...
Summary
...
of
...
the
...
Design
...
Process(Continued):
...
Our
...
next
...
step
...
consists
...
of
...
developing
...
the
...
dual
...
nonlinear
...
scale
...
and
...
the
...
two
...
orifices
...
for
...
our
...
two
...
sets
...
of
...
target
...
alum
...
concentrations:
...
5-25
...
mg/L
...
and
...
20-100
...
mg/L.
...
Given
...
a
...
known
...
maximum
...
plant
...
flow
...
rate(
| Wiki Markup |
|---|
{latex}\large$$Q_{P}$${latex} |
...
and
...
Alum
...
Stock
...
concentration(
| Wiki Markup |
|---|
{latex}\large$$C_{C} $${latex} |
...
we
...
utilized
...
the
...
mass
...
balance
...
equation
...
to
...
determine
...
alum
...
flow
...
rate
...
required
...
for
...
each
...
target
...
alum
...
concentration
...
as
...
shown
...
below:
| Wiki Markup |
|---|
{latex} \large $$ Q_{Alum} = {{Q_P \times C_T } \over {C_C }} $$ {latex} Where |
Where
| Wiki Markup |
|---|
{latex}\large$$Q_{Alum} $${latex} |
...
Flow
...
Rate
...
of
...
Alum
...
Solution
| Wiki Markup |
|---|
{latex}\large$$Q_{P} $${latex} |
...
Plant
...
Flow
...
Rate
| Wiki Markup |
|---|
{latex}\large$$C_{T} $${latex} |
...
Target
...
Alum
...
Concentration
| Wiki Markup |
|---|
{latex}\large$$C_{C} $${latex} |
...
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:
| Wiki Markup |
|---|
{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 |
Where
| Wiki Markup |
|---|
{latex}\large$$Q_{Alum} $${latex} |
...
Flow
...
Rate
...
of
...
Alum
...
Solution
| Wiki Markup |
|---|
{latex}\large$$Q_{P} $${latex} |
...
Plant
...
Flow
...
Rate
| Wiki Markup |
|---|
{latex}\large$$h $${latex} |
...
Head
...
loss
| Wiki Markup |
|---|
{latex}\large$$D_{Orifice} $${latex} |
...
Diameter
...
of
...
the
...
Orifice
| Wiki Markup |
|---|
{latex}\large$$K_{VC} $${latex} |
...
Orifice
...
Constant
...
We
...
then
...
convert
...
these
...
head
...
losses
...
to
...
points
...
along
...
our
...
scale
...
via
...
simple
...
geometry
...
as
...
shown
...
below:
| Wiki Markup |
|---|
{latex} \large $$ scale = {\textstyle{h \over {\sin (\theta _{Max} )}}} $$ {latex} Where |
Where
| Wiki Markup |
|---|
{latex}\large$$scale $${latex} |
...
distance
...
from
...
the
...
pivot
...
to
...
a
...
point
...
on
...
the
...
scale
| Wiki Markup |
|---|
{latex}\large$$h $${latex} |
...
head
...
loss
...
from
...
the
...
previous
...
paragraph
| Wiki Markup |
|---|
{latex}\large$${\theta _{Max} }$${latex} |
...
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:
| Wiki Markup |
|---|
below: !DualScale.png|border=2px solid black,align=center,width=500px|align=center,width=500px,height=75px! {center:class=myclass}h5.Figure 1: Nonlinear Dual Scale{center} |
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
...
...
...
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
...