--- title: "Vertical drop design, Q 1.8 m3/s (drop 0.75 m)" subject: "Irrigation and Drainage Engineering" chapter: 7 key: "semester_6/irrigation_and_drainage_engineering:vertical-drop-q18-drop075" source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/vertical-drop-q18-drop075 site: BCT Engineering --- # Vertical drop design, Q 1.8 m3/s (drop 0.75 m) Irrigation and Drainage Engineering · Chapter 7: Regulating Structures - Asked in: 2073 Magh, 8 marks - Video: [Design of sharda fall | Vertical drop structure | Irrigation Numerical | Most important problem](https://www.youtube.com/watch?v=r_VaWVvL3YY) — Sudip Dhakal - 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/vertical-drop-q18-drop075 - Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-7 ## Question Design a vertical drop structure for the data given below. Full supply discharge u/s and d/s = 1.8 cumecs; Drop height = 0.75 m; FSL u/s and d/s = 106.997 and 106.247; Full Supply depth u/s and d/s = 0.929 m; Bed levels u/s and d/s = 106.068 and 105.318; Bed width u/s and d/s = 1.2 m. Top width of crest = 0.5 m for initial assumption, Cd = 0.415 for rectangular crest. The drop structure is of masonry with specific gravity 2.0. Side slope of the canal is 1:1. The Bligh's coefficient as 6.0 for sandy loam soil at foundation. ## Short answer Crest length 1.20 m, crest level 106.17 m, head 0.87 m. Wall bottom width 1.43 m. Cistern depth 0.30 m, length 4.83 m. Floor thickness 0.65 m near wall tapering to 0.30 m. ## Answer #### Given data and assumptions - $Q = 1.8$ m³/s, bed width $B = 1.2$ m, side slope 1:1, u/s FSL $= 106.997$ m, u/s bed $= 106.068$ m, d/s bed $= 105.318$ m. - Full supply depth u/s $D_u = 0.929$ m, d/s $D_d = 0.929$ m (d/s FSL $= 106.247$ m); drop in water level $H_L = 0.750$ m. - Bligh's coefficient $C = 6$; specific gravity of masonry $G = 2.0$. #### 1. Upstream flow conditions $$ \begin{aligned} A &= (B + mD_u)D_u = (1.2 + 1\times0.929)(0.929) = 1.978\ \text{m}^2 \\ v &= Q/A = 0.910\ \text{m/s}, \qquad h_a = \frac{v^2}{2g} = 0.042\ \text{m} \end{aligned} $$ #### 2. Crest length, head and crest level Discharge over a rectangular crest: $Q = C_d\sqrt{2g}\,L\,H^{3/2}$ with $C_d\sqrt{2g} = 1.838$, where $H$ is the total head over the crest (including $h_a$). Take crest length equal to the bed width, $L = B$: $$ H = \left(\frac{Q}{1.838\,L}\right)^{2/3} = \left(\frac{1.8}{1.838\times1.2}\right)^{2/3} = 0.873\ \text{m} $$ $$ \text{Crest level} = FSL_u + h_a - H = 106.997 + 0.042 - 0.873 = 106.17\ \text{m} $$ Height of crest above d/s bed $d_c = 106.17 - 105.32 = 0.85$ m. #### 3. Cistern (energy dissipation) Discharge per metre length of crest $q = Q/L = 1.500$ m²/s. Energy available above the d/s bed $E_1 = FSL_u + h_a - \text{d/s bed} = 1.721$ m. For a cistern of depth $X$ below the d/s bed, the jump must form with the conjugate depth $y_2$ equal to the tail water over the cistern, $y_2 = D_d + X$. Solving with $E_1 + X = y_1 + q^2/(2gy_1^2)$ and $y_2 = \frac{y_1}{2}(\sqrt{1+8F_1^2} - 1)$: - Required $X = 0.289$ m. Provide **$X = 0.30$ m** (cistern floor level $= 105.02$ m). - With this $X$: $y_1 = 0.255$ m, $F_1 = 3.72$, $y_2 = 1.220$ m. Length of cistern (hydraulic jump length) $L_c = 5(y_2 - y_1) = 5(1.220 - 0.255) = 4.83$ m. #### 4. Crest (drop) wall Top width (assumed) $T = 0.50$ m; check $0.55\sqrt{d_c} = 0.55\sqrt{0.85} = 0.51$ m $\approx 0.50$ m, so it is adequate. Height of wall from cistern floor to crest $H_w = 106.17 - 105.02 = 1.15$ m. Bottom width for a gravity masonry wall: $$ B_w = \frac{H_w + H}{\sqrt{G}} = \frac{1.15 + 0.87}{\sqrt{2}} = 1.43\ \text{m} $$ Adopt bottom width $B_w = 1.43$ m (not less than the top width), with the d/s face vertical or slightly battered. #### 5. Length of impervious floor (Bligh's theory) Total creep length required $L = C\,H_L = 6\times0.750 = 4.50$ m. Cut-offs: u/s $d_1 = 0.6$ m, d/s $d_2 = 0.9$ m. Downstream floor length (Bligh) with $q$ in m²/s: $$ L_d = 2.21\,C\sqrt{H_L\sqrt{q/75}} = 2.21\times6\sqrt{0.750\sqrt{1.500/75}} = 4.32\ \text{m} $$ The d/s floor (measured from the toe of the wall) must also contain the cistern, so adopt $L_d = 4.83$ m. Creep already provided by cut-offs and wall $= 2(d_1 + d_2) + B_w = 4.43$ m, so the u/s floor needed is $$ b_u = L - [2(d_1+d_2) + B_w + L_d] = -4.76\ \text{m} $$ Bligh's creep is already satisfied, so a nominal u/s floor of **1.0 m** is provided. Actual creep $= 10.26$ m $\ge 4.50$ m, safe. Total floor length $= b_u + B_w + L_d = 7.26$ m. #### 6. Thickness of the floor Pressure head at the toe of the wall: creep to that point $= 3.63$ m, so residual head $h_1 = H_L\,\dfrac{L_{act} - 3.63}{L_{act}} = 0.485$ m. At the end of the cistern the creep is 8.46 m and $h_2 = 0.132$ m. $$ t_1 = \frac{4}{3}\frac{h_1}{G-1} = \frac{4}{3}\times\frac{0.485}{1.00} = 0.65\ \text{m} $$ Adopt floor thickness **0.65 m** under the cistern near the wall, tapering to 0.30 m at the end of the floor (minimum 0.30 m). #### Summary | Component | Value | |---|---| | Crest level | 106.17 m | | Crest length / head $H$ | 1.20 m / 0.87 m | | Crest wall top / bottom width | 0.50 m / 1.43 m | | Cistern depth / length | 0.30 m / 4.83 m | | Floor: u/s 1.0 m, d/s 4.83 m, cut-offs 0.6 / 0.9 m | total creep 10.26 m | | Floor thickness | 0.65 m (taper to 0.30 m) | **Answer:** crest level 106.17 m, crest length 1.20 m, crest wall 0.50 m top and 1.43 m bottom width, cistern depth 0.30 m and length 4.83 m, floor length 7.26 m, floor thickness 0.65 m. Sketch: ```text FSL u/s ~~~~~~~~~~~| | crest u/s bed ___________|__ FSL d/s ~~~~ | u/s floor | \ drop ~~~~~ d1 | | \_____cistern________ d/s bed | |<-Lc->| d/s floor | d2 |____ floor thickness __| ``` ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. With L = B = 1.2 m and Q = 1.8 m^3/s, what is q used for the cistern design? A. 0.67 m^2/s B. 2.16 m^2/s C. 1.50 m^2/s D. 1.80 m^2/s Answer: C. q = Q/L = 1.8/1.2 = 1.50 m^2/s. (Key point: Discharge per metre length) 2. Bligh's formula gives L_d = 4.32 m, but 4.83 m is adopted. Why? A. Because 4.83 m is the u/s cut-off depth B. Because the d/s floor must be at least as long as the cistern (jump length) from the wall toe C. Because Bligh's formula always underestimates by 10% D. Because the floor is made equal to the crest length Answer: B. The d/s floor must contain the cistern, whose length is 5(y2 - y1) = 4.83 m, so the larger value governs. (Key point: d/s floor length) 3. Why does this design need a thicker floor (0.65 m) than the earlier designs with similar uplift head? A. Because the crest is lower B. Because the specific gravity is only 2.0, so (G - 1) is smaller and more thickness is needed to balance uplift C. Because the discharge is smaller D. Because the thickness equals the cistern depth Answer: B. t = (4/3) h1/(G - 1); with G = 2.0 the divisor is 1.00 instead of about 1.2, giving 0.65 m. (Key point: Effect of G on floor thickness) 4. For Bligh's coefficient 6 and a drop in water level of 0.75 m, the required creep length is A. 0.125 m B. 4.50 m C. 8.00 m D. 6.75 m Answer: B. Required creep = C x HL = 6 x 0.75 = 4.50 m. (Key point: Required creep length) ## Close variants set in other exams - [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× ## Related in Irrigation and Drainage Engineering - [Vertical drop design, Q 1.8 m3/s (bed 205.05)](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Avertical-drop-q18-bed20505) — Irrigation and Drainage Engineering, chapter 7, asked 4× - [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× - [Vertical drop design, Q 5.1 m3/s](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Avertical-drop-q51) — Irrigation and Drainage Engineering, chapter 7 - [Canal drop structure, Q 5, FSL 110.5](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Acanal-drop-q5-fsl1105) — Irrigation and Drainage Engineering, chapter 7 ## Related in other subjects - [Irrigation canal earthwork with vertical drop](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Acanal-a-drop-0-400) — Estimating and Costing, chapter 6