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Establishment of the scour formula
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
C01b
C01c
C01d
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 7.5: Results of the uncentered polynomial equation (3rd degree) without correction factor (eq. 7.12,
tanφ∗
= tanφ
) (see Fig. 7.1 and 7.3 for explanations)
c) Polynomial function of the 3rd degree - uncentered with vertical adjustment
In order to allow a vertical adjustment in the cross-section, the second boundary condition
(average water depth at the inflection point) is replaced by the condition that the average water
depth over the whole cross-section (integration) is equal to .
The new boundary conditions are:
1. dh s ( R c + ξB) ⁄ dr = tanφ∗
(maximum bed slope).
2. The average water depth over the cross-section is equal to
( R c + B ⁄ 2)
3. dh s ( r o ) ⁄ dr = 0 or dh s ( r i ) ⁄ dr = 0 the transversal bed slope is equal to zero at the outer
or inner side wall.
h m
∫ h ()h s r d = B ⋅ h s
( R c – B ⁄ 2)
m
h m
EPFL Ph.D thesis 2632 - Daniel S. Hersberger November 9, 2002 / page 163