III. Sediment Transport
67
This procedure has been repeated for a range of conditions. Analysis of all results
gave the following relationship :
W s
e a
-for 0.01 _< 1
(19)
t.U,,o) \%)
in which :
co = maximum volume concentration = 0.65
Fig. 5b shows (based on eq. 17) computed and measured (eq. 18) concentrations
for the high-concentration experiment of Ning Chien. Good agreement can be
observed.
2.5
Velocity Profile
In case of low sediment concentrations (c < 0.001 ) and rough hydraulic
conditions, the logarithmic velocity profile can be applied, as follows :
u.,o ¢z)
u= K ln/zTol
(20)
in which :
Zo
K
= current-related bed-shear velocity
= 0.033 ks = zero-velocity level
= constant of Von Karman (~: = 0.4).
Eq. (19) is the well-known Prandtl-Von Karman Equation.
Velocity profiles in high (hyper) concentration flow" have been studied by many
researchers (Einstein-Ning Chien (1955), Coleman (1980) and Winterwerp et al.
(1989).
Einstein-Ning Chien found reduced velocities in the near-bed region, which was
represented as a reduced K-ValUe.
Coleman also observed reduced velocities near the bed. He introduced an
additional tm-bulence-related parameter to represent the effect of the sediment
concentration on the velocities, the K-parameter was kept constant.