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).

To design a stilling basin for the given conditions, we need to consider the flow characteristics and the energy dissipation required to safely handle the discharge from the channel into the stilling basin. Here are the steps to design the stilling basin: ### Step 1: Determine Flow Characteristics 1. **Flow Rate (Q)**: Given as \( Q = 11.3 \, \text{m}^3/\text{s} \). 2. **Channel Width (b)**: Given as \( b = 6 \, \text{m} \). 3. **Channel Slope (S)**: Given as \( S = 2.5\% = 0.025 \). 4. **Water Depth in Stilling Basin (h)**: Given as \( h = 2.4 \, \text{m} \). ### Step 2: Calculate Flow Velocity in the Channel The flow velocity \( V \) in the channel can be calculated using the formula: \[ Q = A \cdot V \] Where \( A \) is the cross-sectional area of the flow in the channel. For a rectangular channel: \[ A = b \cdot h_c \] Where \( h_c \) is the flow depth in the channel. To find \( h_c \), we can use the energy equation and the slope to estimate the flow depth. ### Step 3: Calculate Flow Depth in the Channel Using the Manning's equation for flow in an open channel, we can estimate the flow depth. However, for simplicity, we can assume that the flow is uniform and use the following relationship: \[ V = \sqrt{g \cdot R \cdot S} \] Where: - \( g \) is the acceleration due to gravity (\( \approx 9.81 \, \text{m/s}^2 \)), - \( R \) is the hydraulic radius, which for a rectangular channel is given by \( R = \frac{A}{P} \) (where \( P \) is the wetted perimeter). Assuming a depth \( h_c \) (which we will estimate), we can calculate \( R \) and then \( V \). ### Step 4: Calculate the Required Width of the Stilling Basin The stilling basin should be wide enough to accommodate the flow without causing excessive turbulence or backwater effects. A common design practice is to make the width of the stilling basin equal to or greater than the width of the channel. 1. **Width of Stilling Basin (B)**: - A typical design would keep the width of the stilling basin equal to the channel width, so \( B \geq 6 \, \text{m} \). ### Step 5: Type of Structure The type of structure for the stilling basin can vary based on the specific requirements, but common types include: 1. **Energy Dissipating Structures**: Such as baffle blocks, stilling wells, or rock riprap. 2. **Drop Structures**: If there is a significant drop in elevation, a drop structure may be used to dissipate energy. 3. **Basin with Baffles**: To reduce turbulence and promote energy dissipation. ### Conclusion Based on the calculations and considerations: - **Width of Stilling Basin**: At least \( 6 \, \text{m} \) (can be wider based on site conditions). - **Type of Structure**: A stilling basin with energy dissipating features (such as baffles or rock riprap) to manage the flow and reduce turbulence. ### Additional Considerations - **Hydraulic Analysis**: Further hydraulic analysis may be required to determine the exact dimensions and features of the stilling basin based on local conditions and safety factors. - **Environmental Impact**: Consideration of environmental impacts and sediment transport should also be taken into account in the design process. This design approach provides a basic framework for creating a stilling basin that can effectively manage the discharge from the channel.