Let's break down the design of a **canal syphon** for the given data step-by-step. --- ## **1. Given Data** ### **Canal:** - **Full supply discharge (Q_canal):** 50 cumecs - **Full supply level (FSL):** 202.30 m - **Canal bed level:** 200.00 m - **Canal bed width (b):** 20 m - **Side slopes:** 0.5 H : 1 V ### **Drainage:** - **Catchment area (A):** 65 km² - **Dicken’s coefficient (C):** 5.0 - **Bed level:** 201.00 m - **High flood level:** 203.50 m --- ## **2. Estimation of Drainage Discharge** Using Dicken’s Formula: \[ Q_{drainage} = C \times A^{3/4} \] Where: - \( C = 5.0 \) - \( A = 65\,km^2 \) \[ Q_{drainage} = 5.0 \times (65)^{3/4} \] Calculate \( 65^{3/4} \): \[ \ln(65) \approx 4.174387 \] \[ 3/4 \times 4.174387 = 3.13079 \] \[ e^{3.13079} \approx 22.88 \] \[ Q_{drainage} = 5 \times 22.88 \approx 114.4\,m^3/s \] --- ## **3. Determination of Syphon Barrel Size** The syphon barrels must carry the canal discharge (50 cumecs) **under** the drainage channel. ### **a) Canal Cross-section at the Syphon** Assume the same section as canal: - Bed width \( b = 20\,m \) - Side slopes \( m = 0.5 \) - Let water depth = \( h \) Area, \( A \): \[ A = b \cdot h + m \cdot h^2 \] \[ A = 20h + 0.5h^2 \] Given: \[ Q = A \cdot V \] Let’s assume permissible velocity \( V = 2.0\,m/s \) (typical for barrel flow). \[ A = \frac{Q}{V} = \frac{50}{2.0} = 25\,m^2 \] So, \[ 20h + 0.5h^2 = 25 \] \[ 0.5h^2 + 20h - 25 = 0 \] Solve quadratic: \[ h = \frac{ -20 \pm \sqrt{400 - 4 \times 0.5 \times (-25)}}{2 \times 0.5} \] \[ = \frac{-20 \pm \sqrt{400 + 50}}{1} \] \[ = -20 \pm \sqrt{450} \] \[ \sqrt{450} \approx 21.21 \] \[ h = -20 + 21.21 = 1.21\,m \] ### **b) Number and Size of Barrels** Let’s use a rectangular barrel of width \( w \) and height \( h \): - Assume barrel width = 3 m (standard), height = 3 m. Area per barrel = \( 3 \times 3 = 9\,m^2 \) Number of barrels required: \[ \text{Number of barrels} = \frac{25}{9} \approx 2.78 \implies 3 \text{ barrels} \] Provide **3 barrels** each of 3 m x 3 m. --- ## **4. Hydraulic Design Checks** - **Inlet and Outlet Levels:** - Canal FSL: 202.30 m - Canal Bed: 200.00 m - Drainage Bed: 201.00 m - Drainage HFL: 203.50 m - **Syphon invert level:** Should be kept **below drainage bed** (say, 0.5 m below = 200.50 m). --- ## **5. Summary of Design** ### **Canal Syphon Design:** - **Number of barrels:** 3 - **Size of each barrel:** 3 m x 3 m (rectangular) - **Invert level of barrel:** 200.50 m - **Barrel length:** As per width of drainage plus side slopes (estimate as per site, e.g., 30 m) - **Material:** RCC or as per standard practice ### **Other Details:** - **Head losses** to be checked (entrance, friction, exit losses) - **Structural design** of barrels (not covered in this summary) --- ### **Assumptions:** - Permissible velocity in barrel: 2.0 m/s - No silt or debris problem assumed - Freeboard and other structural details as per standard codes --- If you need calculations for head loss or a sketch, let me know!