Given Hydraulic Radius Calculator

Formula Used:

\[ B_{trap} = \frac{2 \times R_H(Trap) \times d_f(trap) \times \sqrt{z_{trap}^2 + 1} - z_{trap} \times d_f(trap)^2}{d_f(trap) - R_H(Trap)} \]

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

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

Side Slope of Trapezoidal Channel (z_trap):

Width of Trap Channel (B_trap):

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1. What is the Width of Sections given Hydraulic Radius Formula?

The formula calculates the width of a trapezoidal channel section based on hydraulic radius, flow depth, and side slope parameters. It's essential for hydraulic engineering and open channel flow calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ B_{trap} = \frac{2 \times R_H(Trap) \times d_f(trap) \times \sqrt{z_{trap}^2 + 1} - z_{trap} \times d_f(trap)^2}{d_f(trap) - R_H(Trap)} \]

Where:

\( B_{trap} \) — Width of Trap Channel (m)
\( R_H(Trap) \) — Hydraulic Radius of Trapezoidal Channel (m)
\( d_f(trap) \) — Depth of Flow of Trapezoidal Channel (m)
\( z_{trap} \) — Side Slope of Trapezoidal Channel (horizontal to vertical ratio)

Explanation: The formula derives the channel width from hydraulic properties and geometric characteristics of the trapezoidal cross-section.

3. Importance of Width Calculation

Details: Accurate width calculation is crucial for designing efficient hydraulic channels, determining flow capacity, and ensuring structural stability in water conveyance systems.

4. Using the Calculator

Tips: Enter hydraulic radius and depth of flow in meters, and side slope as a dimensionless ratio. All values must be positive, and depth must be greater than hydraulic radius to avoid division by zero.

5. Frequently Asked Questions (FAQ)

Q1: What is hydraulic radius?
A: Hydraulic radius is the ratio of cross-sectional area of flow to the wetted perimeter, representing the efficiency of the channel section.

Q2: How is side slope defined?
A: Side slope is defined as the horizontal to vertical ratio (e.g., 2:1 slope means 2 units horizontal for 1 unit vertical).

Q3: When is this formula applicable?
A: This formula is specifically designed for trapezoidal channel sections with uniform flow conditions.

Q4: What are typical values for side slope?
A: Common side slopes range from 1:1 to 3:1 (horizontal:vertical) depending on soil stability and construction requirements.

Q5: What if I get a division by zero error?
A: This occurs when depth equals hydraulic radius, which is not physically possible in trapezoidal channels. Check your input values.