---
title: "Thickness of launching apron, 7 m shank"
subject: "Irrigation and Drainage Engineering"
chapter: 6
key: "semester_6/irrigation_and_drainage_engineering:launching-apron-shank-7m-q8000"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/launching-apron-shank-7m-q8000
site: BCT Engineering
---

# Thickness of launching apron, 7 m shank

Irrigation and Drainage Engineering · Chapter 6: River Training Works

- Asked in: 2068 Baisakh (old course), 9 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/launching-apron-shank-7m-q8000
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-6

## Question

Calculate the thickness of a 7 m long launching apron of loosed stones for a shank portion of guide bund at a bridge site of a river having design flood of 8000 m³/s and flood depth of 5 m. Assume that average diameter of river bed material at flood time is 0.3 mm.

## Short answer

With d=0.3 mm, f=0.964, R=9.52 m, D'=1.5R−5=9.27 m, t=1.20 m. Volume equality for 7 m width: T×7 = 1.5t×√5×D' → T=5.33 m. Launched thickness 1.80 m; required width 13.91 m, so 7 m apron is thick to compensate.

## Answer

A launching apron of loose stone is laid at the toe of the guide bund. When scour occurs it launches down a 2H:1V slope. The laid thickness is found by equating the stone volume before and after launching.

#### Data
$Q = 8000$ m³/s, flood depth $h = 5$ m, $d = 0.3$ mm, laid width of apron $= 7$ m (shank portion).

#### Step 1. Silt factor and scour depth
$$
\begin{aligned} f &= 1.76\sqrt{d_{mm}} = 1.76\sqrt{0.3} = 0.964 \\ R &= 0.47\left(\frac{Q}{f}\right)^{1/3} = 0.47\left(\frac{8000}{0.964}\right)^{1/3} = 9.52\ \text{m} \end{aligned}
$$

Maximum scour at the shank: $1.5R = 14.27$ m below HFL. Scour below the bed: $D' = 1.5R - h = 14.27 - 5 = 9.27$ m.

#### Step 2. Pitching and launched thickness
$$
t = 0.06\,Q^{1/3} = 0.06\times20.00 = 1.20\ \text{m}, \qquad 1.5t = 1.80\ \text{m}
$$

#### Step 3. Thickness of the 7 m apron before launching
Slope length of launched apron $= \sqrt5\,D' = 2.236\times9.27 = 20.74$ m.

$$
\begin{aligned} T\times7 &= 1.5t\times\sqrt5 D' = 1.80\times20.74 \\ T &= 5.33\ \text{m} \end{aligned}
$$

**Answer:** thickness of the 7 m wide apron as laid $T = 5.33$ m (it launches to 1.80 m thick on the 2:1 slope). A 7 m apron is short against a required width of $1.5D' = 13.91$ m, so a thick apron is needed; it may be better to widen it to $13.9$ m, when $T = 2.68$ m.

```text
  pitching
  ___\__ T = 5.33 m
 bed __|<-- 7 m -->|___ river bed
   after launch: 2H:1V, 1.80 m thick, D' = 9.27 m
```

## Check yourself

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

1. What is the silt factor for d = 0.3 mm?
   A. 1.76 x 0.3 = 0.528
   B. 1.76 / sqrt(0.3) = 3.21
   C. 1.76 sqrt(0.3) = 0.964
   D. 0.3 sqrt(1.76) = 0.40
   Answer: C. Silt factor is 1.76 times the square root of d in mm. (Key point: Silt factor)

2. How is D' found for the shank here?
   A. D' = 2R - h = 14.0 m
   B. D' = 1.5R = 14.27 m
   C. D' = R - h = 4.52 m
   D. D' = 1.5R - h = 14.27 - 5 = 9.27 m
   Answer: D. Max shank scour 1.5R = 14.27 m is below HFL, so subtract the 5 m flood depth. (Key point: Scour below bed)

3. How is the laid thickness T of the 7 m apron obtained?
   A. Equate volumes: T x 7 = 1.5t x sqrt(5)D'
   B. T = 1.5t
   C. T x 7 = t x D'
   D. T = sqrt(5) t regardless of width
   Answer: A. The stone volume per metre laid (T x width) equals that on the launched slope (1.5t x sqrt(5)D'), giving T = 5.33 m. (Key point: Volume equality)

4. What does the answer conclude about a 7 m wide apron?
   A. It is more than adequate, so it can be thinner
   B. It is short of the required 1.5D' = 13.9 m, so it needs a very thick layer (5.33 m); widening to 13.9 m gives T = 2.68 m
   C. It needs no change since T = 1.80 m
   D. It cannot launch at all on a 2:1 slope
   Answer: B. Narrower aprons must be thicker to hold the same volume; the required width is 1.5D'. (Key point: Short apron consequence)

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