--- title: "Aqueduct: canal 35, drainage 350" subject: "Irrigation and Drainage Engineering" chapter: 8 key: "semester_6/irrigation_and_drainage_engineering:aqueduct-q35-drain350-lacey1" source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/aqueduct-q35-drain350-lacey1 site: BCT Engineering --- # Aqueduct: canal 35, drainage 350 Irrigation and Drainage Engineering · Chapter 8: Cross-Drainage structures - Asked in: 2063 Baisakh (old course), 12 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/aqueduct-q35-drain350-lacey1 - Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-8 ## Question Design an aqueduct for the following data. Draw a neat sketch of designed aqueduct showing all dimensions and parameters. Canal: Q = 35 m³/s; FSL = 200.00; CBL = 198.5; B = 22 m; side slope 1.5:1. Drainage: Q = 350 m³/s; HFL = 196.5; DBL = 193.5; GL = 199.0; f (Lacey's) = 1. Assume flumed width of canal = 12 m and depth in transition = canal depth. ## Short answer Drainage waterway: 12 spans of 8 m, clear 96 m (Lacey's P=88.9 m). Canal flumed to 12 m wide trough, depth 1.5 m; velocity 1.944 m/s, friction loss 0.073 m. Total head loss including transitions is 0.189 m, so downstream canal bed is lowered by 0.189 m. ## Answer The canal ($Q$ = 35 m³/s) crosses a drainage of $Q$ = 350 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:** Flumed width of canal 12 m and depth in trough = canal depth 1.5 m (as given); Lacey's $f$ = 1; trough $n$ = 0.015; slab 0.6 m. #### 1. Type of structure Canal bed level (198.50 m) is higher than HFL of the drainage (196.50 m) by 2.00 m, enough for free board and slab depth. The canal can be carried in a trough over the drain with free flow beneath, so an **aqueduct** is suitable. #### 2. Drainage waterway Lacey's regime perimeter (for a natural stream): $$ P = 4.75\sqrt{Q} = 4.75\sqrt{350} = 88.9\ \text{m} $$ Provide **12 spans of 8 m** with piers 1.2 m thick: clear waterway = 12 × 8 = **96 m** (> 88.9 m). Overall length = 96 + 11 × 1.2 = **109.2 m**. Check: mean velocity = Q/(L·d) = 350/(96 × 3.00) = 1.22 m/s. Lacey's regime depth $R = 0.47(Q/f)^{1/3}$ = 3.31 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 $A_1=(B+zD)D$ = (22 + 1.5 × 1.5) × 1.5 = 36.38 m², $V_1$ = 35/36.38 = 0.962 m/s, $h_{v1}=V_1^2/2g$ = 0.0472 m. Top width $T=B+2zD$ = 26.50 m. To save cost, the canal is flumed to a rectangular trough of width $B_t$ = **12 m**, with the same full supply depth 1.5 m (the trough is as long as the drainage waterway, 109.2 m). - Trough area = 12 × 1.5 = 18.00 m²; $V_t$ = 35/18.00 = 1.944 m/s (acceptable, < 2.5 m/s); $h_{vt}$ = 0.1927 m - Froude number = 0.51 < 1, flow is subcritical, so there is no hydraulic jump. - Hydraulic radius $R=A/P$ = 18.00/15.00 = 1.200 m; friction slope $S=(nV/R^{2/3})^2$ = 0.000667 (Manning's n = 0.015); friction loss in trough $h_f=S\,L$ = 0.000667 × 109.2 = 0.073 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 = 26.50 − 12 = **14.5 m** - Outlet length = 3 × (T − B_t)/2 = **21.8 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): $$ \begin{aligned} W_2 &= W_1 + h_{v1} - h_{vt} - 0.3(h_{vt}-h_{v1}) \\ W_3 &= W_2 - h_f \\ W_4 &= W_3 + h_{vt} - h_{v1} - 0.5(h_{vt}-h_{v1}) \end{aligned} $$ $W_1$ = 200.000 m, so $W_2$ = 199.811 m, $W_3$ = 199.738 m, $W_4$ = 199.811 m. Trough bed = water level − 1.5 m. | Section | Location | Bed level (m) | FSL (m) | |---|---|---|---| | 1 | Normal canal, start of inlet transition | 198.500 | 200.000 | | 2 | End of inlet transition = start of trough | 198.311 | 199.811 | | 3 | End of trough = start of outlet transition | 198.238 | 199.738 | | 4 | End of outlet transition = normal canal | 198.311 | 199.811 | Total loss of head = 200.000 − 199.811 = 0.189 m, so the canal bed downstream of the work is 0.189 m lower than upstream. Check: soffit of trough slab (0.6 m thick) = 197.64 m; HFL + free board 0.6 m = 197.10 m. Clearance adequate. #### Sketch of designed aqueduct ```text Longitudinal section along canal FSL 200.00 ~~~~\ /~~~~ 199.81 bed 198.50 ----\_ trough bed 198.31 _/---- inlet | 12 spans x 8 m, piers 1.2 m | outlet (wing walls) (wing walls) HFL 196.50 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ bed 193.50 ------------------------------- Plan: 22 m -> 12 m (2:1 inlet) ... trough 109.2 m ... 12 m -> 22 m (3:1) ``` **Answer:** drainage waterway 96 m clear (12 × 8 m, overall 109.2 m); canal flumed to 12 m wide trough; bed/FSL at the four sections = 198.50/200.00, 198.31/199.81, 198.24/199.74, 198.31/199.81 m. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is an aqueduct (not a siphon aqueduct) suitable here? A. Canal bed (198.50 m) is 2.00 m above drainage HFL (196.50 m), so the trough passes over with free flow beneath B. Drainage HFL is above the canal bed C. The canal discharge is smaller than the drainage discharge D. The canal bed is lower than the ground level Answer: A. When the canal bed is above HFL with room for free board and slab depth, the drain flows freely under the trough. (Key point: Choice of aqueduct) 2. What waterway is provided for the 350 m^3/s drainage? A. P = 88.9 m; 11 spans of 8 m = 88 m B. P = 4.75 sqrt(350) = 88.9 m; 12 spans of 8 m = 96 m clear, overall 109.2 m C. P = 4.75 x 350 = 1662 m D. A single 12 m span equal to the flumed width Answer: B. Lacey's perimeter gives 88.9 m; 96 m clear is provided, and adding 11 piers of 1.2 m gives 109.2 m overall. (Key point: Drainage waterway) 3. In the 12 m flumed trough, what is the check on flow, and what does it show? A. Froude number 1.5, so a jump forms in the trough B. Velocity 0.96 m/s, equal to the normal canal C. Velocity 1.944 m/s and Froude number 0.51 < 1, so flow is subcritical and no hydraulic jump forms D. Froude number is not needed in flumed sections Answer: C. V = 35/18 = 1.944 m/s is below 2.5 m/s and Fr = 0.51 is below 1, so flow is subcritical. (Key point: Flumed trough check) 4. How are the transition lengths found for splays of 2:1 inlet and 3:1 outlet? A. Length = splay x Bt: 24 m and 36 m B. Both transitions are 14.5 m C. Length = splay x (T + Bt)/2 D. Length = splay x (T - Bt)/2 with T = 26.50 m and Bt = 12 m: inlet 14.5 m, outlet 21.8 m Answer: D. Each side contracts by (T - Bt)/2 = 7.25 m, so inlet = 2 x 7.25 = 14.5 m and outlet = 3 x 7.25 = 21.8 m. 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