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as rather small indicating the applicability of the Lindner (
1982
) approach.
Furthermore, the maximum deviation of the measured drag coefficient of a single
element from the calculated mean drag coefficient corresponded to 30%. These
deviations were in a similar range to the deviations reported by Petryk (
1969
),
although Petryk (
1969
) did not take into account blockage effects.
It is also worth mentioning that Lindner (
1982
) reported a decrease of
u
0,
n
/
u
0
with increasing
u
0
and an increase of
u
0,
n
/
u
0
with increasing bed slope
S
. The
hydraulic boundary conditions summarized in Table
1
show that in the present
experiments, both
u
0
and
S
were increased in order to achieve a constant water
depth of
h
0.25 m. Hence, through the increase of
u
0
lower ratios (and hence
lower
C
D
i
-values) would be expected while at the same time larger ratios
u
0,
n
/
u
0
(and hence larger
C
D
i
-values) would be expected through the slope increase. Table
1
shows that calculated
C
D
-values were constant for the different hydraulic boundary
conditions. Hence, it can be concluded that the two expected trends cancel each
other out. This is also reflected by the constant range of drag coefficients
C
D
obtained from the measurements for each of the cylinder arrangements.
¼
5 Summary and Conclusions
In this study, the spatial variability of drag forces within multicylinder arrays was
investigated using experimental data from a laboratory study. Direct measurements
of drag forces within the cylinder array showed that the spatial variability of time-
averaged drag forces, deviating approximately
30% from the spatial mean, is
significant although the arrays were composed of identical elements. A similar result
was obtained for the drag coefficients. The results further confirmed the findings
reported in the studies of Petryk (
1969
), Li and Shen (
1973
), and Lindner (
1982
) that,
for similar cylinder density and hydraulic boundary conditions, larger drag forces
and drag coefficients are expected for a staggered setup than for an in-line setup.
These differences indicated that the wake flow structure plays an important role
in multicylinder arrays. Therefore, the data were used to test the computational
approach outlined by Lindner (
1982
) for the evaluation of the drag coefficients in a
multicylinder array. This test revealed a good agreement between calculated and
measured drag coefficients with deviations of the mean drag coefficient of approxi-
mately
5% for the staggered setup.
The Lindner (
1982
) approach shows that drag forces and drag coefficients
depend on the wake flow structure and hence on cylinder diameter
d
, cylinder
spacing
a
x
and
a
y
, approach velocity of an individual cylinder
u
0
i
, and slope
S
. Thus,
estimating
C
D
values based on the single isolated cylinder analogy is only a crude
approximation of the real drag coefficient.
It is worth mentioning that the presented experiments were carried out with
limited hydraulic and geometrical boundary conditions. Hence, for a global and
more detailed evaluation of the Lindner (
1982
) approach, further measurements
16% for the in-line and
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