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A rectangular concrete channel 6 m wide, on a \( 2.5 \% \) slope, is discharging \( 11.3 \mathrm{~m}^{3} / \mathrm{s} \) into a stilling basin. The basin, also 6 m wide, has a water depth of 2.4 m determined from the downstream channel condition. \( \checkmark \) Design the stilling basin (determine width and type of structure).

Ask by Schneider Burton. in Ethiopia
Jan 10,2025

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The stilling basin should be designed with a width of at least 6 meters and should include a structure suitable for safely handling the 11.3 m³/s discharge at a water depth of 2.4 meters.

Solución

To design the stilling basin, we need to determine the width and type of structure required to safely discharge the water from the rectangular concrete channel into the stilling basin. Given: - Width of the rectangular concrete channel = 6 m - Slope of the channel = 2.5% - Discharge from the channel = 11.3 m³/s - Water depth in the stilling basin = 2.4 m To design the stilling basin, we need to consider the following factors: 1. The width of the stilling basin should be sufficient to accommodate the discharge from the channel without overflowing. 2. The type of structure required in the stilling basin depends on the discharge and the water depth. Let's calculate the width of the stilling basin required to accommodate the discharge from the channel. Numbers by following steps: - step0: Solution: \(11.3\) The discharge from the channel is 11.3 m³/s. Next, we need to determine the width of the stilling basin required to accommodate this discharge. The width of the stilling basin should be at least equal to the width of the channel to ensure safe discharge without overflowing. Therefore, the width of the stilling basin should be at least 6 m. Now, let's consider the type of structure required in the stilling basin. The type of structure depends on the discharge and the water depth in the stilling basin. Based on the given water depth of 2.4 m, we can determine the type of structure required.

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The Deep Dive

To design a stilling basin effectively, understanding the hydraulic conditions is crucial. With a discharge of \( 11.3 \, \mathrm{m}^3/\mathrm{s} \) and a channel width of 6 m, you'll first need to calculate the velocity of water entering the basin. Using the equation \( Q = A \cdot V \) where \( A \) is the cross-sectional area (width × depth), you can determine the velocity. This will guide the basin's dimensions and help ensure it can dissipate energy, preventing erosion downstream. An interesting nugget from engineering history is the use of stilling basins! The first known stilling basin designs date back to the early 1900s as engineers sought solutions for preventing scour and erosion at river outlets and spillways. Recognizing that controlled water flow plays a vital role in infrastructure longevity, modern designs incorporate innovative materials and shapes to maximize efficiency while minimizing environmental impact. Embrace these lessons as you plan your basin!

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