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Chapter 7 - Establishing an empirical 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
0.0
0.1
0.2
Water depth (free WS to BL) [m]
C01b
C01c
0.3
C01d
80%
C01b
C01c
C01d
0.5
Maximum scour depth
60%
40%
0.4
0.5
computed maximum scour depth [m]
0.4
0.3
0.2
0.1
0.0
0.0 0.1 0.2 0.3 0.4 0.5
measured maximum scour depth [m]
sin(beta)
20%
0%
-20%
-40%
-60%
0.00 0.02 0.04 0.06 0.08 0.10
h/r
Figure 7.2: Results of the enhanced equation (eq. 7.6) of Bridge (see Fig. 7.1 and 7.3 for explanations)
c) Problematic of existing scour formulae
All existing scour formulae have one major problem in common: they give the maximum transversal
bed slope at the location of maximum scour. This is due to the used parabolic approximation
of the bed surface in radial direction. Figures 7.1 and 7.2 show that the bed topography in radial
direction is rather s-shaped than parabolic especially for high discharges. Furthermore the plot of
sinβ
as a function of h ⁄ r (Fig. 7.3) demonstrates that the assumption of a constant K is not correct.
Most formulae assume that K is more or less constant, since the used parameters are submitted
to very small variations over the cross-section. In fact, the measurements are adjusted almost
on a ellipse.
Therefore a new approach based on the shape of the radial cross-section profile is described in the
following paragraph.
page 158 / November 9, 2002
Wall roughness effects on flow and scouring