Experimental Methods
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h3. Experimental Methods {float:left|border=2px solid black|width=260px} [!Laboratory Research Set-ups^ACD set up labeled.JPG|width=260px!|Laboratory Research Set-ups] {float} |
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[!Laboratory Research Set-ups^IMG_7223.JPG|width=260px!|Laboratory Research Set-ups]
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Two
...
CD
...
experimental
...
set
...
ups
...
(
...
...
...
...
and
...
...
...
...
)
...
were
...
used
...
in
...
identical
...
experiments
...
to
...
collect
...
data
...
sets
...
relating
...
change
...
in
...
float
...
height
...
to
...
dosing
...
in
...
Fall
...
2008.
...
First
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the
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chemical
...
doser
...
was
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positioned
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at
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5
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cm
...
intervals
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along
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the
...
lever
...
arm.
...
The
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water
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level
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in
...
the
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grit
...
chamber
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bucket
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was
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varied
...
while
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readings
...
were
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taken
...
of
...
the
...
changing
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water
...
height
...
in
...
the
...
collection
...
column
...
(explained
...
below).
...
The
...
7
...
kPa
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pressure
...
sensor
...
at
...
the
...
base
...
of
...
the
...
bucket
...
was
...
calibrated
...
to
...
read
...
in
...
centimeters
...
of
...
water
...
and
...
it
...
was
...
zeroed
...
for
...
the
...
condition
...
when
...
the
...
float
...
just
...
became
...
buoyant
...
and
...
was
...
no
...
longer
...
resting
...
on
...
the
...
bottom
...
of
...
the
...
bucket.
...
The
...
lever
...
arm
...
was
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made
...
horizontal
...
at
...
the
...
point
...
by
...
adjusting
...
the
...
length
...
of
...
fishing
...
line
...
tied
...
to
...
its
...
end.
...
This
...
was
...
checked
...
with
...
a
...
level.
...
By
...
zeroing
...
the
...
pressure
...
sensor
...
at
...
a
...
lever
...
arm
...
height
...
of
...
zero
...
all
...
readings
...
from
...
the
...
bucket
...
pressure
...
sensor
...
were
...
then
...
equivalent
...
to
...
change
...
in
...
float
...
height,
...
which
...
was
...
also
...
equal
...
to
...
negative
...
change
...
in
...
the
...
height
...
of
...
the
...
end
...
of
...
the
...
lever
...
arm
...
because
...
of
...
the
...
fishing
...
line
...
connecting
...
the
...
float
...
to
...
the
...
end
...
of
...
the
...
lever
...
arm.
...
A
...
flow
...
controller
...
(FC)
...
was
...
connected
...
to
...
the
...
chemical
...
dosing
...
tube
...
at
...
the
...
T
...
as
...
is
...
described
...
in
...
the
...
...
...
...
...
.
...
The
...
FC
...
was
...
fed
...
from
...
a
...
bucket
...
of
...
water
...
less
...
than
...
1
...
m
...
above
...
it
...
at
...
all
...
times,
...
ensuring
...
that
...
there
...
were
...
not
...
significant
...
changes
...
in
...
water
...
level
...
within
...
the
...
FC.
...
The
...
FC
...
was
...
positioned
...
at
...
a
...
level
...
even
...
with
...
the
...
lever
...
arm
...
such
...
that
...
it
...
dosed
...
no
...
water
...
when
...
the
...
lever
...
arm
...
was
...
zeroed.
...
The
...
FC
...
began
...
to
...
dose
...
with
...
a
...
change
...
in
...
driving
...
head
...
of
...
1mm
...
from
...
that
...
zero.
...
To
...
measure
...
flowrate
...
from
...
the
...
FC
...
through
...
the
...
CD
...
a
...
7kPa
...
pressure
...
sensor
...
was
...
used
...
at
...
the
...
bottom
...
of
...
the
...
collection
...
column.
...
Water
...
flowed
...
from
...
the
...
FC
...
through
...
the
...
T
...
into
...
the
...
chemical
...
dosing
...
tube
...
and
...
then
...
into
...
the
...
column.
...
The
...
pressure
...
sensor
...
at
...
the
...
base
...
of
...
the
...
collection
...
column
...
was
...
calibrated
...
to
...
read
...
in
...
centimeters
...
of
...
water,
...
and
...
it
...
was
...
zeroed
...
after
...
the
...
valve
...
at
...
the
...
base
...
of
...
the
...
column
...
had
...
been
...
opened
...
and
...
the
...
water
...
completely
...
drained
...
out.
...
As
...
water
...
was
...
dosed
...
from
...
the
...
FC
...
into
...
the
...
column,
...
the
...
pressure
...
sensor
...
transmitted
...
data
...
to
...
a
...
computer
...
running
...
the
...
program
...
Easy
...
Data,
...
which
...
recorded
...
both
...
water
...
level
...
and
...
time
...
lapse
...
in
...
1
...
second
...
steps.
...
Since
...
the
...
column
...
dimensions
...
are
...
known,
...
these
...
variables
...
can
...
then
...
be
...
used
...
to
...
solve
...
for
...
a
...
flowrate.
...
Concurrent
...
data
...
from
...
the
...
pressure
...
sensor
...
at
...
the
...
base
...
of
...
the
...
bucket
...
can
...
be
...
used
...
to
...
show
...
the
...
exact
...
height
...
of
...
the
...
float
...
relative
...
to
...
the
...
apparatus
...
for
...
each
...
flowrate.
...
Data
...
was
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collected
...
at
...
several
...
float
...
heights
...
for
...
each
...
distance
...
the
...
chemical
...
dosing
...
tube
...
was
...
attached
...
along
...
the
...
lever
...
arm
...
or
...
10
...
cm,
...
15
...
cm,
...
20
...
cm,
...
and
...
25
...
cm.
...
Experimental Results
All laboratory data was analyzed using the MathCAD program CDFall08LeverT, which can be found attached to the main CD page. Data arrays of column water height were transformed to flowrates at each float height and chem doser position studied. The data can be seen in the figure below. Each set of color coded data represents readings from one specific chem doser position along the lever arm, given in centimeters out from the pivot.
For the Lab Prototype
The data appears linear when the chem doser was placed 15 cm (pink points on graph below), 20 cm (green), or 25 cm (blue) from the pivot point, but it becomes less predictable at only 10 cm (red). The system also loses reliability around 0.08 mL/sec dosing, as can been seen in both the red and blue data sets below. This is a very low flow rate, and it is possible that surface tension and head loss are playing a significant role in the system at this point.
The final concern with this data is that there is not equal distance in the y-axis direction between the four lines. Theoretically we should expect the slope of each line to equal the sum of the slope of the line below it and the slope of the 5 cm line. In other words, moving out each 5 cm interval along the lever arm should result in a line that is rotated by a consistent angle around the origin. Visual inspection of the graph above shows that the data from the doser being located 15 cm from the pivot (shown in blue) appears to be translated downward slightly. The data does not appear to go through the origin, and it does not lie evenly between the 10 cm and 20 cm data lines when rotated around the origin.
Overall the data does follow an expected pattern, with a few unexpected readings. Flow rate increases as float height and distance from the pivot increases, allowing us to consider the CD reliable enough to dose alum to a precise enough degree.
For the Robust System
Data for the robust CD system is much less accurate than for the prototype. Data for the doser at 5 cm from the pivot (in red points), at 20 cm (in pink), and at 25 cm (in teal) appears to be linear, passing through the origin, and approximately evenly spaced. On the other hand the data from 10 cm and 15 cm out (in blue and green respectively) do not fit the expected pattern. The 10 cm data appears to be higher than expected, with a less steep slope. Similarly to the prototype testing, the 15 cm data appears to have too high of a slope and be translated downwards.
Comparing Both Systems
The inconsistencies become apparent when the data sets are laid on top of one another. In the graph below, the triangle points are data collected with the robust set up, while the circular points are from testing the prototype. Theoretically the two data sets should lay on identical trajectories, but only the 15 cm and 25 cm data sets are close. The 15 cm data sets fit the best, but they are also the farthest off of the theoretical trajectory anticipated.
Sources of Error
The largest source of error is that the system may not have had enough time to come to equilibrium each time it was moved. Changing the position of the dosing tube changed the driving head, which takes an unknown amount of time to re-equilibrate. Also each time the bucket water level was changed, it took and unknown amount of time for the float to come completely back to rest. The bucket was small enough that any mixing from adding or removing water would send relatively large ripples throughout. These visibly caused the float to move, which would in turn directly effect the doser for some period of time.
Another major issue with the experimental set up was that the pressure sensors were not reliable. The pressure sensors became unresponsive and had to be re-zeroed at least twice while testing the robust set up. This may indicate that the sensors were not producing accurate data at other points during the experiment without our noticing.