pdf, 12 MiB - Infoscience - EPFL

Chapter 7 - Establishing an empirical formula
The expression 2ξ ± 1 uses the + if the boundary condition of a horizontal slope is placed at the
inner sidewall and - if placed outside.
Without any correction factor, the following correlations can be obtained:
• R 2 = 0.67 for ξ = 5 % for a horizontal slope at the outer bank
• R 2 = 0.70 for ξ = – 4 % for a horizontal slope at the inner bank
Adding a correction factor (defined by tanφ∗
= c ⋅ tanφ
) the following results are obtained:
• for a horizontal transversal bed slope at the outer bank:
ξ = 8 %, c = 20 ⎛1 58 ⋅ S eall ,
2.35 h m
+ – ⋅ -----⎞
V⋅
R h
⋅
⋅ ----------------- ,
⎝
B ⎠
g ⋅ B 3
R 2 = 0.850 (7.27)
• for a horizontal transversal bed slope at the inner bank:
ξ = 8 %, c = 25 ⎛1 47 ⋅ S eall ,
3.33 h m
+ – ⋅ -----⎞
V⋅
R h
⋅
⋅ ----------------- ,
⎝
B ⎠
g ⋅ B 3
R 2 = 0.856 (7.28)
Cross section in the upper scour hole
Radius from center of the bend [m]
6.5
6.3
measured scour
computed scour
6.1
5.9
5.7
5.5
-0.1
0.0
0.1
0.2
Water depth (free WS to BL) [m]
C01b
C01c
C01d
C01b
C01c
C01d
Maximum scour depth
80%
60%
0.3
0.4
0.5
40%
0.5
computed maximum scour depth [m]
0.4
0.3
0.2
0.1
sin(beta)
20%
0%
-20%
-40%
computed equation
upstream scour
0.0
0.0 0.1 0.2 0.3 0.4 0.5
measured maximum scour depth [m]
-60%
-0.02 0.00 0.02 0.04 0.06 0.08 0.10
h/r
Figure 7.9: Results of the uncentered polynomial equation (5th degree), horizontal bed slope at the inner bank,
with correction factor (eq. 7.27) (see Fig. 7.1 and 7.3 for explanations)
page 168 / November 9, 2002
Wall roughness effects on flow and scouring