the thread of the gauge were towed through the tank by the carriage at velocities of
0.5, 1.0, 1.5, 2.0, and 2.5 m s
−1 , respectively.
The drag measurements of each collector were used to calculate the dimensionless coefficient of drag (C D ) by applying the equation:
C D ¼
2F Drg
q Á A Á v 2
ð11:1Þ
F DRG denotes the measured drag, q the density of water, A is the surface area
exposed to the current of velocity v. While for relatively rigid or bluff organisms the
projected area of the organism across the flow is generally used, we decided to test
an artificial test body (collector) and a fully grown mussel collector as well. For
solid objects being accelerated in fluid in addition to drag a force occurs which is,
commonly described as acceleration reaction (e.g. Daniel 1984; Denny et al. 1985;
Denny 1988). In order to take orbital motions into account the drag F Drg from
Eq. (11.1) has to be written in vector notation, and an acceleration term is added
(Morison et al. 1950):
F
!
Drg ¼ C D Á A Á
1
2
Á q Á v
j j
! Á v
! þ C M Á q Á Q Á
d v
!
d t
ð11:2Þ
where C M is the dynamic drag coefficient and Q the volume of water displaced by the
object. In order to initially avoid uncertainties with C D and the area A for flexible
organisms it is useful to write the first term in Eq. (11.2) in terms of dynamic
pressure ( F
Ã
!
), which can be exactly computed from current measurements:
F
Ã
! ¼
F
!
Drg
C D Á A
ð11:3Þ
i.e.
F
Ã
! ¼
1
2
Á q Á v
j j
! Á v
!
ð11:4Þ
For a detailed demonstration of the time history of drag forces occurring under the
action of tidal currents, wind wave and swell model calculations were carried out
using the software “WaveLoads” developed by Mittendorf et al. (2001), which
solves Eq. (11.2) for offshore structures. The forces were computed for a hypothetical (artificial) test body (cylinder) of 2.5 m in length and such a diameter that
the area exposed to the current corresponded with that of the plan area of a typical
fully grown mussel collector as determined before. The drag coefficients measured
in the towing tank experiments were used instead of the ones determined for
cylinders (Fig. 11.22a–f). The cylinder was exposed perpendicular to the flow
direction. The results render information on the distribution of horizontal and
vertical forces which act on the test bodies and mussel collectors.
11 The German Case Study: Pioneer Projects of Aquaculture …
293
0.5, 1.0, 1.5, 2.0, and 2.5 m s
−1 , respectively.
The drag measurements of each collector were used to calculate the dimensionless coefficient of drag (C D ) by applying the equation:
C D ¼
2F Drg
q Á A Á v 2
ð11:1Þ
F DRG denotes the measured drag, q the density of water, A is the surface area
exposed to the current of velocity v. While for relatively rigid or bluff organisms the
projected area of the organism across the flow is generally used, we decided to test
an artificial test body (collector) and a fully grown mussel collector as well. For
solid objects being accelerated in fluid in addition to drag a force occurs which is,
commonly described as acceleration reaction (e.g. Daniel 1984; Denny et al. 1985;
Denny 1988). In order to take orbital motions into account the drag F Drg from
Eq. (11.1) has to be written in vector notation, and an acceleration term is added
(Morison et al. 1950):
F
!
Drg ¼ C D Á A Á
1
2
Á q Á v
j j
! Á v
! þ C M Á q Á Q Á
d v
!
d t
ð11:2Þ
where C M is the dynamic drag coefficient and Q the volume of water displaced by the
object. In order to initially avoid uncertainties with C D and the area A for flexible
organisms it is useful to write the first term in Eq. (11.2) in terms of dynamic
pressure ( F
Ã
!
), which can be exactly computed from current measurements:
F
Ã
! ¼
F
!
Drg
C D Á A
ð11:3Þ
i.e.
F
Ã
! ¼
1
2
Á q Á v
j j
! Á v
!
ð11:4Þ
For a detailed demonstration of the time history of drag forces occurring under the
action of tidal currents, wind wave and swell model calculations were carried out
using the software “WaveLoads” developed by Mittendorf et al. (2001), which
solves Eq. (11.2) for offshore structures. The forces were computed for a hypothetical (artificial) test body (cylinder) of 2.5 m in length and such a diameter that
the area exposed to the current corresponded with that of the plan area of a typical
fully grown mussel collector as determined before. The drag coefficients measured
in the towing tank experiments were used instead of the ones determined for
cylinders (Fig. 11.22a–f). The cylinder was exposed perpendicular to the flow
direction. The results render information on the distribution of horizontal and
vertical forces which act on the test bodies and mussel collectors.
11 The German Case Study: Pioneer Projects of Aquaculture …
293