Page 242 - Soil and water contamination, 2nd edition

Sediment transport and deposition 229

surface roughness is determined by irregularities, such as ripples or aquatic vegetation, the
value of K is adjusted to an equivalent particle size diameter.
n
Example 12.2 Bottom shear stress in lakes

Estimate the bottom shear stress τ for a shallow lake with the following characteristics:

b
-1
water depth = 90 cm, wind fetch length = 300 m, wind speed = 17 m s (Beaufort scale
wind force 7), D90 of the bed sediment = 70 μm. Given the critical shear stress for both
-2
erosion and deposition = 0.10 N m , say whether the sediment is settling or eroding.
Solution
First, calculate the parameters k , k , γ , and γ :
1 2 1 2
. 0 375
8 . 9 . 0 90 . 0 375
k tanh . 0 833 tanh( . 0 833 . 0 0305 ) tanh( . 0 225 ) . 0 221
1 2
17
. 0 75
8 . 9 . 0 90
k 2 tanh . 0 53 tanh( . 0 53 . 0 0305 . 0 75 ) tanh( . 0 039 ) . 0 039
17 2
. 0 25
8 . 9 300 . 0 25
. 0 077 . 0 077 10 . 17 . 0 138
1 2
17
. 0 42
8 . 9 300 . 0 42
. 0 0125 . 0 0125 10 . 17 . 0 033
2 2
17
Second, calculate the wave height H and wave period T :
w w
17 2 . 0 033
H . 0 283 . 0 039 tanh . 0 325 tanh( . 0 846 ) . 0 325 . 0 689 . 0 224 m
w
8 . 9 . 0 039
17 . 0 138
T w . 7 54 . 0 221 tanh . 2 891 tanh( . 0 624 ) . 2 891 . 0 554 . 1 60 s
8 . 9 . 0 221
To estimate the wave length L , first make an initial estimation by using Equation (12.6):
w
8 . 9 . 1 60 2
L w . 3 99 m
2
In this case, the water depth H is less than the half of the wave length L , so Equation
w
(12.7) should be used to estimate the wave length. Because L appears on both sides of
w
the equation, it should be solved iteratively. For the first estimation, the above initial
estimation is used. The iteration is continued until L no longer changes:
w
2 . 0 90
st
1 iteration: L . 3 99 tanh . 3 99 tanh( . 1 417 ) . 3 99 . 0 889 . 3 55 m
w
. 3 99
2 . 0 90
nd
2 iteration: L . 3 99 tanh . 3 99 tanh( . 1 593 ) . 3 99 . 0 921 . 3 67 m
w
. 3 55
2 . 0 90
rd
3 iteration: L . 3 99 tanh . 3 99 tanh( . 1 541 ) . 3 99 . 0 912 . 3 64 m
w
. 3 67

10/1/2013 6:45:05 PM
Soil and Water.indd 241
Soil and Water.indd 241 10/1/2013 6:45:05 PM