Velocity profile in channel cross-sections

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):

 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.

 ~~~~~~~~~~~~~~~~~~~~~~~
 |   ( ( (  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.

 ~~~~~~~~~~~~~~~~~~
  \    (  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.

 ~~~~~~~~~~~~~~~~~~~~
  \   ( ( 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.