---
title: "Kennedy design: Q 40, slope 1 in 5000"
subject: "Irrigation and Drainage Engineering"
chapter: 4
key: "semester_6/irrigation_and_drainage_engineering:kennedy-q40-slope-15000"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/kennedy-q40-slope-15000
site: BCT Engineering
---

# Kennedy design: Q 40, slope 1 in 5000

Irrigation and Drainage Engineering · Chapter 4: Design of Canals

- Asked in: 2079 Chaitra, 6 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/kennedy-q40-slope-15000
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-4

## Question

Design an irrigation channel to carry 40 cumecs at a slope of 1 in 5000 with Manning's n = 0.0225 and critical velocity ratio (m) = 1.0.

## Short answer

Depth 2.50 m, bed width 15.0 m, side slopes 0.5H:1V, bed slope 1 in 5000, velocity 0.99 m/s (discharge 40.2 m³/s).

## Answer

Given: $Q = 40\ \text{m}^3/\text{s}$, $n = 0.0225$, $S = 0.0002$ (1 in 5000), $m = 1.0$. The side slope is not given, so 0.5H:1V is assumed. Manning's formula is used with the given $n$.

#### Method (Kennedy's silt theory, trial and error)

1. Assume depth $D$.
2. Kennedy's critical velocity: $V_0 = 0.55\,m\,D^{0.64}$.
3. Area $A = Q/V_0$, bed width $B = (A - zD^2)/D$, perimeter $P = B + 2D\sqrt{1+z^2}$, $R = A/P$.
4. Find $V$ from Manning's formula, $V = \frac{1}{n}R^{2/3}S^{1/2}$.
5. Repeat until $V = V_0$.

#### Trials

| D (m) | $V_0$ (m/s) | A (m²) | B (m) | P (m) | R (m) | V (m/s) |
|---|---|---|---|---|---|---|
| 2.00 | 0.857 | 46.67 | 22.34 | 26.81 | 1.741 | 0.910 |
| 2.20 | 0.911 | 43.91 | 18.86 | 23.78 | 1.847 | 0.946 |
| 2.50 | 0.989 | 40.46 | 14.93 | 20.52 | 1.971 | 0.988 |
| 2.70 | 1.039 | 38.51 | 12.91 | 18.95 | 2.032 | 1.008 |

The velocities $V$ and $V_0$ become equal at $D \approx 2.50$ m, so this is the required depth.

#### Final section

Adopt $D = 2.50$ m, $B = 15.0$ m.

$$
\begin{aligned}
A &= (15.0 + 0.5\times 2.50)\times 2.50 = 40.62\ \text{m}^2 \\
P &= 15.0 + 2\times 2.50\sqrt{1+0.5^2} = 20.59\ \text{m},\quad R = 1.973\ \text{m} \\
V &= 0.989\ \text{m/s},\quad V_0 = 0.55\times 1.0\times 2.50^{0.64} = 0.989\ \text{m/s} \\
Q &= AV = 40.62\times 0.989 = 40.17\ \text{m}^3/\text{s}
\end{aligned}
$$

**Answer:** Depth $D \approx 2.50$ m, bed width $B \approx 15.0$ m, side slope 0.5H:1V, bed slope 1 in 5000, velocity $\approx 0.99$ m/s (discharge check 40.2 m³/s, i.e. within about 0.4% of the design value).

## Check yourself

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

1. In Kennedy's method with a known slope and n, what is the condition that fixes the correct depth?
   A. The area A equals the wetted perimeter P
   B. The Manning velocity V equals Kennedy's critical velocity V0
   C. The depth D equals the bed width B
   D. The hydraulic mean radius R equals 1 m
   Answer: B. Assume D, find V0 = 0.55 m D^0.64 and the section from Q/V0, then compute V by Manning; repeat until V = V0. (Key point: Kennedy trial-and-error)

2. Which formula supplies V in the trials, and with what n and S?
   A. Lacey's V = (Q f^2/140)^(1/6)
   B. V = 0.55 m D^0.64 with n = 0.0225
   C. Manning's V = (1/n) R^(2/3) S^(1/2) with n = 0.0225, S = 0.0002
   D. Chezy's formula with S = 5000
   Answer: C. V0 comes from Kennedy; the actual V comes from Manning with the given roughness and slope. (Key point: Manning with given n)

3. At which depth do V and V0 match?
   A. D about 2.00 m
   B. D about 2.70 m
   C. D about 3.50 m
   D. D about 2.50 m (both 0.989 m/s)
   Answer: D. At 2.5 m, V0 = 0.55 x 2.5^0.64 = 0.989 m/s and Manning gives the same. (Key point: Matching depth)

4. What is the adopted bed width?
   A. About 15.0 m
   B. About 22.3 m
   C. About 12.9 m
   D. About 5.0 m
   Answer: A. B = (A - 0.5D^2)/D = 14.93, adopted as 15.0 m. (Key point: Final width)

## Related in Irrigation and Drainage Engineering

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