---
title: "Kennedy design: Q 10, n 0.0245"
subject: "Irrigation and Drainage Engineering"
chapter: 4
key: "semester_6/irrigation_and_drainage_engineering:kennedy-q10-n00245"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/kennedy-q10-n00245
site: BCT Engineering
---

# Kennedy design: Q 10, n 0.0245

Irrigation and Drainage Engineering · Chapter 4: Design of Canals

- Asked in: 2070 Chaitra (old course), 6 marks; 2064 Jestha (old course), 8 marks (asked 2 times)
- 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-q10-n00245
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-4

## Question

Design a canal using Kennedy formulation with following data: Q = 10 cumec, Manning roughness coefficient = 0.0245, slope of bed = 0.0002, m = 1 and side slope of canal 0.5:1 (H:V).

## Short answer

By trial: assume depth, compute V0=0.55D^0.64, then Manning's V= (1/0.0245)R^(2/3)√0.0002. Match occurs at D=0.89 m. Required bed width 21.6 m, side slope 0.5:1, velocity 0.51 m/s, bed slope 1/5000.

## Answer

Given: $Q = 10\ \text{m}^3/\text{s}$, $n = 0.0245$, $S = 0.0002$ (1 in 5000), $m = 1$, 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) |
|---|---|---|---|---|---|---|
| 0.70 | 0.438 | 22.84 | 32.28 | 33.85 | 0.675 | 0.444 |
| 0.80 | 0.477 | 20.97 | 25.82 | 27.61 | 0.760 | 0.481 |
| 0.89 | 0.510 | 19.59 | 21.57 | 23.56 | 0.832 | 0.510 |
| 1.00 | 0.550 | 18.18 | 17.68 | 19.92 | 0.913 | 0.543 |

The velocities $V$ and $V_0$ become equal at $D \approx 0.89$ m, so this is the required depth.

#### Final section

Adopt $D = 0.89$ m, $B = 21.6$ m.

$$
\begin{aligned}
A &= (21.6 + 0.5\times 0.89)\times 0.89 = 19.62\ \text{m}^2 \\
P &= 21.6 + 2\times 0.89\sqrt{1+0.5^2} = 23.59\ \text{m},\quad R = 0.832\ \text{m} \\
V &= 0.511\ \text{m/s},\quad V_0 = 0.55\times 1\times 0.89^{0.64} = 0.510\ \text{m/s} \\
Q &= AV = 19.62\times 0.511 = 10.02\ \text{m}^3/\text{s}
\end{aligned}
$$

**Answer:** Depth $D \approx 0.89$ m, bed width $B \approx 21.6$ m, side slope 0.5H:1V, bed slope 1 in 5000, velocity $\approx 0.51$ m/s (discharge check 10.0 m³/s, i.e. within about 0.2% of the design value).

## Check yourself

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

1. How is a Kennedy channel designed in this answer?
   A. Assume D, compute V0, then A, B, P, R and Manning's V; repeat until V = V0
   B. Compute V directly from Q and f
   C. Assume the slope and compute f
   D. Choose P = 4.75 sqrt(Q) and find D
   Answer: A. Kennedy design is trial and error on depth until the Manning velocity equals critical velocity. (Key point: Kennedy method)

2. For m = 1 and D = 0.89 m, V0 = 0.55 m D^0.64 is about
   A. 0.89 m/s
   B. 0.51 m/s
   C. 0.28 m/s
   D. 1.2 m/s
   Answer: B. 0.89^0.64 = 0.928, so V0 = 0.55 x 0.928 = 0.51 m/s. (Key point: Critical velocity)

3. How is the bed width found from the trial depth?
   A. B = A/D^2
   B. B = P - D
   C. B = (A - zD^2)/D with A = Q/V0
   D. B = 4.75 sqrt(Q)
   Answer: C. For a trapezoid A = BD + zD^2, so B = (A - zD^2)/D. (Key point: Area and width)

4. What section does the final answer give?
   A. D about 1.27 m, B about 18.4 m
   B. D about 0.70 m, B about 32.3 m
   C. D about 1.00 m, B about 17.7 m
   D. D about 0.89 m, B about 21.6 m
   Answer: D. At D = 0.89 m, V = V0 = 0.51 m/s and Q = AV = 10.02 m^3/s. (Key point: Result)

## Close variants set in other exams

- [Kennedy design: Q 40, n 0.018](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Akennedy-q40-n018-s00020) — Irrigation and Drainage Engineering, chapter 4, asked 3×

## Related in Irrigation and Drainage Engineering

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- [Kennedy design: Q 7 cumec](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Akennedy-q7-n025-m11) — Irrigation and Drainage Engineering, chapter 4, asked 2×
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