---
title: "Syphonic aqueduct levels, Q 36"
subject: "Irrigation and Drainage Engineering"
chapter: 8
key: "semester_6/irrigation_and_drainage_engineering:siphon-aqueduct-q36-bed28"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/siphon-aqueduct-q36-bed28
site: BCT Engineering
---

# Syphonic aqueduct levels, Q 36

Irrigation and Drainage Engineering · Chapter 8: Cross-Drainage structures

- Asked in: 2071 Magh, 10 marks
- Video: [Siphon Aqueduct | Cross Drainage Structure | Irrigation Engineering| IOE, TU](https://www.youtube.com/watch?v=VKfu13VWL2Y) — Parash Joshi - Civil Construction and Tutor
- 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/siphon-aqueduct-q36-bed28
- 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: 36 cumecs, Full supply depth: 1.5 m, Bed width: 28 m, Bed level: 210.4 m, Side slope: 1.5 H:1 V. Drainage Data: Discharge: 400 cumecs, HFL: 211.0 m, Bed width: 14 m, Bed level: 208.6 m, General ground level: 210.5 m. Determine bed and water level at four critical locations of the canal waterway at transitions of syphonic aqueduct.

## Short answer

Bed and water levels at four sections: normal canal start: 210.40/211.90 m; start of trough: 210.25/211.75 m; end of trough: 210.19/211.69 m; normal canal outlet: 210.25/211.75 m. (Canal flumed to 14 m wide trough, losses by Bernoulli with contraction 0.3Δhv and expansion 0.5Δhv.)

## Answer

At a syphonic aqueduct the canal is flumed into a rectangular trough over the drainage barrels. The levels follow from Bernoulli's equation between the normal canal and the trough, allowing losses of 0.3 Δh_v in the contraction (inlet) and 0.5 Δh_v in the expansion (outlet).

**Assumptions:** A drainage bed width of 14 m is far too narrow to carry 400 m³/s at a depth of 2.4 m, so the given 14 m is taken as the flumed width of the canal trough; trough $n$ = 0.015; Lacey's waterway is used only to find the trough length.

#### Normal canal
$A_1=(B+zD)D=(28+1.5\times1.5)\times1.5$ = 45.38 m², $V_1$ = 36/45.38 = 0.793 m/s, $h_{v1}$ = 0.0321 m, FSL $W_1$ = 210.40 + 1.5 = 211.90 m.

#### Trough
Drainage waterway by Lacey: $P=4.75\sqrt{400}$ = 95.0 m, so the trough is about 109.2 m long (12 spans of 8 m, piers 1.2 m). Canal flumed to $B_t$ = 14 m, depth 1.5 m:
- $V_t$ = 36/(14 × 1.5) = 1.714 m/s, $h_{vt}$ = 0.1498 m, Froude number 0.45 (subcritical)
- $R$ = 1.235 m, $S=(nV/R^{2/3})^2$ = 0.000499 (n = 0.015), $h_f$ = 0.000499 × 109.2 = 0.054 m
- Inlet length (2:1 splay) = T − B_t = 32.50 − 14 = 18.5 m; outlet length (3:1 splay) = 27.8 m

#### Levels at the four sections

$$
\begin{aligned} W_2 &= W_1 + h_{v1} - h_{vt} - 0.3(h_{vt}-h_{v1}) \\ W_3 &= W_2 - h_f \\ W_4 &= W_3 + h_{vt} - h_{v1} - 0.5(h_{vt}-h_{v1}) \end{aligned}
$$

| Section | Location | Bed level (m) | Water level (m) |
|---|---|---|---|
| 1 | Normal canal, start of inlet transition | 210.400 | 211.900 |
| 2 | Start of trough (end of inlet) | 210.247 | 211.747 |
| 3 | End of trough (start of outlet) | 210.193 | 211.693 |
| 4 | Normal canal, end of outlet transition | 210.251 | 211.751 |

Total head lost in the work = 211.900 − 211.751 = 0.149 m. Trough bed = water level − 1.5 m.

Check: with a 0.6 m slab the barrel soffit is at 209.59 m, below the HFL of 211.00 m by 1.41 m, so the barrels run full (syphonic).

**Answer:** bed/water levels = 210.40/211.90, 210.25/211.75, 210.19/211.69, 210.25/211.75 m.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. For the normal canal (B = 28 m, D = 1.5 m, z = 1.5, Q = 36 m3/s), how are the velocity and velocity head found?
   A. Area = B x D = 42 m2 and V = Q x A
   B. Area = (B + zD) D = 45.38 m2, V = Q/A = 0.793 m/s, hv = V^2/2g = 0.0321 m
   C. Area = (B + 2zD) D, then V = Q/A^2
   D. hv = V/2g = 0.0404 m
   Answer: B. The trapezoidal area (B + zD)D gives 45.38 m2, V = 36/45.38 = 0.793 m/s and hv = V^2/2g = 0.0321 m. (Key point: Normal canal section properties)

2. Which relation gives the water level W2 at the start of the trough?
   A. W2 = W1 - hv1 + hvt
   B. W2 = W1 + hv1 - hvt - 0.3(hvt - hv1)
   C. W2 = W1 + hvt - hv1 + 0.5(hvt - hv1)
   D. W2 = W1 - hf
   Answer: B. Velocity head rises in the trough, so water surface drops by the gain in velocity head plus the contraction loss 0.3 delta hv. (Key point: Water level at start of trough)

3. At section 2 the water level is 211.747 m and the trough depth is 1.5 m. What is the trough bed level?
   A. 213.247 m
   B. 211.747 m
   C. 210.247 m, because bed = water level - full supply depth
   D. 209.747 m
   Answer: C. The trough keeps the same depth 1.5 m, so bed = 211.747 - 1.5 = 210.247 m. (Key point: Bed level from water level in trough)

4. The barrel soffit is at 209.59 m and HFL is 211.00 m. What does this show?
   A. Soffit is below HFL by 1.41 m, so the barrels run full and the aqueduct is syphonic
   B. The soffit is above HFL, so the barrels run with a free surface
   C. The trough is at the same level as HFL
   D. The barrels are too deep to function
   Answer: A. HFL stands above the soffit, so the barrels flow full under pressure, which is syphonic action. (Key point: Siphonic action check)

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