---
title: "Velocity profile in channel cross-sections"
subject: "Hydraulics"
chapter: 5
key: "semester_4/hydraulics:velocity-profile-channel-shapes"
source: https://www.bctengineer.com/q/semester_4/hydraulics/velocity-profile-channel-shapes
site: BCT Engineering
---

# Velocity profile in channel cross-sections

Hydraulics · Chapter 5: Basics of Open channel flow

- Asked in: 2068 Bhadra, 3 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/hydraulics/velocity-profile-channel-shapes
- Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-5

## Question

Draw and explain the velocity profile in a cross-section of rectangular, triangular and trapezoidal channel shapes.

## Short answer

In all shapes, velocity is zero at the bed and banks due to no-slip, increases inward, and maximum occurs slightly below the free surface on the centre line. In rectangular channels, isovels are nearly parallel in the middle, curving up near sides; in triangular and trapezoidal, they follow the sloping sides and flatten in the middle, with lowest velocity in corners.

## Answer

#### Nature of velocity distribution
In an open channel, velocity is zero at the bed and banks (no-slip) and increases away from the boundary. The maximum velocity does not occur at the free surface but a little below it, at about 0.05 to 0.25 of the depth below the surface. This is because of the surface shear of air and the secondary currents. The lines joining points of equal velocity are called **isovels**.

Mean velocity in a vertical is nearly equal to the velocity at $0.6y$ from the surface (or the average of velocities at $0.2y$ and $0.8y$).

Vertical velocity profile (any shape):
```text
 WS ~~~~~~~~~~~~~
    |    --->
    |     ---->      <- v_max just below surface
    |   --->
    |  ->
 bed|_>  (v = 0)
```

#### Rectangular channel
Isovels are roughly parallel to the bed in the middle and curve upward near the sides. The maximum velocity is at the centre line, below the surface. In a wide channel the profile at the centre follows the logarithmic law.
```text
 ~~~~~~~~~~~~~~~~~~~~~~~
 |   ( ( (  v_max ) ) ) |
 |   (  (    )  )  )    |
 |___(______)__________|
```

#### Triangular channel
The deepest point is at the centre. Isovels are curved, and the maximum velocity is at the centre line just below the surface. Velocity near the sloping sides is small.
```text
 ~~~~~~~~~~~~~~~~~~
  \    (  v_max )   /
   \   (    )     /
    \   (  )    /
     \  ______/
```

#### Trapezoidal channel
Similar to the triangular and rectangular shapes. Isovels follow the sloping sides near the banks and become flatter in the middle. The maximum velocity occurs on the centre line below the surface; the lowest velocities occur in the corners where bed meets sides.
```text
 ~~~~~~~~~~~~~~~~~~~~
  \   ( ( v_max ) )  /
   \  (  (   )  )  /
    \_(____________)/
```
In all shapes, the velocity distribution is affected by roughness, shape, bends and the presence of vegetation; velocity is smaller at the corners.

## Check yourself

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

1. Where does the maximum velocity usually occur in an open channel vertical?
   A. At the free surface
   B. At the bed
   C. Slightly below the free surface, about 0.05 to 0.25 of the depth
   D. At mid-depth exactly
   Answer: C. Surface shear of air and secondary currents push v_max a little below the surface. (Key point: Maximum velocity location)

2. What is the velocity at the bed and banks?
   A. Maximum
   B. Zero, because of no-slip
   C. Equal to the surface velocity
   D. Equal to the mean velocity
   Answer: B. Velocity is zero at the boundary and increases away from it. (Key point: No-slip)

3. Where does the velocity in a vertical approximately equal the mean velocity?
   A. At 0.6 of the depth from the surface
   B. At the surface
   C. At the bed
   D. At 0.1 of the depth
   Answer: A. Velocity at 0.6y from the surface, or the average of that at 0.2y and 0.8y, is close to the mean. (Key point: Mean velocity)

4. What are isovels?
   A. Lines of equal depth
   B. Lines joining points of equal velocity
   C. Lines of equal pressure
   D. Streamlines at the bed
   Answer: B. Isovels join points of equal velocity in the cross-section. (Key point: Isovels)

## Related in Hydraulics

- [Best trapezoidal section and half-hexagon proof](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Atrapezoidal-proportions-half-hexagon-proof) — Hydraulics, chapter 6, asked 2×
- [Critical depth in four channel sections](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Acritical-depth-four-channel-sections-6-cumecs) — Hydraulics, chapter 7
- [Trapezoidal to rectangular transition with bed lowering](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Atrapezoid-to-rectangular-transition-bed-lowering) — Hydraulics, chapter 7
- [Economical triangular section hydraulic radius](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Amost-economical-triangular-section-hydraulic-radius) — Hydraulics, chapter 6
- [Hydraulic exponents for rectangular and triangular](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Ahydraulic-exponents-rect-triangular-numerical) — Hydraulics, chapter 6
- [Program for critical depth in trapezoidal channel](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Aalgorithm-critical-depth-trapezoidal) — Hydraulics, chapter 7

## Related in other subjects

- [Efficient trapezoidal section and triangular channel depth](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Atriangular-channel-normal-depth-trap) — Hydro Power, chapter 1, asked 2×
- [Efficient rectangular section and triangular channel depth](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Atriangular-channel-normal-depth-rect) — Hydro Power, chapter 1, asked 2×
- [Profile and cross-section levelling](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aprofile-and-cross-section-leveling) — Surveying I, chapter 5, asked 10×
- [Most economical triangular channel section](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Aeconomical-triangular-section) — Hydro Power, chapter 1