---
title: "Design by permissible velocity approach"
subject: "Hydraulics"
chapter: 10
key: "semester_4/hydraulics:max-permissible-velocity-design-procedure"
source: https://www.bctengineer.com/q/semester_4/hydraulics/max-permissible-velocity-design-procedure
site: BCT Engineering
---

# Design by permissible velocity approach

Hydraulics · Chapter 10: Flow in mobile boundary channel

- Asked in: 2075 Baisakh, 4 marks; 2074 Bhadra, 4 marks; 2073 Bhadra, 4 marks (asked 3 times)
- Video: [ST-030 Permissible velocity method](https://www.youtube.com/watch?v=UgrfXmpj0qQ) — Dr. Philip De Groot
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/hydraulics/max-permissible-velocity-design-procedure
- Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-10

## Question

Explain the procedure of designing a channel (rigid / mobile boundary) by the maximum (minimum) permissible velocity approach, with appropriate expressions.

## Short answer

For rigid channels, select a minimum velocity Vmin (~0.6–0.9 m/s) to avoid sedimentation. For mobile channels, select a maximum permissible velocity Vmax from material tables or Kennedy's V0 = 0.55 m y^0.64. Then find A = Q/V, hydraulic radius from Manning, solve geometry for b and y, and verify velocity limits.

## Answer

The **maximum permissible velocity** is the greatest mean velocity that will not erode the channel boundary; the **minimum permissible velocity** is the smallest that prevents silting and weed growth. The velocity is chosen from tables or empirical formulas for the boundary material.

#### Rigid boundary (minimum velocity approach)

1. Choose a minimum velocity $V_{min}$ (typically 0.6 to 0.9 m/s for lined canals) to avoid sedimentation and weeds.
2. Choose side slope $z$, Manning's $n$ (from the lining) and the bed slope $S_0$.
3. Required area: $A = Q/V$ with $V \ge V_{min}$.
4. Manning's equation gives the hydraulic radius: $R = \left(\dfrac{nV}{\sqrt{S_0}}\right)^{3/2}$, and the wetted perimeter $P = A/R$.
5. Solve for depth and width from $A = (b + zy)y$ and $P = b + 2y\sqrt{1 + z^2}$.
6. Check that the velocity is below the permissible limit of the lining, and add freeboard.

#### Mobile boundary (maximum velocity approach)

1. Select the **maximum permissible velocity** $V_{max}$ for the material (for example Fortier and Scobey's values: fine sand about 0.5 m/s, coarse gravel about 1.2 to 1.5 m/s, hard clay higher) or use Kennedy's critical velocity

$$
V_0 = 0.55\,m\,y^{0.64}\ \text{(m/s, } y \text{ in m)}
$$

where $m$ is the critical velocity ratio.
2. Choose the side slope $z$ (as steep as the soil permits) and Manning's $n$.
3. Area: $A = Q/V_{max}$.
4. Hydraulic radius from Manning's equation: $R = \left(\dfrac{nV_{max}}{\sqrt{S_0}}\right)^{3/2}$ (if $S_0$ is not fixed, it is found from $S_0 = \dfrac{n^2V^2}{R^{4/3}}$ for a chosen $R$).
5. Solve the geometry for $b$ and $y$: $P = A/R$, $A = (b + zy)y$, $P = b + 2y\sqrt{1 + z^2}$.
6. Check that $V \le V_{max}$ and $V \ge V_{min}$, and adjust $z$, $b$ and $y$ if not.

**Limitation:** the method uses only the mean velocity and ignores the side-slope effect and the shear stress distribution, so the tractive force method is preferred for important designs.

## Check yourself

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

1. In the permissible velocity method, how is the required flow area found?
   A. A = Q x V
   B. A = Q / V with V the permissible velocity
   C. A = Q / S0
   D. A = Q / R
   Answer: B. Continuity gives A = Q/V. (Key point: Required area)

2. How is the hydraulic radius found for a given V, n and S0?
   A. R = V^2 / g
   B. R = A x P
   C. R = (nV / sqrt(S0))^(3/2) from Manning's equation
   D. R = (V / n)^2
   Answer: C. Rearranging V = (1/n) R^(2/3) S0^(1/2) gives R = (nV/sqrt(S0))^(3/2). (Key point: Hydraulic radius)

3. What is the main limitation of this method?
   A. It cannot use Manning's equation
   B. It only works for rigid channels
   C. It needs the Shields diagram
   D. It uses mean velocity only and ignores side-slope effect and shear distribution
   Answer: D. Because of this, the tractive force method is preferred for important designs. (Key point: Limitation)

## Related in Hydraulics

- [Mobile boundary design: three approaches](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Adesign-three-methods-mobile-boundary) — Hydraulics, chapter 10
- [Rigid versus mobile boundary design principle](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Arigid-vs-mobile-boundary-design-principle) — Hydraulics, chapter 10, asked 3×
- [Depth for maximum velocity in circular channel](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Amost-economical-circular-max-velocity-depth) — Hydraulics, chapter 6, asked 2×
- [Maximum permissible slope in 60 mm gravel](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Agravel-channel-max-permissible-slope) — Hydraulics, chapter 10
- [Permissible roughness for minimum energy loss](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Aone-metre-pipe-permissible-roughness) — Hydraulics, chapter 1
- [Boundary shear stress and compound channel flow](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Ashear-stress-boundary-compound-channel-flow) — Hydraulics, chapter 6

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