Let's break down the design steps for a canal syphon (also known as a syphon aqueduct) with the given data: --- ### **Given Data:** #### **Canal:** - Full supply discharge, \( Q_c \) = 50 cumecs (m³/s) - Full supply level (FSL) = 202.30 m - Canal bed level = 200.00 m - Canal bed width = 20 m - Side slopes = 0.5H : 1V #### **Drainage:** - Catchment area = 65 km² (65,000,000 m²) - Dicken's coefficient, \( C \) = 5.0 - Drainage bed level = 201.00 m - High flood level = 203.50 m --- ## **Step 1: Calculate Maximum Drainage Discharge** Using Dicken's formula: \[ Q_d = C \cdot A^{3/4} \] Where: - \( Q_d \) = peak discharge in cumecs - \( C \) = Dicken's coefficient = 5.0 - \( A \) = catchment area in km² = 65 \[ Q_d = 5.0 \times (65)^{3/4} \] First, calculate \( 65^{3/4} \): \[ 65^{3/4} = (65^{0.75}) \approx 21.69 \] \[ Q_d = 5.0 \times 21.69 = 108.45 \text{ cumecs} \] --- ## **Step 2: Fix General Levels** - **Canal FSL:** 202.30 m - **Canal Bed Level:** 200.00 m - **Drainage Bed Level:** 201.00 m - **High Flood Level (Drainage):** 203.50 m Since HFL of drainage is higher than canal FSL, a syphon aqueduct is indeed required. --- ## **Step 3: Design Waterway for Drainage** ### **Assume Permissible Velocity (V):** For syphon barrels, permissible velocity is usually 2.5–3.0 m/s. Assume \( V = 2.5 \) m/s. \[ A = \frac{Q_d}{V} = \frac{108.45}{2.5} = 43.38 \text{ m}^2 \] --- ## **Step 4: Decide Number and Size of Barrels** Assume rectangular barrels for ease. Assume barrel height = 2.5 m (typically 2–3 m for maintenance). \[ \text{Width of one barrel} = \frac{A}{\text{height}} = \frac{43.38}{2.5} = 17.35 \text{ m} \] A single barrel of 17.35 m width is not practical. Let's provide 3 barrels. \[ \text{Width of each barrel} = \frac{17.35}{3} \approx 5.78 \text{ m} \] Provide 3 barrels of 2.5 m height × 5.8 m width (rounded up). --- ## **Step 5: Check Afflux / Head Loss** Estimate head loss using Unwin’s formula for syphon barrels: \[ h_L = \left( \frac{V^2}{2g} \right) \left[ 1 + (4f \frac{L}{D}) + K \right] \] Where: - \( f \) = friction factor (assume 0.01 for concrete) - \( L \) = length of barrel (assume 20 m) - \( D \) = equivalent diameter (for rectangular: \( D = \frac{2ab}{a+b} \)), \( a=2.5 \), \( b=5.8 \) - \( K \) = entrance/exit loss coefficient, typically 0.5 Calculate the equivalent diameter: \[ D = \frac{2 \times 2.5 \times 5.8}{2.5 + 5.8} = \frac{29}{8.3} \approx 3.5 \text{ m} \] Now calculate velocity: \[ V = 2.5 \text{ m/s} \rightarrow V^2 = 6.25 \] \[ h_L = \left( \frac{6.25}{2 \times 9.81} \right) \left[ 1 + (4 \times 0.01 \times \frac{20}{3.5}) + 0.5 \right] \] \[ = 0.32 \times [1 + (0.228) + 0.5] = 0.32 \times 1.728 = 0.55 \text{ m} \] Total head loss is approximately **0.55 m**. --- ## **Step 6: Canal Section over Syphon** Design canal trough (rectangular): - Canal bed width = 20 m - Depth of water = FSL - bed level = 202.3 - 200.0 = 2.3 m - Assume freeboard = 0.5 m - Trough width = 20 m (same as bed width) - Trough depth = 2.3 + 0.5 = 2.8 m --- ## **Step 7: Overall Layout** - **3 barrels**, each **2.5 m high × 5.8 m wide** - Canal passes over drainage in a **rectangular trough** of **20 m width × 2.8 m depth** --- ### **Summary Table** | Item | Value | |-----------------------|------------------------| | No. of Barrels | 3 | | Barrel Size | 2.5 m × 5.8 m | | Barrel Velocity | 2.5 m/s | | Canal Trough Width | 20 m | | Canal Trough Depth | 2.8 m | | Total Head Loss | 0.55 m | | Peak Drainage Discharge | 108.45 cumecs | --- **Note:** For a detailed drawing, reinforcement, and further checks (uplift, foundation, etc.), more data and assumptions are needed. --- **If you need calculations for any specific part (like structural design, reinforcement), please specify!**

Certainly! Here is the detailed design process divided into 6 parts, each with its explanation at the end: --- ### **Part 1: Gathering and Calculating Basic Data** **Given Data:** - Canal Full Supply Discharge \( Q_c \) = 50 m³/s - Canal Full Supply Level (FSL) = 202.30 m - Canal Bed Level = 200.00 m - Canal Bed Width = 20 m - Side slopes = 0.5H : 1V - Catchment Area = 65 km² - Dicken’s Coefficient \( C \) = 5.0 - Drainage Bed Level = 201.00 m - High Flood Level (HFL) = 203.50 m **Calculations:** - Maximum drainage discharge \( Q_d \), using Dicken’s formula: \[ Q_d = C \times A^{3/4} \] \[ Q_d = 5.0 \times (65)^{0.75} \approx 5.0 \times 21.69 = 108.45 \text{ m}^3/\text{s} \] **Explanation:** This step establishes the key parameters and computes the maximum expected drainage flow based on catchment area and Dicken’s coefficient, confirming the size of the drain that the syphon must accommodate. --- ### **Part 2: Fixing Levels and Checking the Need for a Syphon** **Levels:** - Canal FSL = 202.30 m - Canal bed = 200.00 m - Drainage bed = 201.00 m - HFL of drainage = 203.50 m Since the drainage high flood level (203.50 m) exceeds the canal FSL, a syphon aqueduct is necessary to safely carry drainage over the canal without flooding. **Explanation:** Choosing proper levels ensures the syphon intercepts the drainage flow at a safe level, preventing backflow or flooding of the canal. The HFL being above the canal FSL indicates the need for a syphon to carry drainage across the canal. --- ### **Part 3: Determining Waterway Cross-Section for Drainage** **Assumption:** - Permissible velocity \( V = 2.5 \) m/s (to avoid erosion and ensure smooth flow) - Cross-sectional area \( A = Q_d / V \): \[ A = \frac{108.45}{2.5} = 43.38 \text{ m}^2 \] **Designing Barrels:** - Assume rectangular barrels with height \( h_b = 2.5 \) m - Width of each barrel: \[ b_b = \frac{A}{h_b} = \frac{43.38}{2.5} \approx 17.35 \text{ m} \] - Using 3 barrels: \[ \text{Width per barrel} \approx \frac{17.35}{3} \approx 5.78 \text{ m} \] **Explanation:** This step estimates the size of the waterway (barrels) to carry the drainage flow at safe velocities, ensuring efficient flow capacity without excessive headloss or structural issues. --- ### **Part 4: Head Loss Estimation in the Syphon Barrel** **Parameters:** - Assume length of each barrel \( L = 20 \) m - Rectangular cross-section: \( h_b = 2.5 \) m, \( b_b = 5.8 \) m - Equivalent diameter \( D \): \[ D = \frac{2 a b}{a + b} = \frac{2 \times 2.5 \times 5.8}{2.5 + 5.8} \approx 3.5 \text{ m} \] - Friction factor \( f = 0.01 \) **Head loss calculation:** \[ h_L = \frac{V^2}{2g} \left[ 1 + 4f \frac{L}{D} + K \right] \] \[ h_L = 0.32 \times [1 + 4 \times 0.01 \times \frac{20}{3.5} + 0.5] \] \[ h_L \approx 0.32 \times 1.728 \approx 0.55 \text{ m} \] **Explanation:** Calculating head losses due to friction and entrance/exit effects helps determine the energy losses in the syphon barrel, which is critical for ensuring the structure's adequacy and safety. --- ### **Part 5: Designing the Canal Trough over the Syphon** **Design considerations:** - Canal bed width = 20 m (matches existing canal width) - Water depth at FSL = 202.30 m minus bed level = 2.3 m - Allowance for freeboard = 0.5 m - Total depth of canal section: \[ \text{Canal depth} = 2.3 + 0.5 = 2.8 \text{ m} \] **Cross-section of Trough:** - Width = 20 m - Depth = 2.8 m This provides sufficient capacity for the canal flow and accommodates the structural and safety considerations. **Explanation:** Designing a suitable canal trough ensures proper flow capacity, structural stability, and safety margin, preventing overflow and maintaining flow efficiency over the syphon. --- ### **Part 6: Summary of Design and Final Remarks** | Item | Value | |-----------------------|--------------------------------| | Number of barrels | 3 | | Barrel size | 2.5 m high × 5.8 m wide | | Velocity in barrels | 2.5 m/s | | Total flow capacity | 108.45 m³/s | | Head loss in barrels | approximately 0.55 m | | Canal trough width | 20 m | | Canal depth | 2.8 m | **Final notes:** - Structural and reinforcement details require further analysis. - Foundation, uplift pressure, and safety margins should be checked. - This initial design provides a feasible framework for a syphon to carry drainage across the canal. **If further detailed structural calculations or drawings are needed, please specify!**