Side Slope of Section given Wetted Area of Trapezoidal Calculator

Formula Used:

\[ Side Slope of Trapezoidal Channel = \frac{\left(\frac{Wetted Surface Area of Trapezoidal Channel}{Depth of Flow of Trapezoidal Channel} - Width of Trap Channel\right)}{Depth of Flow of Trapezoidal Channel} \] \[ z_{trap} = \frac{\left(\frac{S_{Trap}}{d_{f(trap)}} - B_{trap}\right)}{d_{f(trap)}} \]

Wetted Surface Area of Trapezoidal Channel:

m²

Depth of Flow of Trapezoidal Channel:

Width of Trap Channel:

Side Slope of Trapezoidal Channel:

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1. What is Side Slope of Trapezoidal Channel?

Side slope of Trapezoidal Channel is defined as the horizontal to vertical ratio of the channel sides. It represents the steepness or gradient of the channel walls in a trapezoidal cross-section.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ z_{trap} = \frac{\left(\frac{S_{Trap}}{d_{f(trap)}} - B_{trap}\right)}{d_{f(trap)}} \]

Where:

\( z_{trap} \) — Side slope of Trapezoidal Channel (horizontal:vertical)
\( S_{Trap} \) — Wetted Surface Area of Trapezoidal Channel (m²)
\( d_{f(trap)} \) — Depth of Flow of Trapezoidal Channel (m)
\( B_{trap} \) — Width of Trap Channel (m)

Explanation: The formula calculates the side slope by first determining the top width from the wetted area and depth, then subtracting the bottom width, and finally dividing by the depth to get the horizontal component per unit vertical.

3. Importance of Side Slope Calculation

Details: Calculating side slope is crucial for hydraulic engineering design, determining channel stability, calculating flow characteristics, and ensuring proper water conveyance in trapezoidal channels.

4. Using the Calculator

Tips: Enter wetted surface area in square meters, depth of flow in meters, and width of trap channel in meters. All values must be positive numbers with depth and area greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for side slopes in trapezoidal channels?
A: Side slopes typically range from 1:1 to 3:1 (horizontal:vertical), depending on soil stability and design requirements.

Q2: How does side slope affect channel capacity?
A: Steeper side slopes increase channel capacity but may reduce stability, while flatter slopes provide better stability but require more land area.

Q3: Can this calculator be used for partially filled channels?
A: Yes, the formula works for any flow depth as long as the wetted area corresponds to the actual flow conditions.

Q4: What units should be used for input values?
A: All input values should be in consistent metric units: square meters for area and meters for linear dimensions.

Q5: How accurate is this calculation method?
A: The calculation is mathematically exact for ideal trapezoidal channels with uniform side slopes and consistent cross-sections.