...
Data
...
Analysis
...
New
...
Tasks
...
for
...
Spring
...
2013
...
Floc
...
sedimentation
...
velocity
...
vs
...
coagulant
...
dose
...
| Excerpt |
|---|
...
Process |
...
the |
...
data |
...
from |
...
Karen |
...
Swetland’s research |
...
to |
...
extract |
...
the |
...
average |
...
floc |
...
sedimentation |
...
velocity |
...
as |
...
a |
...
function |
...
of |
...
coagulant |
...
dosage. |
...
It |
...
should |
...
be |
...
possible |
...
to |
...
assess |
...
which |
...
coagulant, |
...
PACl |
...
or |
...
alum, |
...
produces |
...
flocs |
...
with |
...
a |
...
higher |
...
sedimentation |
...
velocity |
...
given |
...
the |
...
same |
...
aluminum |
...
concentration. |
...
This |
...
task |
...
does |
...
not |
...
require |
...
any |
...
additional |
...
laboratory |
...
work. |
...
It |
...
will |
...
require |
...
writing |
...
code |
...
to |
...
streamline |
...
the |
...
data |
...
extraction |
...
process. |
...
Think |
...
carefully |
...
about |
...
the |
...
best |
...
way |
...
to |
...
measure |
...
the |
...
time |
...
at |
...
which |
...
the |
...
turbidity |
...
is |
...
at |
...
50% |
...
of |
...
the |
...
flocculated |
...
water |
...
turbidity. |
...
Some |
...
data |
...
smoothing |
...
or |
...
line |
...
fitting |
...
may |
...
be |
...
needed |
...
to |
...
get |
...
a |
...
reasonable |
...
estimate |
...
of |
...
the |
...
time. |
...
Create |
...
graphs |
...
of |
...
mean |
...
floc |
...
size |
...
as |
...
a |
...
function |
...
of |
...
coagulant |
...
dose |
...
for |
...
each |
...
of |
...
the |
...
turbidities |
...
that |
...
are |
...
available. |
...
Determine |
...
if |
...
the |
...
ratio |
...
of |
...
mass |
...
of |
...
coagulant |
...
per |
...
mass |
...
of |
...
clay |
...
is |
...
a |
...
good |
...
predictor |
...
of |
...
floc |
...
sedimentation |
...
velocity. |
...
Analyze |
...
the |
...
results |
...
using |
...
the |
...
insights |
...
from |
...
our |
...
new |
...
flocculation |
...
model |
...
that |
...
emphasizes |
...
the |
...
role |
...
of |
...
fractional |
...
surface |
...
coverage. |
...
Determine |
...
if |
...
equilibrium |
...
floc |
...
size |
...
can |
...
be |
...
predicted |
...
from |
...
the |
...
fractional |
...
surface |
...
coverage |
...
or |
...
if |
...
a |
...
more |
...
complex |
...
analysis |
...
is |
...
required. |
...
Make |
...
sure |
...
to |
...
take |
...
into |
...
account |
...
that |
...
for |
...
low |
...
turbidity |
...
samples |
...
more |
...
of |
...
the |
...
coagulant |
...
ends |
...
up |
...
on |
...
the |
...
flocculator |
...
walls. |
...
Past Research
Overview
During each experiment,data
...
are
...
automatically
...
recorded
...
in
...
an
...
Excel
...
file
...
(see
...
example).
...
The
...
address
...
for
...
the
...
excel
...
file
...
is
...
recorded
...
into
...
the
...
Meta
...
file
...
which
...
is
...
a
...
spreadsheet
...
with
...
all
...
the
...
directories
...
of
...
the
...
experimental
...
data
...
that
...
will
...
be/has
...
been
...
analyzed.
...
Process
...
Controller
...
will
...
be
...
referring
...
to
...
the
...
Meta
...
file
...
in
...
order
...
to
...
acquire
...
appropriate
...
information
...
on
...
the
...
experiment
...
being
...
analyzed;
...
the
...
Meta
...
file
...
will
...
be
...
an
...
address
...
book
...
for
...
Data
...
Processor
...
to
...
efficiently
...
access
...
data.
...
The
...
first
...
graphs
...
produced
...
by
...
the
...
Mathcad
...
file
...
are
...
the
...
plots
...
of
...
the
...
raw
...
turbidity
...
data
...
vs.
...
time
...
and
...
raw
...
turbidity
...
vs.
...
settling
...
velocity.
...
The
...
settling
...
velocity
...
(Vs)
...
is
...
calculated
...
by
...
dividing
...
the
...
distance
...
between
...
the
...
ball
...
valve
...
and
...
the
...
zone
...
illuminated
...
by
...
the
...
infrared
...
LED
...
(z)
...
of
...
FRETA
...
by
...
the
...
time
...
elapsed(t).
| Latex |
|---|
} \large $$ V_s = {z \over t} $$ {latex} |
For
...
experiments
...
involving
...
varying
...
alum
...
dosage,
...
another
...
graph
...
was
...
produced
...
to
...
obtain
...
the
...
residual
...
turbidity
...
vs.
...
settling
...
velocity.
...
Residual
...
turbidity
...
is
...
the
...
turbidity
...
resulting
...
from
...
the
...
flocs
...
that
...
failed
...
to
...
reach
...
the
...
capture
...
velocity,
...
which
...
is
...
0.12
...
mm/s
...
for
...
the
...
sedimentation
...
tanks
...
of
...
the
...
AguaClara
...
plants.
...
From
...
this,
...
we
...
can
...
get
...
the
...
mean
...
residual
...
turbidity
...
for
...
each
...
variation
...
of
...
alum
...
dose.
...
The
...
mean
...
residual
...
turbidity
...
is
...
the
...
mean
...
of
...
all
...
the
...
raw
...
turbidity
...
measured
...
after
...
a
...
time
...
of
...
approximately
...
22
...
min
...
till
...
the
...
end
...
of
...
the
...
sedimentation
...
state.
...
It
...
corresponds
...
to
...
a
...
range
...
of
...
sedimentation
...
velocities
...
from
...
0.12
...
mm/s
...
to
...
0.089
...
mm/s.
...
See
...
example
...
of
...
the
...
residual
...
turbidity
...
graph:
...
...
...
...
...
.
...
TThen
...
data
...
smoothing
...
and
...
normalization
...
are
...
performed
...
on
...
the
...
raw
...
turbidity
...
data.
...
The
...
smoothing
...
allows
...
us
...
to
...
exclude
...
outlying
...
data
...
points
...
caused
...
by
...
really
...
large
...
flocs
...
passing
...
in
...
front
...
of
...
the
...
light
...
sensor
...
of
...
FRETA,
...
which
...
create
...
turbidity
...
fluctuations.
...
The
...
normalization
...
allows
...
us
...
to
...
compare
...
data
...
sets
...
with
...
varying
...
influent
...
turbidities.
...
The
...
plot
...
of
...
normalized
...
turbidity
...
vs.
...
Vs
...
(settling
...
velocity)
...
can
...
be
...
interpreted
...
as
...
a
...
cumulative
...
distribution
...
function
...
(CFD)
...
of
...
turbidity
...
with
...
respect
...
to
...
Vs.
...
A
...
CFD
...
describes
...
the
...
probability
...
that
...
a
...
variable
...
is
...
less
...
than
...
or
...
equal
...
to
...
some
...
value.
...
To
...
make
...
the
...
analysis
...
more
...
robust,
...
the
...
experimental
...
data
...
was
...
fit
...
to
...
a
...
gamma
...
distribution.
...
Then
...
a
...
derivative
...
of
...
the
...
CFD
...
of
...
the
...
gamma
...
distribution
...
gives
...
a
...
probability
...
distribution
...
of
...
the
...
particle
...
population
...
with
...
respect
...
to
...
Vs.
...
From
...
the
...
fitted
...
data,
...
the
...
data
...
processor
...
retrieves
...
the
...
mean
...
sedimentation
...
velocity
...
for
...
each
...
alum
...
dose
...
as
...
well
...
as
...
the
...
coefficient
...
of
...
variation
...
of
...
the
...
distribution.
...
The
...
coefficient
...
of
...
variation
...
is
...
the
...
standard
...
deviation
...
of
...
the
...
distribution
...
divided
...
by
...
the
...
mean.
...
It
...
is
...
an
...
indication
...
of
...
the
...
width
...
of
...
the
...
sedimentation
...
velocity
...
distribution.
...
For
...
more
...
discussion
...
of
...
the
...
data
...
analysis,
...
see
...
Ian
...
Tse's
...
...
(Chapter
...
I,
...
data
...
analysis).
...
See
...
an
...
example
...
of
...
the
...
gamma
...
...
graph:
...
...
...
...
...
...
...
.
...
Analysis
...
Process
...
The
...
data
...
analysis
...
process
...
of
...
the
...
current
...
project
...
emphasizes
...
organization
...
and
...
accuracy.
...
The
...
following
...
is
...
a
...
step-by-step
...
guide
...
for
...
the
...
analysis
...
process.
...
1.
...
Go
...
to
...
the
...
file
...
containing
...
the
...
desired
...
experimental
...
data
...
2.
...
Skim
...
through
...
the
...
datalog
...
(excel
...
sheet
...
with
...
experimental
...
data)
...
to
...
check
...
for
...
any
...
apparent
...
error.
...
(Wrong
...
influent
...
turbidity,
...
no
...
variation
...
in
...
alum
...
dose...)
...
3.
...
If
...
no
...
apparent
...
error
...
is
...
found,
...
open
...
the
...
Meta
...
file
...
and
...
record
...
the
...
appropriate
...
information*
...
*
...
-------------------------------------------------------------------------------------------
...
-
...
**Meta
...
File
...
Information
...
-The
...
Meta
...
File
...
is
...
like
...
as
...
an
...
address
...
book
...
for
...
the
...
datalogs.
...
It
...
is
...
important
...
to
...
update
...
this
...
file
...
after
...
an
...
experiment
...
for
...
the
...
Data
...
Processor
...
to
...
access.
...
The
...
steps
...
following
...
will
...
show
...
how
...
information
...
is
...
recorded
...
into
...
the
...
Meta
...
File:
...
a.
...
Put
...
the
...
appropriate
...
ID
...
Tag
...
number
...
in
...
the
...
A
...
column
...
b.
...
If
...
the
...
duration
...
of
...
the
...
experiment
...
was
...
three
...
days,
...
put
...
the
...
first
...
day
...
in
...
the
...
B
...
column,
...
the
...
second
...
day
...
in
...
the
...
C
...
column,
...
and
...
the
...
third
...
day
...
in
...
the
...
D
...
column;
...
if
...
the
...
experiment
...
only
...
lasted
...
for
...
2
...
days,
...
C
...
column
...
will
...
be
...
left
...
as
...
zero,
...
and
...
the
...
following
...
will
...
be
...
applied
...
for
...
an
...
experiment
...
with
...
a
...
one
...
day
...
duration-only
...
the
...
B
...
column
...
will
...
be
...
filled.
...
c.
...
Record
...
the
...
appropriate
...
directory
...
and
...
flocculator
...
length
...
in
...
column
...
F
...
and
...
G
...
d.
...
Column
...
J
...
will
...
be
...
adjusted
...
according
...
to
...
the
...
datalog;
...
it
...
will
...
be
...
the
...
first
...
row
...
in
...
the
...
datalog
...
where
...
the
...
settle
...
state
...
has
...
been
...
activated.
...
**Note,
...
for
...
most
...
experiments,
...
start
...
row
...
is
...
not
...
adjusted
...
e.
...
Comment
...
on
...
the
...
experiment
...
the
...
datalog
...
is
...
referring
...
to
...
(eg.
...
influent
...
turbidity,
...
alum
...
dose,
...
etc.)
...
Remember
...
to
...
save
...
the
...
Meta
...
file.
...
If
...
not,
...
the
...
Data
...
Processor
...
won't
...
be
...
able
...
to
...
access
...
the
...
data
...
!
...
---------------------------------------------------------------------------------------------
...
-
...
4.
...
Open
...
Data
...
Processor
...
on
...
MathCad
...
5.
...
Change
...
the
...
directory
...
Data
...
Processor
...
is
...
referring
...
to
...
for
...
data
...
(Enter
...
the
...
ID
...
tag)
...
*
...
*
...
**Reference
...
address
...
will
...
be
...
located
...
at
...
the
...
top
...
of
...
Data
...
Processor,
...
and
...
only
...
the
...
last
...
portion
...
of
...
the
...
directory
...
will
...
need
...
to
...
be
...
changed-which
...
is
...
the
...
ID
...
tag
...
appearing
...
on
...
the
...
Meta
...
file.
...
To
...
see
...
where
...
to
...
put
...
the
...
MetaID,
...
see
...
figure
...
1
Figure 1: MetaID location in Data Processor
6. Run the Data Processor; this program will automatically give graphic forms of the data and calculate needed values.
7. In the data processor you will need to change a value. FirstFittedcolumn.
The Data processor cannot fit the data for alum dose too low. This will enable you to eliminate the data that would not be fitted from the data vector. To see where to put the fixed FirstFittedcolumn see figure 2.
Figure 2: FirstFittedColumn location in Data Processor