---
title: "Kennedy design: Q 40, n 0.018"
subject: "Irrigation and Drainage Engineering"
chapter: 4
key: "semester_6/irrigation_and_drainage_engineering:kennedy-q40-n018-s00020"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/kennedy-q40-n018-s00020
site: BCT Engineering
---

# Kennedy design: Q 40, n 0.018

Irrigation and Drainage Engineering · Chapter 4: Design of Canals

- Asked in: 2073 Magh, 8 marks
- Video: [Design of canal by Kennedy's method problem 1](https://www.youtube.com/watch?v=FsoX7uIfxwo) — Simpleciviltamil
- 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-n018-s00020
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-4

## Question

Design a canal using Kennedy's formula with the following data: Q = 40 m³/s, Manning's roughness coefficient (n) = 0.018, bed slope(s) = 0.00020, m = 1.0 and side slope = 0.5:1 (H:V).

## Short answer

Depth 3.78 m, bed width 6.3 m, side slopes 0.5H:1V, bed slope 1 in 5000, velocity 1.29 m/s (discharge 39.9 m³/s).

## Answer

Given: $Q = 40\ \text{m}^3/\text{s}$, $n = 0.018$, $S = 0.0002$ (1 in 5000), $m = 1.0$, side slope 0.5H:1V. 

#### 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) |
|---|---|---|---|---|---|---|
| 3.00 | 1.111 | 36.00 | 10.50 | 17.21 | 2.092 | 1.285 |
| 3.40 | 1.204 | 33.23 | 8.07 | 15.68 | 2.120 | 1.297 |
| 3.78 | 1.288 | 31.05 | 6.33 | 14.78 | 2.101 | 1.289 |
| 4.20 | 1.378 | 29.03 | 4.81 | 14.20 | 2.044 | 1.265 |

The velocities $V$ and $V_0$ become equal at $D \approx 3.78$ m, so this is the required depth.

#### Final section

Adopt $D = 3.78$ m, $B = 6.3$ m.

$$
\begin{aligned}
A &= (6.3 + 0.5\times 3.78)\times 3.78 = 30.96\ \text{m}^2 \\
P &= 6.3 + 2\times 3.78\sqrt{1+0.5^2} = 14.75\ \text{m},\quad R = 2.099\ \text{m} \\
V &= 1.288\ \text{m/s},\quad V_0 = 0.55\times 1.0\times 3.78^{0.64} = 1.288\ \text{m/s} \\
Q &= AV = 30.96\times 1.288 = 39.87\ \text{m}^3/\text{s}
\end{aligned}
$$

**Answer:** Depth $D \approx 3.78$ m, bed width $B \approx 6.3$ m, side slope 0.5H:1V, bed slope 1 in 5000, velocity $\approx 1.29$ m/s (discharge check 39.9 m³/s, i.e. within about 0.3% 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. After finding A and B for an assumed D, how are P and R obtained for side slope 0.5:1?
   A. P = B + 2D and R = P/A
   B. P = B + D sqrt(1.5) and R = A x P
   C. P = B + 2D sqrt(1 + 0.5^2) and R = A/P
   D. P = B + 0.5D and R = A/B
   Answer: C. The sloping sides have length D sqrt(1 + z^2) each. (Key point: Perimeter and R)

3. What depth and bed width satisfy V = V0 here?
   A. D about 3.00 m and B about 10.5 m
   B. D about 4.20 m and B about 4.8 m
   C. D about 2.50 m and B about 15 m
   D. D about 3.78 m and B about 6.3 m
   Answer: D. At D = 3.78 m, V = V0 = 1.288 m/s. (Key point: Result)

4. What check confirms the adopted section?
   A. Q = A x V = 30.96 x 1.288 = 39.87, close to 40 m^3/s
   B. P equals B exactly
   C. R equals D/2 exactly
   D. V0 equals 1 m/s
   Answer: A. The rounded section carries within about 0.3% of the design discharge. (Key point: Discharge check)

## Close variants set in other exams

- [Kennedy design: Q 10, n 0.0245](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Akennedy-q10-n00245) — Irrigation and Drainage Engineering, chapter 4, asked 3×

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