Particle size for Vc, m (ft)
D
=
D50
=
Particle size in a mixture of which 50 percent are smaller, m (ft)
=
Coefficient derived in Chapter 3
Ku
Ku
=
6.19 SI units
=
11.25 English units
Ku
Live-Bed Contraction Scour. A modified version of Laursen's 1960 equation for live-bed
scour at a long contraction is recommended to predict the depth of scour in a contracted
section. The modification is to eliminate the ratio of Manning's n (see the following Note #3).
6/7
k1
y 2 Q2
W1
=
(7.2)
y1 Q1
W2
y s = y 2 - y o = average scour depth
(7.3)
where:
=
Average depth in the upstream main channel, m (ft)
y1
y2
=
Average depth in the contracted section, m (ft)
=
Existing depth in the contracted section before scour, m (ft) (see Note 7)
yo
Flow in the upstream channel transporting sediment, m3/s (ft3/s)
Q1
=
Flow in the contracted channel, m3/s (ft3/s)
=
Q2
W1
=
Bottom width of the upstream main channel, m (ft)
W2
=
Bottom width of the main channel in the contracted section less pier
width(s), m (ft)
=
Exponent determined below
k1
V*/ω
k1
Mode of Bed Material Transport
<0.50
0.59
Mostly contact bed material discharge
0.50 to 2.0
0.64
Some suspended bed material discharge
>2.0
0.69
Mostly suspended bed material discharge
(τo/ρ) = (gy1 S1), shear velocity in the upstream section, m/s (ft/s)
=
V*
ω
=
Fall velocity of bed material based on the D50, m/s (Figure 3.1)
For fall velocity in English units (ft/s) multiply fall velocity in m/s by 3.28
g
=
S1
=
Slope of energy grade line of main channel, m/m (ft/ft)
Shear stress on the bed, Pa (N/m2) (lb/ft2)
τo
=
Density of water (1000 kg/m3) (1.94 slugs/ft3)
ρ
=
Notes:
1. Q2 is the total flow going through the bridge opening.
2. Q1 is the flow in the main channel upstream of the bridge, not including overbank flows.
3. The Manning's n ratio is eliminated in Laursen's live-bed equation to obtain Equation 7.2.
This was done for the following reasons. The ratio can be significant for a condition of
7.10
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