---
title: "Kennedy: Q 30, V 1.75 m/s"
subject: "Irrigation and Drainage Engineering"
chapter: 4
key: "semester_6/irrigation_and_drainage_engineering:kennedy-q30-velocity-175"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/kennedy-q30-velocity-175
site: BCT Engineering
---

# Kennedy: Q 30, V 1.75 m/s

Irrigation and Drainage Engineering · Chapter 4: Design of Canals

- Asked in: 2077 Chaitra, 8 marks
- Video: [Design of Channel by Kennedy's theory || Type 1 Kennedy's solved example with detail design steps](https://www.youtube.com/watch?v=aQtoJkNRygQ) — Professor Nidhi Trivedi
- 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-q30-velocity-175
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-4

## Question

An irrigation channel is to carry a full supply discharge of 30 m³/s at a velocity of 1.75 m/s. The side slopes are to be 1:1. The ratio of full supply depth to bed width is to be 1:6. Assuming the Manning's n as 0.018, calculate the full supply depth, bed width, and bed slope of the channel using Kennedy's method.

## Short answer

Full supply depth 1.56 m, bed width 9.39 m, bed slope 1 in 1339 (0.000747). Note: critical velocity ratio m=2.39 exceeds typical alluvial range; section suitable only for lined or well-protected channel.

## Answer

Given: $Q = 30\ \text{m}^3/\text{s}$, $V = 1.75$ m/s, side slope 1H:1V, $D:B = 1:6$, $n = 0.018$.

#### Step 1: Area

$$
A = \frac{Q}{V} = \frac{30}{1.75} = 17.143\ \text{m}^2
$$

#### Step 2: Depth and bed width

With $B = 6D$ and $z = 1$:

$$
\begin{aligned}
A &= (B + zD)D = (6D + D)D = 7D^2 \\
D &= \sqrt{17.143/7} = 1.565\ \text{m} \approx 1.56\ \text{m} \\
B &= 6D = 9.39\ \text{m}
\end{aligned}
$$

#### Step 3: Bed slope (Manning)

$$
\begin{aligned}
A &= (9.39 + 1.56)\times 1.56 = 17.08\ \text{m}^2 \\
P &= B + 2D\sqrt{2} = 9.39 + 2\times 1.56\times 1.4142 = 13.80\ \text{m} \\
R &= \frac{A}{P} = 1.238\ \text{m} \\
S &= \left(\frac{Vn}{R^{2/3}}\right)^2 = \left(\frac{1.75\times 0.018}{1.238^{2/3}}\right)^2 = 0.000747 = \frac{1}{1339}
\end{aligned}
$$

#### Step 4: Kennedy check

Critical velocity $V_0 = 0.55D^{0.64} = 0.55\times 1.56^{0.64} = 0.731$ m/s, so the critical velocity ratio is $m = V/V_0 = 2.39$. This is much higher than the usual 0.8-1.2, so a velocity of 1.75 m/s suits only a stable boundary (a lined or well-protected channel), not an ordinary alluvial earth canal.

**Answer:** Full supply depth $\approx 1.56$ m, bed width $\approx 9.39$ m, bed slope $\approx 1$ in 1339 (0.000747).

## Check yourself

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

1. How is the flow area obtained here?
   A. A = Q x V = 52.5 m^2
   B. A = Q/V0 using Kennedy's V0
   C. A = Q/V = 30/1.75 = 17.14 m^2
   D. A = V/Q = 0.058 m^2
   Answer: C. Discharge and the given velocity fix the area directly. (Key point: Area from velocity)

2. With B = 6D and side slope 1:1, what is the area in terms of D, and what is D?
   A. A = 6D^2, so D = 1.69 m
   B. A = 8D^2, so D = 1.46 m
   C. A = 7D, so D = 2.45 m
   D. A = (B + D)D = 7D^2, so D = sqrt(17.143/7) = 1.56 m
   Answer: D. (6D + D)D = 7D^2, so D = 1.565 m and B = 9.39 m. (Key point: Depth from D:B ratio)

3. How is the bed slope found?
   A. From Manning: S = (V n / R^(2/3))^2 with R = A/P
   B. From Kennedy's V0 = 0.55 D^0.64
   C. From Lacey's S = f^(5/3)/(3340 Q^(1/6))
   D. From S = D/B
   Answer: A. Given V, n and R, rearranging Manning's formula gives S = 0.000747, about 1 in 1339. (Key point: Bed slope)

4. The Kennedy check gives m = V/V0 = 2.39. What does this mean?
   A. The channel will silt up heavily
   B. The velocity is far above the usual 0.8-1.2, so it suits only a lined or protected channel
   C. The design is ideal for an ordinary earth canal
   D. The side slope must be flatter than 1:1
   Answer: B. V0 = 0.731 m/s, and V is 2.39 times it, so an unprotected alluvial canal would scour. (Key point: Kennedy check)

## Related in Irrigation and Drainage Engineering

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