--- title: "Cross drainage: Q 25, HFD 360" subject: "Irrigation and Drainage Engineering" chapter: 8 key: "semester_6/irrigation_and_drainage_engineering:cd-q25-bed30-fsd2-hfd360" source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/cd-q25-bed30-fsd2-hfd360 site: BCT Engineering --- # Cross drainage: Q 25, HFD 360 Irrigation and Drainage Engineering · Chapter 8: Cross-Drainage structures - Asked in: 2073 Bhadra, 10 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/cd-q25-bed30-fsd2-hfd360 - Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-8 ## Question Following data are obtained at the crossing of a canal and drainage. Canal Data: Discharge: 25 cumec, Full supply depth: 2.0 m, Bed width: 30 m, Bed level: 210.3 m, Side slope: 1.5H:1V. Drainage Data: Discharge: 360 cumec, HFL: 211.0 m, Bed level: 208.5 m, General ground level: 210.5 m. Design the drainage waterway, canal waterway and find the bed levels and FSL at four different sections of the canal trough. ## Short answer Siphon aqueduct chosen as HFL (211.0m) > canal bed (210.3m). Drainage waterway: 12 spans of 8m (clear 96m) via Lacey's formula. Canal flumed to 7m wide rectangular trough (2m depth). Transitions: inlet 2:1 (29.0m), outlet 3:1 (43.5m). Bed levels/FSL: Sec1 (210.300/212.300), Sec2 (210.098/212.098), Sec3 (210.041/212.041), Sec4 (210.119/212.119). Head loss 0.181m. ## Answer The canal ($Q$ = 25 m³/s) crosses a drainage of $Q$ = 360 m³/s. Design is done in four steps: type of work, drainage waterway, canal waterway (flumed trough) and bed/water levels of the trough. **Assumptions:** Lacey's $f$ = 1; trough $n$ = 0.015; slab 0.6 m. #### 1. Type of structure HFL of the drainage (211.00 m) is above the canal bed (210.30 m) by 0.70 m, so the trough cannot be kept above HFL without a very high, costly structure. The drainage is passed under the trough through barrels flowing under pressure (siphonic action). A **siphon aqueduct** is suitable. Drainage depth at HFL = 211.00 − 208.50 = 2.50 m. #### 2. Drainage waterway Lacey's regime perimeter (for a natural stream): $$ P = 4.75\sqrt{Q} = 4.75\sqrt{360} = 90.1\ \text{m} $$ Provide **12 spans of 8 m** with piers 1.2 m thick: clear waterway = 12 × 8 = **96 m** (> 90.1 m). Overall length = 96 + 11 × 1.2 = **109.2 m**. Check: mean velocity = Q/(L·d) = 360/(96 × 2.50) = 1.50 m/s. Lacey's regime depth $R = 0.47(Q/f)^{1/3}$ = 3.34 m (with $f$ = 1); foundations of piers and abutments are taken about 1.5R = 5.0 m below HFL, with cut-offs and aprons for scour. #### 3. Canal waterway (flumed rectangular trough) Normal canal: area $A_1=(B+zD)D$ = (30 + 1.5 × 2) × 2 = 66.00 m², $V_1$ = 25/66.00 = 0.379 m/s, $h_{v1}=V_1^2/2g$ = 0.0073 m. Top width $T=B+2zD$ = 36.00 m. To save cost, the canal is flumed to a rectangular trough of width $B_t$ = **7 m**, with the same full supply depth 2 m (the trough is as long as the drainage waterway, 109.2 m). - Trough area = 7 × 2 = 14.00 m²; $V_t$ = 25/14.00 = 1.786 m/s (acceptable, < 2.5 m/s); $h_{vt}$ = 0.1625 m - Froude number = 0.40 < 1, flow is subcritical, so there is no hydraulic jump. - Hydraulic radius $R=A/P$ = 14.00/11.00 = 1.273 m; friction slope $S=(nV/R^{2/3})^2$ = 0.000520 (Manning's n = 0.015); friction loss in trough $h_f=S\,L$ = 0.000520 × 109.2 = 0.057 m #### 4. Transitions and levels ```text FSL ---. .--- FSL '--.______________________.--' bed ---. .--- bed '--.______________________.--' normal inlet flumed trough outlet normal canal (2:1) (3:1) canal ``` Wing-wall (straight) transitions: inlet splay 2:1 (contraction) and outlet splay 3:1 (expansion), measured on each side: - Inlet length = 2 × (T − B_t)/2 = 36.00 − 7 = **29.0 m** - Outlet length = 3 × (T − B_t)/2 = **43.5 m** Bernoulli's equation between sections (loss in contraction = 0.3 Δh_v, in expansion = 0.5 Δh_v; Δh_v = difference of velocity heads): $$ \begin{aligned} W_2 &= W_1 + h_{v1} - h_{vt} - 0.3(h_{vt}-h_{v1}) \\ W_3 &= W_2 - h_f \\ W_4 &= W_3 + h_{vt} - h_{v1} - 0.5(h_{vt}-h_{v1}) \end{aligned} $$ $W_1$ = 212.300 m, so $W_2$ = 212.098 m, $W_3$ = 212.041 m, $W_4$ = 212.119 m. Trough bed = water level − 2 m. | Section | Location | Bed level (m) | FSL (m) | |---|---|---|---| | 1 | Normal canal, start of inlet transition | 210.300 | 212.300 | | 2 | End of inlet transition = start of trough | 210.098 | 212.098 | | 3 | End of trough = start of outlet transition | 210.041 | 212.041 | | 4 | End of outlet transition = normal canal | 210.119 | 212.119 | Total loss of head = 212.300 − 212.119 = 0.181 m, so the canal bed downstream of the work is 0.181 m lower than upstream. Check: with trough slab 0.6 m thick, soffit of the barrels = 209.44 m, i.e. 0.94 m above the drainage bed; HFL stands 1.56 m above the soffit, which gives the siphonic head. Since the clear height is less than 1.5 m, the drainage bed is depressed under the barrels to RL 207.94 m (1.5 m clear height) with a 1 in 4 slope at both ends. **Answer:** drainage waterway 96 m clear (12 × 8 m, overall 109.2 m); canal flumed to 7 m wide trough; bed/FSL at the four sections = 210.30/212.30, 210.10/212.10, 210.04/212.04, 210.12/212.12 m. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. HFL (211.0 m) is 0.70 m above canal bed (210.30 m). What is provided? A. Aqueduct B. Siphon aqueduct C. Canal siphon D. Level crossing Answer: B. HFL higher than canal bed requires pressure flow through barrels under the trough. (Key point: Structure choice) 2. Q = 360 m3/s gives P = 90.1 m. What is provided? A. 12 x 8 m = 96 m clear, overall 109.2 m B. 90.1 m clear only C. 12 x 8 m, overall 96 m D. 10 x 8 m = 80 m Answer: A. Clear waterway 96 m > 90.1 m; 11 piers of 1.2 m make overall 109.2 m. (Key point: Drainage waterway) 3. Why is a 7 m trough acceptable? A. Velocity 1.79 m/s < 2.5 m/s and Froude 0.40 < 1 B. Velocity is 0.38 m/s C. Velocity exceeds 5 m/s D. Froude number exceeds 1 Answer: A. V = 25/14 = 1.786 m/s, subcritical flow. (Key point: Flumed trough) 4. Which sequence of FSL is right? A. 212.30, 212.10, 212.04, 212.12 B. 212.30, 212.50, 212.60, 212.30 C. 212.30, 212.10, 212.10, 212.30 D. 212.30, 212.04, 212.10, 212.12 Answer: A. Level drops at inlet, drops by friction in the trough (W3 = W2 - hf), then partially recovers at the outlet; total loss 0.181 m. (Key point: Levels at four sections) ## Close variants set in other exams - [Cross drainage: Q 50, bed 35 m, FSD 1.6](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Acd-q50-bed35-fsd16-hfd400) — Irrigation and Drainage Engineering, chapter 8, asked 2× ## Related in Irrigation and Drainage Engineering - [Cross drainage: Q 30, HFL 311 m](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Acd-q30-canal-bed310-hfl311) — Irrigation and Drainage Engineering, chapter 8 - [Cross drainage: Q 50, HFD 550](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Acd-q50-bed30-fsd21-hfd550) — Irrigation and Drainage Engineering, chapter 8, asked 2× - [Cross drainage: Q 50, HFD 450](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Acd-q50-bed30-fsd21-hfd450) — Irrigation and Drainage Engineering, chapter 8, asked 2× - [Cross drainage: Q 40, 45 cumec drainage](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Acd-q40-bed30-fsd16-syphonic) — Irrigation and Drainage Engineering, chapter 8 - [Balancing depth: bed width 25 m](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Abalancing-depth-bed25) — Irrigation and Drainage Engineering, chapter 3, asked 3× - [Cross drainage: canal 300, drainage 500](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Acd-q300-canal-n0016-drain500) — Irrigation and Drainage Engineering, chapter 8 ## Related in other subjects - [Canal earthwork, bed 3 m, free board 0.44 m](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Achannel-q-portion) — Estimating and Costing, chapter 6