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Chapter 7 - Establishing an empirical formula
h s,max h s,max /h m tan(β max )
1 2 12 1 2 12 1 2 12
V*/V 0.043 0.058 0.055 0.207 0.087 0.210 0.296 0.078 0.153
Fr* 0.061 0.019 0.050 0.060 0.035 0.050 0.031 0.042 0.040
Fr d 0.263 0.152 0.230 0.006 0.031 0.010 0.001 0.262 0.137
Fr 0.013 0.000 0.016 0.210 0.044 0.231 0.089 0.016 0.036
Sigma 0.130 0.020 0.079 0.087 0.009 0.056 0.086 0.036 0.005
d/h m 0.028 0.055 0.028 0.251 0.053 0.275 0.205 0.026 0.064
Re* 0.775 0.734 0.822 0.348 0.140 0.338 0.153 0.163 0.165
Re 0.798 0.759 0.832 0.477 0.201 0.475 0.232 0.188 0.204
V*R h /sqrt(g*B^3) 0.812 0.751 0.839 0.475 0.210 0.477 0.229 0.204 0.217
V*R h /sqrt(g*h m^3) 0.814 0.785 0.863 0.452 0.175 0.445 0.212 0.151 0.168
S e,in 0.031 0.475 0.251 0.169 0.571 0.464 0.001 0.404 0.175
S e,mr 0.057 0.553 0.301 0.128 0.673 0.564 0.002 0.303 0.125
S e,all 0.079 0.161 0.099 0.512 0.170 0.518 0.366 0.109 0.186
S e,bend 0.004 0.027 0.005 0.268 0.071 0.285 0.186 0.012 0.041
Rc/B 0.529 0.442 0.564 0.279 0.227 0.277 0.253 0.473 0.470
h m /B 0.662 0.532 0.628 0.486 0.262 0.521 0.228 0.297 0.295
r/B 0.502 0.416 0.535 0.263 0.218 0.262 0.240 0.460 0.455
V^2/g/r 0.040 0.011 0.026 0.019 0.026 0.016 0.054 0.148 0.153
R c *h m /B^2 0.699 0.586 0.696 0.441 0.261 0.458 0.256 0.376 0.377
(R c +h m )/B 0.537 0.448 0.571 0.287 0.230 0.285 0.255 0.472 0.469
V * 0.807 0.735 0.855 0.329 0.130 0.321 0.150 0.119 0.126
V*R h * 0.798 0.759 0.832 0.477 0.201 0.475 0.232 0.188 0.204
Table 7.2: Table of correlations R 2 for the tests without macro-roughness
Re*: computed with d 90 , S e,in and S e,mr are computed without Peter’s data.
1: first scour hole, 2: second scour hole, 12: maximum of the two scour holes
Correlations over 0.5 are in bold characters, correlations below 0.4 on a grey background.
* parameter with a dimension
It can easily be seen that the frequently used parameters V∗ ⁄ V , Fr d have almost no influence on
the scour process. The particle Froude number seems to have a little influence on the absolute
scour depth h max and it may be useful to introduce it in combination with other parameters in a
scour formula.
The Reynolds number seems to be an important parameter; but since there is no plausible reason
to consider the influence of the viscosity in the scour process, this phenomenon is an expression
of the correlation between the velocity and the scour depth. This fact is confirmed if we consider
the correlations between the velocity V , the product of the velocity with the hydraulic radius
V ⋅ R h with the absolute and relative maximum scour depth. To replace the Reynolds number, a
new dimensionless ratio V⋅ R h ⁄ g⋅
B 3 is proposed. It has about the same correlation as the
Reynolds number. Replacing B by in this ratio would reduce the correlation.
h m
page 152 / November 9, 2002
Wall roughness effects on flow and scouring