Let's break down the problem step by step: ### **Given Data** - Discharge (\( Q \)) = **24 m³/s** - Depth of flow (\( h \)) = **1.8 m** - Bed width (\( b \)) = **20 m** - Upstream FSL = **118.20 m** - Downstream FSL = **117.00 m** - Drop = **1.20 m** - Bed level U/S = **116.40 m** - Bed level D/S = **115.20 m** - Coefficient of creep (Bligh’s) = **8** --- ## **(a) Design the dimensions of the crest and cistern downstream of the fall** ### **1. Crest Length (L)** For a Sarda (rectangular) fall, crest length is generally kept equal to the bed width. - **Crest length, \( L = 20 \) m** ### **2. Crest Level** The crest is usually kept 0.15 to 0.30 m above the downstream bed level. - **Crest level = Downstream bed level + 0.15 to 0.30 m** - Let's take 0.20 m as a typical value: \[ \text{Crest level} = 115.20 + 0.20 = \boxed{115.40 \text{ m}} \] ### **3. Crest Width** Width of crest is generally kept between 0.6 m and 1.0 m. Let’s take 0.75 m. ### **4. Cistern Dimensions** Cisterns are provided to dissipate energy. Typical dimensions: - **Length of cistern** (\( L_c \)) = \( 4 \times \text{Drop} \) - **Depth of cistern** (\( d_c \)) = \( 0.3 \times \text{Drop} \) So, - \( L_c = 4 \times 1.2 = 4.8 \) m - \( d_c = 0.3 \times 1.2 = 0.36 \) m - **Cistern bed level = Downstream bed level - 0.36 = 115.20 - 0.36 = \boxed{114.84 \text{ m}}** --- ## **(b) Design the floor on Bligh's creep theory (Coefficient = 8)** ### **Bligh’s Creep Theory:** \[ L = C \times H \] where \( L \) = Length of floor \( C \) = Bligh’s coefficient of creep (here, 8) \( H \) = Head over the floor \[ H = \text{Upstream FSL} - \text{Downstream FSL} = 118.20 - 117.00 = 1.20 \text{ m} \] \[ L = 8 \times 1.20 = 9.6 \text{ m} \] --- ## **Summary of Answers** ### **(a) Crest and Cistern Dimensions** - **Crest length**: 20 m - **Crest width**: 0.75 m (typical range 0.6-1.0 m) - **Crest level**: 115.40 m - **Cistern length**: 4.8 m - **Cistern depth**: 0.36 m - **Cistern bed level**: 114.84 m ### **(b) Floor Length (Bligh’s Theory)** - **Total length of floor required:** 9.6 m --- **If you need detailed sketches or further design (like thickness, reinforcement, etc.), let me know!**

Certainly! Below is the detailed answer divided into two parts, each with its explanation at the end: --- ### **Part 1: Design of Crest and Cistern** **1. Crest Length (L):** For a Sarda (rectangular) fall, the crest length is typically equal to the bed width of the channel to ensure proper flow transition. \[ \boxed{L = 20\, \text{m}} \] **2. Crest Level:** The crest should be positioned above the downstream bed level to prevent backflow and ensure smooth flow over the fall. Usually, it is kept 0.15 to 0.30 m above the downstream bed. Choosing 0.20 m as a standard height: \[ \text{Crest level} = 115.20\, \text{m} + 0.20\, \text{m} = \boxed{115.40\, \text{m}} \] **3. Crest Width:** The width of the crest is generally between 0.6 m and 1.0 m for stability and safety. We'll take a typical value: \[ \boxed{0.75\, \text{m}} \] **4. Cistern Dimensions:** Cisterns are provided to dissipate the energy of the falling water. Their dimensions are based on the drop height: - **Length of cistern (L_c):** \[ L_c = 4 \times \text{Drop} = 4 \times 1.20\, \text{m} = \boxed{4.8\, \text{m}} \] - **Depth of cistern (d_c):** \[ d_c = 0.3 \times \text{Drop} = 0.3 \times 1.20\, \text{m} = \boxed{0.36\, \text{m}} \] - **Cistern bed level:** It is typically placed below the downstream bed level by the depth of the cistern. \[ \text{Cistern bed level} = 115.20\, \text{m} - 0.36\, \text{m} = \boxed{114.84\, \text{m}} \] **_Explanation:_** In this part, we established the primary dimensions for the crest, ensuring it is appropriately positioned and wide enough for stability. The cistern dimensions are designed to handle the energy dissipation effectively, following standard engineering practices. --- ### **Part 2: Design of Floor Using Bligh’s Creep Theory** **Bligh’s Creep Theory:** This theory helps determine the length of the floor needed to stabilize the downstream flow and prevent scouring. It states that the length of the floor is proportional to the head of water over the floor, with a coefficient known as Bligh’s coefficient (here, 8). - **Head over the floor (H):** \[ H = \text{Upstream FSL} - \text{Downstream FSL} = 118.20\, \text{m} - 117.00\, \text{m} = \boxed{1.20\, \text{m}} \] - **Length of the floor (L):** \[ L = C \times H = 8 \times 1.20\, \text{m} = \boxed{9.6\, \text{m}} \] This length ensures the flow is stabilized and reduces the risk of erosion due to creeping of the bed. **_Explanation:_** In this part, we applied Bligh’s creep theory to compute the length of the floor needed downstream of the fall. Using the coefficient of 8 and the head difference, we determined the minimum length necessary for safe and stable flow conditions. --- **Summary:** - **Crest length:** 20 m - **Crest level:** 115.40 m - **Crest width:** 0.75 m - **Cistern length:** 4.8 m - **Cistern depth:** 0.36 m - **Cistern bed level:** 114.84 m - **Floor length (Bligh's theory):** 9.6 m Let me know if you'd like further elaboration or sketches!