Page 243 - Soil and water contamination, 2nd edition

230 Soil and Water Contamination
2 . 0 90
th
4 iteration: L . 3 99 tanh . 3 99 tanh( . 1 554 ) . 3 99 . 0 914 . 3 65
w
. 3 64
2 . 0 90
th
5 iteration: L . 3 99 tanh . 3 99 tanh( . 1 549 ) . 3 99 . 0 914 . 3 65 m
w
. 3 65
th
After the 5 iteration with L = 3.65 m, we have achieved convergence. Now, the
w
amplitude of the wave motion at the lake bottom A is calculated using Equation (12.10):
b
. 0 224 . 0 224 . 0 224
A . 0 050 m
b
2 sinh( 2 . 0 90 . 3 / 65 ) 2 sinh( . 1 549 ) 2 . 2 247
The maximum water velocity at the lake bottom due to wave motion is then estimated
using Equation (12.3):
. 0 224 1 1
u , b max . 0 440 . 0 196 m s -1
. 1 60 sinh 2 ( . 0 90 . 3 / 65 ) . 2 247
The friction coefficient is calculated using Equation (12.9) (note that K = D90 = 70 μm
n
-6
= 70·10 m):
. 0 75
6
70 10 . 0 75 3 3
C 4 . 0 4 . 0 . 0 0014 4 . 0 2 . 7 10 9 . 2 10
f
. 0 050
Finally, calculate the bottom shear stress τ using Equation (12.2):

b
2
1000 9 . 2 10 3 . 0 196 . 0 111 N m -2
b
As the bottom shear stress is slightly larger than the critical shear stress for erosion and
-2
deposition, which is 0.10 N m , some of the bottom sediment is resuspended into the
water column.
12.4 SEDIMENT DEPOSITION
If the shear stress at the soil–water interface is less then the critical value τ , the sediment
b,d
in the water column settles and the net sediment flux J (see Equation 12.1) becomes a
s
deposition flux, which can be formulated as:
J w C (12.11)
d s b
-2
-1
where J = sedimentation flux [M L T ], α = a delay factor [-], w = the maximum settling
d s
-1
velocity of the suspended sediment when τ = 0 [L T ], and C = the suspended sediment
b b
-3
concentration just above the soil–water interface [M L ]. If the variation in suspended
sediment concentration over the vertical profile is small (this holds for turbulent streams),
the vertically averaged concentration (C) can be adopted for C . Note that in this case the
b
removal of sediment from the water column follows first-order kinetics (combine Equation
12.11 (C = C) with the transport Equation 12.1). If only sedimentation is considered, then
b
the differential equation becomes:
C J s w s
C (12.12)
t H H

10/1/2013 6:45:06 PM
Soil and Water.indd 242
Soil and Water.indd 242 10/1/2013 6:45:06 PM