--- title: "Cross drainage: Q 50, bed 35 m, FSD 1.6" subject: "Irrigation and Drainage Engineering" chapter: 8 key: "semester_6/irrigation_and_drainage_engineering:cd-q50-bed35-fsd16-hfd400" source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/cd-q50-bed35-fsd16-hfd400 site: BCT Engineering --- # Cross drainage: Q 50, bed 35 m, FSD 1.6 Irrigation and Drainage Engineering · Chapter 8: Cross-Drainage structures - Asked in: 2072 Asoj, 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-q50-bed35-fsd16-hfd400 - 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: 50 cumec, Full supply depth: 1.6 m, Bed width: 35 m, Bed level: 210.3 m, Side slope: 1.5H:1V. Drainage Data: Discharge: 400 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 adopted as HFL (211.0m) > canal bed (210.3m). Drainage waterway: 12 spans of 8m (clear 96m) via Lacey's formula. Canal flumed to 17m wide rectangular trough (1.6m depth). Transitions: inlet 2:1 (22.8m), outlet 3:1 (34.2m). Bed levels/FSL: Sec1 (210.300/211.900), Sec2 (210.122/211.722), Sec3 (210.067/211.667), Sec4 (210.135/211.735). Head loss 0.165m. ## Answer The canal ($Q$ = 50 m³/s) crosses a drainage of $Q$ = 400 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): $$ P = 4.75\sqrt{Q} = 4.75\sqrt{400} = 95.0\ \text{m} $$ Provide **12 spans of 8 m** with piers 1.2 m thick: clear waterway = 12 × 8 = **96 m** (> 95.0 m). Overall length = 96 + 11 × 1.2 = **109.2 m**. Check: mean velocity = Q/(L·d) = 400/(96 × 2.50) = 1.67 m/s. Lacey's regime depth $R = 0.47(Q/f)^{1/3}$ = 3.46 m (with $f$ = 1); foundations of piers and abutments are taken about 1.5R = 5.2 m below HFL, with cut-offs and aprons for scour. #### 3. Canal waterway (flumed rectangular trough) Normal canal: area $A_1=(B+zD)D$ = (35 + 1.5 × 1.6) × 1.6 = 59.84 m², $V_1$ = 50/59.84 = 0.836 m/s, $h_{v1}=V_1^2/2g$ = 0.0356 m. Top width $T=B+2zD$ = 39.80 m. To save cost, the canal is flumed to a rectangular trough of width $B_t$ = **17 m**, with the same full supply depth 1.6 m (the trough is as long as the drainage waterway, 109.2 m). - Trough area = 17 × 1.6 = 27.20 m²; $V_t$ = 50/27.20 = 1.838 m/s (acceptable, < 2.5 m/s); $h_{vt}$ = 0.1722 m - Froude number = 0.46 < 1, flow is subcritical, so there is no hydraulic jump. - Hydraulic radius $R=A/P$ = 27.20/20.20 = 1.347 m; friction slope $S=(nV/R^{2/3})^2$ = 0.000511 (Manning's n = 0.015); friction loss in trough $h_f=S\,L$ = 0.000511 × 109.2 = 0.056 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 = 39.80 − 17 = **22.8 m** - Outlet length = 3 × (T − B_t)/2 = **34.2 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): $$ \begin{aligned} W_2 &= W_1 + h_{v1} - h_{vt} - 0.3(h_{vt}-h_{v1}) \\ W_3 &= W_2 - h_f \\ W_4 &= W_3 + h_{vt} - h_{v1} - 0.5(h_{vt}-h_{v1}) \end{aligned} $$ $W_1$ = 211.900 m, so $W_2$ = 211.722 m, $W_3$ = 211.667 m, $W_4$ = 211.735 m. Trough bed = water level − 1.6 m. | Section | Location | Bed level (m) | FSL (m) | |---|---|---|---| | 1 | Normal canal, start of inlet transition | 210.300 | 211.900 | | 2 | End of inlet transition = start of trough | 210.122 | 211.722 | | 3 | End of trough = start of outlet transition | 210.067 | 211.667 | | 4 | End of outlet transition = normal canal | 210.135 | 211.735 | Total loss of head = 211.900 − 211.735 = 0.165 m, so the canal bed downstream of the work is 0.165 m lower than upstream. Check: with trough slab 0.6 m thick, soffit of the barrels = 209.47 m, i.e. 0.97 m above the drainage bed; HFL stands 1.53 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 207.97 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 17 m wide trough; bed/FSL at the four sections = 210.30/211.90, 210.12/211.72, 210.07/211.67, 210.13/211.73 m. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. HFL (211.00 m) is only 0.70 m above the canal bed (210.30 m). Why is a siphon aqueduct still adopted? A. Because HFL is above the canal bed, a trough above HFL would be very high and costly, so the drainage runs under pressure through barrels B. Because the canal is smaller than the drainage, the canal must go over the drainage C. Because HFL is below the canal bed, an ordinary aqueduct is impossible D. Because the drainage has a bed width of 35 m Answer: A. HFL above the canal bed rules out an ordinary aqueduct economically; barrels flowing under pressure give a siphon aqueduct. (Key point: Choice of structure) 2. For Q = 400 m3/s, P = 4.75 sqrt(400) = 95 m. What waterway is provided? A. 95 m exactly, with piers inside this width B. 12 spans of 8 m = 96 m clear, overall length 109.2 m with 11 piers of 1.2 m C. 10 spans of 8 m = 80 m clear D. A single 35 m span equal to the canal bed width Answer: B. The clear waterway must be at least the Lacey perimeter; 12 x 8 = 96 m is chosen and piers add 11 x 1.2 m to give 109.2 m. (Key point: Drainage waterway) 3. Section 1 FSL is 211.900 m and section 4 FSL is 211.735 m. What does this mean for the canal downstream of the work? A. The downstream bed is 0.165 m higher than upstream B. The downstream bed is at the same level as upstream C. The downstream bed is 0.165 m lower than upstream because that head is lost in the work D. The canal needs no change in bed level Answer: C. Total loss = 211.900 - 211.735 = 0.165 m, so the downstream bed and FSL are 0.165 m lower. (Key point: Total head loss and downstream bed) 4. The barrel soffit is only 0.97 m above the drainage bed. What is done? A. The slab thickness is reduced to 0.2 m B. The barrels are left as they are because the siphonic head is large C. The canal bed is raised D. The drainage bed is depressed under the barrels to give 1.5 m clear height, with 1 in 4 slopes at both ends Answer: D. A clear height below 1.5 m is inadequate for flow and maintenance, so the drainage bed is depressed to RL 207.97 m with 1 in 4 slopes. (Key point: Depressing the drainage bed under barrels) ## Close variants set in other exams - [Cross drainage: Q 25, HFD 360](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Acd-q25-bed30-fsd2-hfd360) — Irrigation and Drainage Engineering, chapter 8, asked 2× ## Related in Irrigation and Drainage Engineering - [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 - [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× - [Siphon aqueduct: Q 60, bed 35 m](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Asiphon-aqueduct-q60-bed35-hfd500) — Irrigation and Drainage Engineering, chapter 8, asked 2× - [Siphon aqueduct: Q 50, bed 32 m](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Asiphon-aqueduct-q50-bed32-hfd400) — Irrigation and Drainage Engineering, chapter 8, asked 2× ## Related in other subjects - [Side-long ground hill road, 0-400 m](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Aside-long-road-n) — Estimating and Costing, chapter 6 - [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