Open Channel Flow - Sediment Transport in Irrigation Canals: A New Approach - page 26

Investigations in laboratories and measurements in the field have resulted
in the following expression, proposed by White and Colebrook, for the
coefficient C :

12 R

C = 18 log (2.33)

k + δ/ 3 . 5

where:
k

= length characterizing the roughness (Nikuradse)

δ = th ickne ss of the laminar sub-layer = 11.6 ν/v ∗

v ∗ = gRS o
ν

20 ◦ C)
Values of the de Chézy coefficient as function of the hydraulic radius
R , the wall roughness k and the thickness of the laminar sub-layer δ are
presented in Figure 2.10.

10 − 6 m 2 /s (for T

= =

R
k

10000

Re = 2 x10 6

5000

Hydraulically
rough

Re = 1 x10 6
Re = 500 x10 3

2000

1000

Re = 200 x10 3
Re = 100 x10 3
Re = 50 x10 3

500

R

200

100

Re = 20 x10 3
Re = 10 x10 3
Re = 5 x10 3

50

20

Figure 2.10. Values of the de
Chézy coefficient C as function
of the hydraulic radius R , the
wall roughness k and the
thickness of the laminar
sub-layer δ .

Re = 2 x10 3
Re = 1 x10 3

10

5

Hydraulically
smooth

Re = 500

2

Another, frequently used, equation for uniform flow is the Manning
equation with n for the roughness:

1
n R 2 / 3 S 1 / 2

=

v (2.34)

o

In some countries, the Strickler equation is preferred; this equation uses
k s for the roughness.

k s R 2 / 3 S 1 / 2

v = (2.35)

o