--- title: "Weir design by Bligh's theory, 3200 m3/s" subject: "Irrigation and Drainage Engineering" chapter: 5 key: "semester_6/irrigation_and_drainage_engineering:diversion-weir-vertical-drop-bligh-q3200" source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/diversion-weir-vertical-drop-bligh-q3200 site: BCT Engineering --- # Weir design by Bligh's theory, 3200 m3/s Irrigation and Drainage Engineering · Chapter 5: Diversion Headworks - Asked in: 2081 Chaitra, 8 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/diversion-weir-vertical-drop-bligh-q3200 - Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-5 ## Question Determine the length of water way, crest level, depth of upstream and downstream pile and length of impervious floor for a vertical drop weir using Bligh's theory for the following data. And also check the exit gradient. Given data: maximum flood discharge = 3200 m³/sec; HFL before construction = 185.0 m; downstream bed level = 178.0 m; canal FSL = 184.0 m; allowable afflux = 1 m; coefficient of creep = 12; permissible exit gradient = 1/6; Assume head loss through head regulator is 0.5 m, weir coefficient is 1.7, depth of retrogression is 0.5 m and silt factor is 1.0. ## Short answer Using Bligh's theory: waterway 270 m from Lacey's perimeter; crest level 182.35 m with shutters to pond level 184.5 m; upstream pile depth 2.5 m, downstream pile depth 6.5 m from scour depth; impervious floor length 66 m between piles (total creep 84 m); exit gradient 0.145 < 1/6, safe. ## Answer #### Data and assumptions $Q = 3200$ m³/s, HFL before construction $= 185.0$ m, d/s bed $= 178.0$ m, canal FSL $= 184.0$ m, afflux $= 1.0$ m, $C = 12$, $f = 1.0$, safe exit gradient 1/6, regulator loss $= 0.5$ m, weir coefficient $1.7$, retrogression $0.5$ m. The u/s bed is assumed equal to the d/s bed (178.0 m). #### 1. Length of waterway (Lacey) $$ P = 4.75\sqrt{Q} = 4.75\sqrt{3200} = 268.7\ \text{m} \Rightarrow \text{adopt } L = 270\ \text{m} $$ #### 2. Levels and crest - Pond level $=$ FSL $+$ regulator loss $= 184.0 + 0.5 = 184.5$ m. - HFL after construction $= 185.0 + 1.0 = 186.0$ m. - Discharge per metre $q = 3200/270 = 11.85$ m³/s/m. - Head over the crest from $Q = 1.7\,L\,H^{3/2}$: $$ H = \left(\frac{3200}{1.7\times 270}\right)^{2/3} = 3.65\ \text{m} $$ - Crest level (open flood) $= 186.0 - 3.65 = 182.35$ m. The pond level of 184.5 m is held by shutters or gates of height $184.5 - 182.35 = 2.15$ m above this crest. #### 3. Scour depth and pile depths $$ R = 1.35\left(\frac{q^2}{f}\right)^{1/3} = 1.35\left(\frac{11.85^2}{1.0}\right)^{1/3} = 7.02\ \text{m} $$ - U/s pile bottom $= 186.0 - 1.5R = 175.47$ m, so depth below bed $d_1 = 178.0 - 175.47 = 2.53$ m, adopt 2.5 m. - D/s pile bottom $= 185.0 - 2R = 170.96$ m. The bed after retrogression is $178.0 - 0.5 = 177.5$ m, so $d_2 = 177.5 - 170.96 = 6.54$ m, adopt 6.5 m. #### 4. Length of impervious floor (Bligh) Maximum static head $H_s = 184.5 - 177.5 = 7.0$ m. Total creep length $$ L_c = C H_s = 12\times 7.0 = 84\ \text{m} $$ $$ L_c = 2d_1 + 2d_2 + b \Rightarrow b = 84 - 2(2.53 + 6.54) = 65.9\ \text{m} $$ Adopt a horizontal floor length $b \approx 66$ m between the piles. #### 5. Exit gradient check $$ \alpha = \frac{b}{d_2} = \frac{65.9}{6.54} = 10.08,\quad \lambda = 5.565,\quad G_E = \frac{H_s}{d_2}\cdot\frac{1}{\pi\sqrt{\lambda}} = \frac{7.0}{6.54}\times\frac{1}{\pi\sqrt{5.565}} = 0.145 $$ $G_E = 0.145 < 1/6 = 0.167$, so the floor is safe against piping. **Answer:** Waterway $\approx 270$ m; crest level $\approx 182.35$ m (shutters to 184.5 m); u/s pile $\approx 2.5$ m deep; d/s pile $\approx 6.5$ m deep; impervious floor $\approx 66$ m between piles (total creep 84 m); exit gradient $= 0.145$ (safe). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What waterway does Lacey's perimeter give for Q = 3200 m3/s? A. About 268.7 m (adopt 270 m) B. About 150 m C. About 540 m D. About 56.6 m Answer: A. P = 4.75 sqrt(3200) = 268.7 m. (Key point: Waterway) 2. Crest level is found as: A. Pond level 184.5 m minus H B. HFL after construction (186.0 m) minus head over crest H = 3.65 m, giving 182.35 m C. Canal FSL minus 3.65 m D. HFL before construction plus H Answer: B. HFL after afflux is 186.0 m; H = (Q/(1.7L))^(2/3) = 3.65 m, so the crest is at 182.35 m, with shutters up to pond level. (Key point: Crest level) 3. How are the u/s and d/s pile bottoms fixed? A. u/s: HFL - 1.5R; d/s: HFL before - 2R, depth measured from retrogressed bed B. Both at 1.5R below bed C. u/s: 2R; d/s: 1.5R D. Both equal to the afflux Answer: A. Here R = 7.02 m, giving u/s depth about 2.5 m and d/s about 6.5 m below the retrogressed bed. (Key point: Pile depths) 4. Total creep length and floor length are obtained as: A. Lc = C Hs = 84 m, then b = Lc - 2(d1 + d2) about 66 m B. Lc = Hs/C = 0.58 m C. b = Lc + 2(d1 + d2) D. b = Lc/2 Answer: A. Static head 7.0 m x C = 12 gives 84 m; subtracting the vertical creep 2(d1+d2) leaves the horizontal floor. (Key point: Bligh floor length) 5. The exit gradient 0.145 is safe because: A. It is larger than 1/6 B. It is less than the permissible 1/6 = 0.167 C. It equals 1 D. It is calculated with the u/s pile Answer: B. Safety against piping requires G_E to be below the permissible gradient. (Key point: Exit gradient check) ## Related in Irrigation and Drainage Engineering - [Diversion weir: Bligh and Khosla, 4000 m3/s](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Adiversion-weir-bligh-khosla-q4000) — Irrigation and Drainage Engineering, chapter 5 - [Minimum impervious floor length, 10000 m3/s](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Abarrage-min-floor-length-q10000) — Irrigation and Drainage Engineering, chapter 5, asked 2× - [Crest width, cistern length of vertical drop, Q 1.55](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Avertical-drop-q155-drop075) — Irrigation and Drainage Engineering, chapter 7, asked 2× - [Vertical drop design, Q 7.5 m3/s](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Avertical-drop-q75) — Irrigation and Drainage Engineering, chapter 7, asked 4× - [Vertical drop design, Q 5.2 m3/s](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Avertical-drop-q52) — Irrigation and Drainage Engineering, chapter 7, asked 4× - [Vertical drop design, Q 2.1 m3/s](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Avertical-drop-q21) — Irrigation and Drainage Engineering, chapter 7, asked 4×