Page 240 - Soil and water contamination, 2nd edition

Sediment transport and deposition 227

10 u
b x
5 . 0
u b
x
10
The flow velocity is also given by
Q Q
u
x
A 10 H
The stage–discharge relationship can be rewritten in
1
Q 6 . 1
H . 0 503 Q . 0 625
0 . 3
Combining the three latter equations gives
5 . 0
Q b
u
x . 0 625
. 5 03 Q 10
5 . 0
Q . 0 375 . 5 03 b
10
. 1 333
Q 74 . 28 b
10
Thus, the discharge at which the bottom shear stress equals the critical shear stress for
deposition is
. 1 333
. 0 45 3 -1
Q 74 . 28 2 . 1 m s
10
and the discharge at which the bottom shear stress equals the critical shear stress for
erosion is
. 1 333
. 0 95
3
Q 74 . 28 2 . 3 m s -1
10
In lakes it is more difficult to determine the shear stress due to wind-induced waves at the
interface between bed sediment and water, because of the complex three-dimensional water
movement. Nevertheless, there are relatively simple relationships for deriving the water flow
velocity at the lake bottom. These relationships can then be used to derive the shear stress.
Water moves in an orbital motion (circular path) as a wave passes by; if the water is not
too deep, this orbital motion diminishes to a to-and-fro motion over the lake bottom. The
maximum water velocity during this motion is thus a function of the water depth and the
wave height, length and period:
H 1
u w (12.3)
, b max
T sinh 2 ( H / L )
w w
-1
where u = the maximum velocity at the bottom [L T ], H = the wave height [L],
b,max w
T = the wave period [T], sinh = the hyperbolic sine function, which is defined as
w

10/1/2013 6:45:04 PM
Soil and Water.indd 239 10/1/2013 6:45:04 PM
Soil and Water.indd 239