--- title: "Cross drainage: Q 50, HFD 450" subject: "Irrigation and Drainage Engineering" chapter: 8 key: "semester_6/irrigation_and_drainage_engineering:cd-q50-bed30-fsd21-hfd450" source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/cd-q50-bed30-fsd21-hfd450 site: BCT Engineering --- # Cross drainage: Q 50, HFD 450 Irrigation and Drainage Engineering · Chapter 8: Cross-Drainage structures - Asked in: 2078 Poush - 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-bed30-fsd21-hfd450 - Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-8 ## Question The cross-drainage structure across an irrigation channel has following data: Discharge of canal = 50 cumec; Bed width of canal = 30 m; Full supply depth of canal = 2.1 m; Bed level of the canal = 160.00 m; Side slope of canal = 1.5:1 (H:V); High flood discharge of drainage = 450 cumec; High flood level of drainage = 161.00 m; Bed level of drainage = 158.00 m; General ground level = 160.00 m. Design the drainage waterway and canal waterway and find the bed levels and FSL at four different sections of the canal trough. ## Short answer A siphon aqueduct with 11 spans of 10 m (110 m clear waterway) passes 450 m³/s drainage. Canal flumed to 13 m wide rectangular trough (2.1 m depth) over 125.0 m. Four section levels: 1) Bed 160.000, FSL 162.100; 2) Bed 159.812, FSL 161.912; 3) Bed 159.761, FSL 161.861; 4) Bed 159.833, FSL 161.933. Total head loss 0.167 m. ## Answer The canal ($Q$ = 50 m³/s) crosses a drainage of $Q$ = 450 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, concrete trough with $n$ = 0.015, piers 1.0–1.5 m thick, slab thickness 0.6 m. #### 1. Type of structure HFL of the drainage (161.00 m) is above the canal bed (160.00 m) by 1.00 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 = 161.00 − 158.00 = 3.00 m. #### 2. Drainage waterway Lacey's regime perimeter (for a natural stream): $$ P = 4.75\sqrt{Q} = 4.75\sqrt{450} = 100.8\ \text{m} $$ Provide **11 spans of 10 m** with piers 1.5 m thick: clear waterway = 11 × 10 = **110 m** (> 100.8 m). Overall length = 110 + 10 × 1.5 = **125.0 m**. Approach velocity at HFL = Q/(L·d) = 450/(110 × 3.00) = 1.36 m/s (the velocity through the barrels is checked at the end). Lacey's regime depth $R = 0.47(Q/f)^{1/3}$ = 3.60 m (with $f$ = 1); foundations of piers and abutments are taken about 1.5R = 5.4 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 × 2.1) × 2.1 = 69.61 m², $V_1$ = 50/69.61 = 0.718 m/s, $h_{v1}=V_1^2/2g$ = 0.0263 m. Top width $T=B+2zD$ = 36.30 m. To save cost, the canal is flumed to a rectangular trough of width $B_t$ = **13 m**, with the same full supply depth 2.1 m (the trough is as long as the drainage waterway, 125.0 m). - Trough area = 13 × 2.1 = 27.30 m²; $V_t$ = 50/27.30 = 1.832 m/s (acceptable, < 2.5 m/s); $h_{vt}$ = 0.1710 m - Froude number = 0.40 < 1, flow is subcritical, so there is no hydraulic jump. - Hydraulic radius $R=A/P$ = 27.30/17.20 = 1.587 m; friction slope $S=(nV/R^{2/3})^2$ = 0.000408 (Manning's n = 0.015); friction loss in trough $h_f=S\,L$ = 0.000408 × 125.0 = 0.051 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 = 36.30 − 13 = **23.3 m** - Outlet length = 3 × (T − B_t)/2 = **34.9 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): $$ \begin{aligned} W_2 &= W_1 + h_{v1} - h_{vt} - 0.3(h_{vt}-h_{v1}) \\ W_3 &= W_2 - h_f \\ W_4 &= W_3 + h_{vt} - h_{v1} - 0.5(h_{vt}-h_{v1}) \end{aligned} $$ $W_1$ = 162.100 m, so $W_2$ = 161.912 m, $W_3$ = 161.861 m, $W_4$ = 161.933 m. Trough bed = water level − 2.1 m. | Section | Location | Bed level (m) | FSL (m) | |---|---|---|---| | 1 | Normal canal, start of inlet transition | 160.000 | 162.100 | | 2 | End of inlet transition = start of trough | 159.812 | 161.912 | | 3 | End of trough = start of outlet transition | 159.761 | 161.861 | | 4 | End of outlet transition = normal canal | 159.833 | 161.933 | Total loss of head = 162.100 − 161.933 = 0.167 m, so the canal bed downstream of the work is 0.167 m lower than upstream. Check: with a trough slab 0.6 m thick, the soffit of the barrels = 159.761 − 0.6 = 159.16 m, only 1.16 m above the drainage bed, while HFL stands 1.84 m above the soffit, so the barrels run full under pressure. Since the clear height is less than 1.5 m, the drainage bed under the barrels is depressed to RL 157.66 m (1.5 m clear height) with 1 in 4 slopes at both ends. Barrel velocity = 450/(110 × 1.5) = 2.73 m/s, which is acceptable. **Answer:** drainage waterway 110 m clear (11 × 10 m, overall 125.0 m); canal flumed to 13 m wide trough; bed/FSL at the four sections = 160.00/162.10, 159.81/161.91, 159.76/161.86, 159.83/161.93 m. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which structure is chosen when HFL (161.00 m) exceeds canal bed (160.00 m) and the canal is above the drain? A. Aqueduct B. Siphon aqueduct C. Super-passage D. Canal siphon Answer: B. Drain HFL above the canal bed means the barrels flow under pressure, which is a siphon aqueduct. (Key point: Type of structure) 2. For Q = 450 m3/s, what is the Lacey regime perimeter and what is provided? A. 100.8 m, provided as 11 spans of 10 m = 110 m clear B. 134 m, provided as 12 spans C. 100.8 m, provided as 10 spans of 8 m D. 75 m, provided as 8 spans of 10 m Answer: A. P = 4.75 sqrt(450) = 100.8 m; 11 x 10 = 110 m exceeds it. (Key point: Drainage waterway) 3. Why is no hydraulic jump expected in the 13 m wide trough? A. Froude number is 0.40, so the flow is subcritical B. The trough is very long C. The velocity is below 0.5 m/s D. The slopes are 2:1 Answer: A. Fr < 1 gives subcritical flow, so there is no jump. (Key point: Flow in the trough) 4. How is the trough bed level at each section found? A. Water level minus the full supply depth of 2.1 m B. Water level plus 2.1 m C. Same as the drain bed D. General ground level Answer: A. The depth is kept at 2.1 m, so bed = FSL - 2.1 m. (Key point: Bed level at trough) ## Close variants set in other exams - [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× ## Related in Irrigation and Drainage Engineering - [Cross drainage: Q 50, HFD 450, uplift on roof](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Acd-q50-fsd15-hfd450-uplift-roof) — Irrigation and Drainage Engineering, chapter 8, asked 2× - [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× - [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× - [Cross drainage: Q 50, HFD 400, d 1.55 m](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Acd-q50-fsd155-hfd400) — Irrigation and Drainage Engineering, chapter 8, asked 2× - [Cross drainage: canal 125, drainage 64](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Acd-table-q125-drain64) — 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 ## Related in other subjects - [Irrigation channel earthwork, bed 5 m, 1 in 3000](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Airrigation-channel-j) — Estimating and Costing, chapter 6 - [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 - [Irrigation canal earthwork, 0-600 m](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Airrigation-canal-k-drop) — 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