Sediment Transport Concepts - Sediment Transport in Irrigation Canals: A New Approach - page 131

y

z

C

F

y

u z,y

θ A

h 1

h

Zero shear line

B

(90- /2) θ

Figure 5.21. Definition sketch
for calculation of depth-averaged
velocity (Yang et al., 2004).

ED

z

u ∗ y
u ∗ h

f = (5.87)

where:
u z ,y = velocity at points in the shaded column

u ∗ = overall mean shear velocity (m/s)

u ∗ y = local shear velocity based on local boundary shear stress (m/s)

u ∗ h = local shear velocity at the centre of the canal (m/s)

k /30 for a rough boundary, where k is the roughness height (m)
To compute the depth-averaged velocity over the column CD, the
following assumptions are made:
•

z 0 =

the roughness in the bed and on the sides are equal, so the line of zero
shear (EF) is the bisector of the angle between the bed and side slope;

• the local shear velocity can be replaced by the local average shear on

either the bed or the sidewall.

Integration of the equation along the column CD gives the relation for
the depth-averaged velocity ( u y ) in a stream column (Yang et al., 2004):

2 . 5ln f h 1
z 0

cos θ

u y
u ∗ =

− 2 . 5(1 + β ) (5.88)

In non-wide canals and near the sidewalls in wide canals the maximum
velocity is located below the free surface, which is known as the dip phe-
nomena. The second term in the right hand side of the equation accounts
for the dip phenomena by β , being the correction factor for the dip
phenomenon. For a smooth canal the value of β is given by:

sin θ exp

1 . 3 y

h 1

β = − (5.89)