Environmental Engineering Reference
In-Depth Information
15 cm. Both basins are connected by a channel 15 cm long and variable width (the
channel width lies in the interval 4-18 cm.). In order to produce a variable flow rate
we use a block connected to a stepper motor through a crankshaft mechanism. The
block, made in styrofoam and plexiglas, is partially submerged in the liquid layer and
develops a periodically vertical motion. The experiments were made under the fol-
lowing conditions: the depth of the liquid layer was 4 cm and the amplitude of vertical
motion of the block was set to 3 cm. We have chosen two different driving frequen-
cies, namely, 0.05 and 0.08Hz and three different channel widths are considered:
2.5, 3 and 5 cm. In the experiments we cover the bottom of the channel and a fraction
of the large domain with a thin layer of sand. The sizes of these particles are in all
cases less than 1mm. To follow the evolution of the system we use a high definition
video camera, so that the images have a resolution of 1920
1080 pixels. One image
is recorded every second for a time interval greater than 12h. During this interval
we observe the appearance of regions where particles are expelled or accumulated.
To estimate the flow rate and other parameters, we proceed as follows. When the
block is submerged into the fluid, a certain amount of liquid is displaced. The volume
displaced is equal to the volume of the block into the fluid:
×
V
(
t
) =
l
×
a
×
h
(
t
),
(1)
where l is the block length, a is the block width, and h
(
t
) =
h m +
h 0 sin
(
2
ˀʽ
t
)
is
the distance from the free surface to the bottom block ( h m is the mean value of h
(
t
)
).
=
In our experiments l
57.5 cm and we have used two different blocks, one with
=
=
(
)
a
8 cm and the other with a
2.5 cm. The flow rate is the time derivative of V
t
:
dV
)
dt =
(
t
Q
=
2
ˀʽ
l
×
a
×
h 0 cos
(
2
ˀʽ
t
).
(2)
The maximum flow rate Q 0 is:
Q 0 =
2
ˀʽ
l
×
a
×
h 0 .
(3)
The representative velocity is the quotient of Q 0 and the cross section of the liquid
layer in the channel ( A ):
Q max
A
U 0 =
.
(4)
P , where H is the width of the channel and P is
the depth of the liquid layer. In all experiments the depth of liquid is P
In this last equation, A
=
H
×
=
4cm.
 
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