...
Summary
...
of
...
the
...
Design
...
Process(Continued):
...
Our
...
next
...
step
...
consists
...
of
...
developing
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the
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dual
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nonlinear
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scale
...
and
...
the
...
two
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orifices
...
for
...
our
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two
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sets
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of
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target
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alum
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concentrations:
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5-25
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mg/L
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and
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20-100
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mg/L.
...
Given
...
a
...
known
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maximum
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plant
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flow
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rate(
...
| Latex |
|---|
...
\large$$Q_{P}$$ |
...
...
and
...
Alum
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Stock
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concentration(
...
| Latex |
|---|
...
\large$$C_{C} $$ |
...
...
we
...
utilized
...
the
...
mass
...
balance
...
equation
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to
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determine
...
alum
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flow
...
rate
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required
...
for
...
each
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target
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alum
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concentration
...
as
...
shown
...
below:
| Latex |
|---|
} \large $$ Q_{Alum} = {{Q_P \times C_T } \over {C_C }} $$ {latex} Where {latex} |
Where
| Latex |
|---|
\large$$Q_{Alum} $$ |
...
...
Flow
...
Rate
...
of
...
Alum
...
Solution
...
| Latex |
|---|
...
\large$$Q_{P} $$ |
...
...
Plant
...
Flow
...
Rate
...
| Latex |
|---|
...
\large$$C_{T} $$ |
...
...
Target
...
Alum
...
Concentration
...
| Latex |
|---|
...
\large$$C_{C} $$ |
...
...
Alum
...
Concentration
...
in
...
the
...
Stock
...
Tank
...
Because
...
the
...
orifice
...
controls
...
the
...
flow
...
of
...
this
...
alum
...
solution,
...
we
...
again
...
use
...
the
...
orifice
...
equation.
...
This
...
time
...
we
...
use
...
it
...
to
...
solve
...
for
...
the
...
head
...
loss
...
necessary
...
to
...
achieve
...
these
...
different
...
flow
...
rates.
...
These
...
head
...
losses,
...
or
...
the
...
difference
...
in
...
height
...
from
...
the
...
orifice
...
to
...
the
...
water
...
height
...
in
...
the
...
constant
...
head
...
tank,
...
are
...
calculated
...
as
...
shown
...
below:
| Latex |
|---|
} \large $$ h = {{\left( {{\textstyle{{Q_{Alum} } \over {K_{VC} \times {\textstyle{{D_{Orifice} ^2 } \over 4}} \times \pi }}}} \right)^2 } \over {C_C }} $$ {latex} Where {latex} |
Where
| Latex |
|---|
\large$$Q_{Alum} $$ |
...
...
Flow
...
Rate
...
of
...
Alum
...
Solution
...
| Latex |
|---|
...
\large$$Q_{P} $$ |
...
...
Plant
...
Flow
...
Rate
...
| Latex |
|---|
...
\large$$h $$ |
...
...
Head
...
loss
...
| Latex |
|---|
...
\large$$D_{Orifice} $$ |
...
...
Diameter
...
of
...
the
...
Orifice
...
| Latex |
|---|
...
\large$$K_{VC} $$ |
...
...
Orifice
...
Constant
...
We
...
then
...
convert
...
these
...
head losses to
...
points
...
along
...
our
...
scale
...
via
...
simple
...
geometry
...
as
...
shown
...
below:
| Latex |
|---|
} \large $$ scale = {\textstyle{h \over {\sin (\theta _{Max} )}}} $$ {latex} Where {latex} |
Where
| Latex |
|---|
\large$$scale $$ |
...
...
distance
...
from
...
the
...
pivot
...
to
...
a
...
point
...
on
...
the
...
scale
...
| Latex |
|---|
...
\large$$h $$ |
...
...
head
...
loss
...
from
...
the
...
previous
...
paragraph
...
| Latex |
|---|
...
\large$${\theta _{Max} }$$ |
...
...
Maximum
...
Angle
...
Deflection
...
So
...
that
...
"scale"
...
variable
...
above
...
corresponds
...
to
...
a
...
specific
...
head
...
loss
...
which
...
corresponds
...
to
...
a
...
specific
...
alum
...
flow
...
rate,
...
which
...
corresponds
...
to
...
the
...
target
...
alum
...
concentration
...
that
...
we
...
want
...
in
...
our
...
plant
...
flow.
...
Since
...
we
...
have
...
nine
...
target
...
dosages,
...
we
...
utilized
...
Mathcad
...
to
...
turn
...
the
...
nine
...
target
...
dosages
...
into
...
an
...
array
...
and
...
apply
...
the
...
relationships
...
shown
...
above
...
to
...
produce
...
arrays
...
of
...
corresponding
...
alum
...
flow
...
rates,
...
head
...
losses,
...
and
...
scale
...
points.
...
The
...
array
...
of
...
scale
...
points
...
is
...
essentially
...
the
...
scale
...
for
...
our
...
nonlinear
...
scale.
...
Since
...
all
...
above
...
mentioned
...
parameters
...
are
...
related
...
to
...
one
...
another
...
in
...
a
...
nonlinear
...
relationship,
...
the
...
scale
...
that
...
is
...
generated
...
is
...
nonlinear
...
as
...
shown
...
below:
...
| Center | ||
|---|---|---|
| ||
Figure 1: Nonlinear Dual Scale |
Utilizing our Mathcad file, we varied the orifice diameter until we created a scale that maximized the total available length of the lever arm for the scale which for this lever arm is 0.4 m. We can also manipulate the alum stock concentration to affect orifice size. As the above mentioned equations show, lowering the stock alum concentration means more alum flow which means that we can use a greater orifice diameter while utilizing the same length of the scale part of the lever arm.
Results and Discussions
Currently, our orifices are 3.175 mm for an alum dosage range of 20 to 100 mg/L in 10 mg/L increments and 1.587 mm for an alum dosage range of 5 to 25 mg/L with 2.5 mg/L increments. Our lever arm is 80 cm in length with the pivot point located directly in the center of the arm. The tubing is made up of PVC and has a diameter of 9.525 mm, which is wide and smooth enough to produce negligible head loss on the alum flow. The tubes length is .5 m which can be lowered. For ease of operation, whenever this lever arm is used in the field, it can be delivered to the Aguaclara plant with the dual scales already engraved on the arm. The operator simply has to calibrate the maximum dosage to the maximum flow rate and the lever arm will be ready for operation. The complete calibration procedures can be found on the float page.
We are currently conducting research on the reason why the doser in Honduras is clogging. If alum precipitation is the cause, an option to remedy the problem is to decrease the alum stock concentration which would lead to an increase in orifice size. More dilute stock concentration means less likelihood of alum precipitation while a larger orifice means less chance of alum precipitate getting lodged.
Although negligible, head loss via the tube is a source of error. At most the discrepancy between the scale generated by taking both the orifice and tube head loss into account and the scale generated using only the orifice head loss is only .409 cm, which only occurs at the maximum dosage of 100 mg/L. Currently our PVC tubing is 9.525 mm in diameter and 50 cm long. We can further reduce the error by increasing the diameter and decreasing the length.
Our upcoming goals are to build the lever arm prototype, to set up our hydraulic components and engrave our dual scale. Afterwards, we want to test the lever arm at different dosages and measure the actual flow rates to confirm that the error resulting from tube head loss is negligible.
Bibliography
- CEE4540 Flow Control Measurement Notes at https://confluence.cornell.edu/display/cee4540/Syllabus
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