...
Data
...
Acquisition
...
The
...
Flocculator
...
Residual
...
Turbidity
...
Analyzer
...
(FReTA)
...
allows
...
us
...
to
...
gather
...
data
...
and
...
investigate
...
a
...
number
...
of
...
different
...
factors
...
affecting
...
flocculator
...
performance,
...
including
...
shear
...
(G),
...
residence
...
time
...
(θ),
...
alum
...
dose,
...
and
...
influent
...
turbidity.
...
The
...
shear
...
rate
...
in
...
the
...
flocculator
...
can
...
be
...
controlled
...
in
...
...
...
by
...
either
...
holding
...
constant
...
or
...
varying
...
the
...
plant
...
flow
...
rate
...
as
...
desired.
...
A
...
given
...
flow
...
rate
...
will
...
define
...
a
...
particular
...
shear
...
rate
...
in
...
the
...
flocculator.
...
The
...
shear
...
rates
...
in
...
the
...
tube
...
flocculator
...
can
...
be
...
calculated
...
from
...
flow
...
rates
...
and
...
other
...
characteristics
...
of
...
the
...
setup
...
using
...
the
...
following
...
equations:
...
The
...
following
...
equations
...
and
...
methods
...
were
...
developed
...
to
...
describe
...
shear
...
in
...
FReTA
...
by
...
Ian
...
Tse
...
in
...
his
...
thesis:
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
Based on dimensional analysis, the velocity gradient G can be expressed as a function of the average energy dissipation rate (ε) and kinematic viscosity of the fluid (ν):
| Wiki Markup |
|---|
performance_|Tube Floc Data Acquisition^Ian Tse MS Thesis.doc]_ _Based on dimensional analysis, the velocity gradient G can be expressed as a function of the average energy dissipation rate (ε) and kinematic viscosity of the fluid (ν):_ {latex} \large $$ G = \sqrt {{\varepsilon \over \nu }} $$ {latex} _ |
(1.3)
...
Using
...
conservation
...
of
...
energy,
...
ε
...
can
...
be
...
expressed
...
as
...
kinetic
...
energy
...
loss
...
over
...
a
...
period
...
of
...
time:
| Wiki Markup |
|---|
_ {latex} \large $$ \varepsilon = {{gh_L } \over \theta } $$ {latex} _ |
(1.4)
...
where:
...
g
...
is
...
gravitational
...
acceleration,
...
hL
...
is
...
head
...
loss
...
and
...
θ
...
is
...
average
...
hydraulic
...
residence
...
time.
...
The
...
head
...
loss
...
through
...
a
...
straight
...
tube
...
can,
...
in
...
turn,
...
be
...
defined
...
as
...
(Robertson
...
et
...
al,
...
1993):
| Wiki Markup |
|---|
_ {latex} \large $$ h_L = f_s {L \over d}{{U^2 } \over {2g}} $$ {latex} _ |
(1.5)
...
where:
...
L
...
is
...
the
...
length
...
of
...
the
...
flocculator
...
and
...
fs
...
is
...
the
...
friction
...
factor
...
in
...
a
...
straight
...
tube.
...
For
...
laminar
...
flow,
...
the
...
friction
...
factor
...
fs
...
=
...
64/Red,
...
and
...
Red
...
is
...
the
...
Reynolds
...
number
...
as
...
defined
...
as:
| Wiki Markup |
|---|
_ {latex} \large $$ {\mathop{\rm Re}\nolimits} _d = {{Ud} \over \nu } $$ {latex} _ |
(1.6)
...
where:
...
U
...
is
...
the
...
average
...
axial
...
velocity
...
and
...
d
...
is
...
the
...
tube
...
inner
...
diameter.
...
The
...
formulation
...
for
...
G
...
derived
...
by
...
Gregory
...
(1981)
...
(see
...
Equation
...
1.2)
...
can
...
also
...
be
...
derived
...
from
...
algebraic
...
rearrangement
...
of
...
Equations
...
1.3-1.6.
...
A
...
correlation
...
factor
...
(Mishra
...
&
...
Gupta
...
1979)
...
can
...
be
...
applied
...
to
...
Equation
...
1.7
...
to
...
replace
...
fs
...
with
...
fc
...
and
...
correct
...
for
...
the
...
differences
...
in
...
head
...
loss
...
between
...
straight
...
and
...
curved
...
tubes.
| Wiki Markup |
|---|
_ {latex} \large $$ {{f_c } \over {f_s }} = 1 + 0.033\log \left( {De} \right)^4 $$ {latex} _ |
(1.7)
...
where:
...
De
...
is
...
the
...
nondimensional
...
Dean
...
Number
...
and
...
characterizes
...
the
...
effect
...
of
...
curvature
...
on
...
fluid
...
flow:
| Wiki Markup |
|---|
_ {latex} \large $$ De = \sqrt {{r \over {R_c }}} {\mathop{\rm Re}\nolimits} _d $$ {latex} _ |
(1.8)
...
where:
...
r
...
is
...
the
...
inner
...
radius
...
of
...
the
...
tube,
...
Rc
...
is
...
the
...
radius
...
of
...
curvature.
...
The
...
average
...
head
...
loss
...
measured
...
as
...
the
...
pressure
...
drop
...
across
...
the
...
tube
...
flocculator
...
was
...
within
...
2%
...
of
...
the
...
head
...
loss
...
calculated
...
using
...
Equations
...
1.5
...
and
...
1.7
...
(Figure
...
1.4).
...
The
...
figure
...
eight
...
coil
...
configuration
...
used
...
in
...
this
...
research
...
was
...
different
...
from
...
the
...
flow
...
regime
...
modeled
...
by
...
Mishra
...
and
...
Gupta.
...
The
...
fact
...
that
...
our
...
data
...
agrees
...
with
...
their
...
model
...
suggests
...
that
...
the
...
change
...
in
...
direction
...
of
...
the
...
coil
...
had
...
only
...
a
...
small
...
effect
...
on
...
total
...
head
...
loss.
...
The
...
following
...
G
...
value
...
obtained
...
from
...
combining
...
Equations
...
1.3-1.8
...
was
...
used
...
to
...
design
...
the
...
experimental
...
runs.
| Wiki Markup |
|---|
_ {latex} \large $$ G_c = G_s \left( {1 + 0.033\log \left( {De} \right)^4 } \right)^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}} $$ {latex} _ |
(1.9)
...
We
...
can
...
also
...
study
...
the
...
effect
...
of
...
increasing
...
the
...
residence
...
time
...
in
...
the
...
flocculator
...
and
...
holding
...
shear
...
constant
...
by
...
increasing
...
the
...
length
...
of
...
the
...
flocculator
...
while
...
holding
...
the
...
flow
...
rate
...
constant;
...
this
...
will
...
increase
...
the
...
amount
...
of
...
time
...
water
...
spends
...
in
...
the
...
flocculator
...
without
...
changing
...
the
...
shear
...
rate.
...
Currently,
...
setup
...
can
...
easily
...
be
...
modified
...
to
...
handle
...
three
...
different
...
flocculator
...
lengths,
...
27.96
...
m,
...
55.92
...
m,
...
and
...
83.88
...
m.
...
...
...
can
...
also
...
be
...
used
...
to
...
vary
...
alum
...
dosage,
...
and
...
set
...
the
...
desired
...
influent
...
turbidity
...
for
...
the
...
raw
...
water.
...
This
...
allows
...
us
...
complete
...
control
...
over
...
what
...
enters
...
the
...
flocculator,
...
how
...
long
...
it
...
spends
...
in
...
the
...
flocculator,
...
and
...
how
...
quickly
...
it
...
moves
...
through
...
the
...
flocculator.
...
When
...
running
...
an
...
experiment
...
on
...
FReTA,
...
we
...
allow
...
1.5-2
...
flocculator
...
residence
...
times
...
to
...
pass
...
before
...
collecting
...
data.
...
This
...
ensures
...
that
...
the
...
alum
...
has
...
the
...
necessary
...
time
...
to
...
react
...
with
...
the
...
clay
...
particles
...
in
...
order
...
to
...
produce
...
a
...
steady
...
state
...
distribution
...
of
...
flocs
...
at
...
the
...
end
...
of
...
the
...
flocculator.
...
After
...
this
...
loading
...
time,
...
...
...
begins
...
the
...
actual
...
data
...
collection.
...
The
...
pumps
...
ramp
...
down
...
gradually,
...
and
...
a
...
ball
...
valve
...
is
...
used
...
to
...
seal
...
off
...
the
...
settling
...
column
...
(see
...
...
...
)
...
from
...
the
...
rest
...
of
...
the
...
flocculator
...
over
...
a
...
period
...
of
...
6
...
seconds.
...
The
...
reason
...
for
...
this
...
gradual
...
shut
...
down
...
is
...
to
...
prevent
...
turbulence
...
that
...
could
...
disrupt
...
flocs
...
in
...
the
...
settling
...
column.
...
...
...
then
...
records
...
the
...
residual
...
turbidity
...
every
...
second
...
for
...
half
...
an
...
hour
...
(1800
...
s)
...
at
...
which
...
point
...
the
...
valves
...
open
...
to
...
begin
...
backwashing
...
for
...
a
...
new
...
run.
...
The
...
settling
...
velocities
...
corresponding
...
to
...
the
...
time
...
range
...
we
...
are
...
studying
...
are
...
calculated
...
by
...
dividing
...
the
...
distance
...
between
...
the
...
valve
...
and
...
the
...
effluent
...
turbiditmeter
...
in
...
the
...
settling
...
column
...
(16
...
cm)
...
by
...
the
...
time
...
since
...
settling
...
began.
...
Thus,
...
the
...
remaining
...
turbidity
...
after
...
10
...
s
...
of
...
settling
...
would
...
correspond
...
to
...
all
...
particles
...
with
...
a
...
settling
...
velocity
...
of
...
greater
...
than
...
1.6
...
cm/s.
...
We
...
are
...
not
...
interested
...
in
...
recording
...
data
...
after
...
half
...
an
...
hour
...
because
...
this
...
corresponds
...
to
...
extremely
...
low
...
settling
...
velocities
...
(>0.0889
...
mm/s).
...
Additionally,
...
we
...
define
...
residual
...
turbidity
...
as
...
the
...
turbidity
...
with
...
settling
...
velocity
...
less
...
than
...
0.12
...
mm/s.
...
This
...
is
...
the
...
capture
...
velocity
...
of
...
the
...
plate
...
settlers,
...
so
...
any
...
particles
...
with
...
lower
...
setting
...
velocities
...
will
...
exit
...
with
...
the
...
effluent.