---
title: "Bell's waterway and guide bund, 7500 m3/s"
subject: "Irrigation and Drainage Engineering"
chapter: 6
key: "semester_6/irrigation_and_drainage_engineering:barrage-waterway-bells-guide-bund"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/barrage-waterway-bells-guide-bund
site: BCT Engineering
---

# Bell's waterway and guide bund, 7500 m3/s

Irrigation and Drainage Engineering · Chapter 6: River Training Works

- Asked in: 2078 Chaitra, 8 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/barrage-waterway-bells-guide-bund
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-6

## Question

A barrage is to be constructed across a river, having 100 year flood discharge of 7500 m³/s and high flood level is 238.00 m. River bed level is 232.00 m and average diameter of bed material is 5.07 mm. Find out the desired waterway for the barrage. Design Bell's guide bunds including launching apron.

## Answer

#### Desired waterway of the barrage
Lacey's regime waterway (wetted perimeter) is
$$
W = 4.75\sqrt{Q} = 4.75\sqrt{7500} = 411.4\ \text{m}
$$
For a barrage the waterway is generally kept equal to this regime width (1.0 to 1.2 times); adopt **$W = 411$ m** between abutments. Flood depth $h = 238.0 - 232.0 = 6.0$ m.

#### Data and design basis (Bell's guide bund)
- Bell's guide bund is designed on Lacey's regime width; bed material is gravel (5.07 mm).
- Silt factor (Lacey): $f = 1.76\sqrt{d_{mm}} = 1.76\sqrt{5.07} = 3.96$
- Flood depth above bed: $h = 238.0 - 232.0 = 6.00$ m
- Design discharge for scour/apron: $Q = 7500$ m³/s

#### 1. Waterway and length of guide bund
Lacey's regime waterway: $W = 4.75\sqrt{Q} = 4.75\sqrt{7500} = 411.36$ m. Adopt $W \approx 411$ m.
Length of guide bund (Garg): upstream shank $=1.0$ to $1.5\,W$, downstream tail $=0.2$ to $0.5\,W$. Adopt
$$
\begin{aligned} L_{us} &= 1.25W = 1.25\times 411 = 514\ \text{m} \\ L_{ds} &= 0.25W = 103\ \text{m} \end{aligned}
$$
Curved heads: upstream radius $R_u \approx 0.5W = 206$ m with sweep $120^\circ$ to $145^\circ$ (adopt $120^\circ$); downstream radius $R_d \approx 0.25W = 103$ m with sweep about $45^\circ$.
Arc length of upstream head $= R_u\theta = 206\times 2.094 = 430$ m, so total length on the upstream side $\approx 944$ m.

#### 2. Thickness of stone pitching
$$
t = 0.06\,Q^{1/3} = 0.06\times 7500^{1/3} = 0.06\times 19.57 = 1.17\ \text{m}
$$
Adopt $t \approx 1.2$ m (pitching on the river side slope 2:1, over a 0.15 to 0.3 m graded filter).

#### 3. Scour depth and launching apron
Lacey's normal scour depth:
$$
R = 0.47\left(\frac{Q}{f}\right)^{1/3} = 0.47\left(\frac{7500}{3.96}\right)^{1/3} = 5.81\ \text{m}
$$
Maximum scour below HFL: $2R$ at the upstream nose, $1.5R$ at the shank (straight portion).
The apron must launch to the slope $2H:1V$, so its horizontal width is $1.5D'$ and, when launched, it covers a slope length $\sqrt5\,D'$ with thickness $1.5t$.

| Portion | Scour factor | Scour depth below HFL | Depth below bed $D'$ | Apron length $1.5D'$ |
|---|---|---|---|---|
| Nose (u/s curved head) | 2.0R | 11.63 m | 5.63 m | 8.44 m |
| Shank (straight) | 1.5R | 8.72 m | 2.72 m | 4.08 m |

Thickness: pitching $t = 1.17$ m, so the launched apron thickness is $1.5t = 1.5\times1.17 = 1.76$ m. Equating volumes per metre, the thickness as laid over $1.5D'$ width is $T = \dfrac{1.5t\times\sqrt5 D'}{1.5D'} = \sqrt5\,t = 2.63$ m (about $2.25t$).

#### Summary
| Item | Value |
|---|---|
| Lacey waterway $W$ | 411.36 m (adopt 411 m) |
| Length of guide bund (u/s) | 514 m; d/s tail 103 m |
| Pitching thickness $t$ | 1.17 m |
| Apron at shank: width $1.5D'$ / thickness | 4.08 m / 1.76 m launched (2.63 m laid) |
| Apron at nose: width / thickness | 8.44 m / 1.76 m launched (2.63 m laid) |

#### Sketches
Plan of guide bunds:
```text
 U/S                                          D/S
                       bridge / weir axis
   Shank (straight)                |
 ________________________________  |  ___
/  1.0-1.5 W upstream            \ | /   \  tail
\________________________________/=|=\___/  0.25 W
 curved head                       |
 R, sweep 120 deg    <-- waterway W -->
 ________________________________  |  ___
/                                \ | /   \
\________________________________/=|=\___/
```
Section at the shank (straight portion):
```text
           top width 6 m
         ___________  <- HFL + 1.5 m
        /           \
 HFL ---/-------------\---  2:1 slopes
       / pitching t    \
 bed__/__ filter ______ \___
      \_ launching apron _/ (launches at 2:1)
```

## Check yourself

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

1. For a design flood of 7500 m3/s, the guide bund design is based on the Lacey regime width. Which value is obtained?
   A. W = 4.75 sqrt(Q) = 411 m
   B. W = 4.75 Q^(1/3) = much smaller (about 93 m)
   C. W = 2.71 sqrt(Q) (about 235 m)
   D. W = 0.47 (Q/f)^(1/3) (about 9 m)
   Answer: A. Lacey's regime waterway is W = 4.75 sqrt(Q); it fixes the guide bund lengths and radii. (Key point: Lacey regime waterway)

2. The silt factor for bed material with d = 5.07 mm is calculated using:
   A. f = 1.76 d_mm = 8.9
   B. f = 0.47 sqrt(d_mm) = 1.06
   C. f = 1.76 sqrt(d_mm) = 3.96
   D. f = 4.75 sqrt(d_mm) = 10.7
   Answer: C. Lacey's silt factor f = 1.76 sqrt(d in mm); coarse gravel gives a large f and a smaller scour depth. (Key point: Lacey silt factor)

3. With Q = 7500, f = 3.96, Lacey's normal scour depth R = 0.47 (Q/f)^(1/3) equals about:
   A. 11.63 m
   B. 5.81 m
   C. 8.72 m
   D. 2.72 m
   Answer: B. R = 0.47 (1894)^(1/3) = 5.81 m; 11.63 m is the nose scour 2R, and 8.72 m is the shank scour 1.5R. (Key point: Scour depth)

4. Lacey scour depth R = 5.81 m and flood depth h = 6.0 m. What is the apron horizontal width at the nose (scour 2.0R below HFL, launching slope 2H:1V)?
   A. Width = 2.0R = 11.62 m (forgetting to subtract the flood depth)
   B. Width = 2D' = 11.26 m
   C. Width = D' = 5.63 m
   D. D' = 2.0R - h = 5.63 m, so width 1.5D' = 8.44 m
   Answer: D. The apron must cover scour below the bed: D' = (factor x R) - h. At 2H:1V the apron width laid is 1.5D'. (Key point: Depth below bed and apron width)

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