...
Rotameter
...
Head
...
Loss
...
Experiment
Overview
A rotameter can be included between the constant head tank and the flow control orifice in the dose controller to verify the flow rate of chemical. The motivation for this experiment was to determine whether the use of a rotameter would be feasible in the chemical dose controlling system. The head loss through the rotameter would need to follow the relationship of head loss proportional to the square of the flow rate. The head loss through the rotameter was measured to determine if it is suitable for use in the dose controller.
Experimental Setup
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h3. Overview A rotameter can be included between the constant head tank and the flow control orifice in the dose controller to verify the flow rate of chemical. The motivation for this experiment was to determine whether the use of a rotameter would be feasible in the chemical dose controlling system. The head loss through the rotameter would need to follow the relationship of head loss proportional to the square of the flow rate. The head loss through the rotameter was measured to determine if it is suitable for use in the dose controller. h3. Experimental Setup !Rotameter Experiment.JPG|border=2px solid black,align=center,width=500px|align=center,width=500px,height=350px! {center:class=myclass}h5.Figure 1: Experimental Setup{center} |
The
...
head
...
loss
...
through
...
the
...
rotameter
...
was
...
be
...
determined
...
using
...
the
...
setup
...
that
...
is
...
diagrammed
...
in
...
Figure
...
1.
...
A
...
peristalic
...
pump
...
was
...
used
...
to
...
circulate
...
the
...
fluid
...
at
...
a
...
certain
...
flow
...
rate.
...
Two
...
attenuators
...
were
...
used
...
to
...
minimize
...
the
...
effect
...
of
...
the
...
pulsing
...
from
...
the
...
peristalic
...
pump,
...
and
...
one
...
pressure
...
sensor
...
was
...
used
...
to
...
measure
...
the
...
pressure
...
difference
...
before
...
and
...
after
...
the
...
rotameter.
...
A
...
ramp
...
function
...
in
...
process
...
controller
...
was
...
used
...
to
...
control
...
the
...
flow
...
rate
...
of
...
the
...
circulating
...
fluid.
...
The
...
flow
...
rate
...
was
...
gradually
...
increased
...
from
...
8
...
ml/min
...
to
...
380
...
ml/min.
...
The
...
head
...
loss
...
was
...
be
...
determined
...
by
...
performing
...
an
...
energy
...
balance
...
around
...
the rotameter.
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{float}{float} |
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rotameter. !Rotameterguide.png|border=2px solid black,align=center,width=300px|align=center,width=300px,height=350px! {float} {center:class=myclass}h5.Figure 2: Measurement Diagram{center} |
From
...
the
...
energy
...
equation
...
head
...
loss
...
can
...
be
...
expressed
...
as
...
a
...
function
...
of
...
the
...
difference
...
in
...
the
...
pressure,
...
velocity,
...
and
...
height
...
difference.
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{latex}$$ h_L = {P_1 - P_2\over {pg}} + {V_1^2 - V_2^2\over {2g}} + {z_1 - z_2} $${latex} |
Since
...
flow
...
is
...
controlled
...
by
...
the
...
peristalic
...
pump,
...
the
...
flow
...
is
...
constant,
...
and
...
since
...
the
...
tube
...
diameter
...
is
...
also
...
constant,
...
there
...
would
...
be
...
no
...
difference
...
in
...
the
...
velocity.
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{latex}$$ h_L = {P_1 - P_2\over {pg}} + 0 + {z_1 - z_2} $${latex} |
If
...
the
...
pressure
...
difference
...
is
...
measured
...
when
...
there
...
is
...
no
...
flow,
...
then
...
the
...
head
...
loss
...
and
...
the
...
velocity
...
terms
...
from
...
the
...
energy
...
equation
...
would
...
be
...
zero.
...
This
...
allows
...
the
...
height
...
difference
...
to
...
be
...
expressed
...
as
...
the
...
pressure
...
reading
...
from
...
the
...
standing
...
water.
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{latex}$$ {P_{1standing} - P_{2standing}\over {pg}} = z_2 - z_1 $${latex} |
The
...
pressure
...
reading
...
from
...
the
...
standing
...
water
...
is
...
subtracted
...
from
...
the
...
measured
...
pressure
...
difference
...
values
...
to
...
cancel
...
out
...
the
...
height
...
term.
...
The
...
resulting
...
pressure
...
difference
...
corresponds
...
directly
...
to
...
head
...
loss
...
of
...
the
...
rotameter.
...
Results
The experiment looked at the response of the rotameter to flow rates of 8 to 380 mL/min.
...
This
...
range
...
is
...
in
...
the
...
alum
...
flow
...
range
...
of
...
5
...
to
...
100
...
mL/min,
...
at
...
which
...
the
...
current
...
nonlinear
...
doser
...
operates.
...
For
...
larger
...
plants
...
which
...
would
...
have
...
higher
...
plant
...
flow
...
rates
...
and
...
thus
...
would
...
require
...
higher
...
dosing,
...
the
...
maximum
...
alum
...
flow
...
rate
...
would
...
be
...
larger.
...
Thus,
...
the
...
range
...
investigate
...
in
...
this
...
experiment
...
appropriately
...
depicted
...
reasonable
...
flow
...
rates
...
through
...
the
...
doser.
...
As
...
seen
...
in
...
Figures
...
2
...
and
...
3,
...
the
...
experimental
...
data
...
fit
...
best
...
to
...
a
...
0.09
...
in
...
orifice
...
with
...
a
...
2
...
cm
...
offset
...
in
...
pressure.
...
This
...
2
...
cm
...
of
...
extra
...
head
...
needed
...
to
...
fit
...
the
...
0.09
...
in
...
orifice
...
model
...
has
...
been
...
hypothesized
...
to
...
be
...
caused
...
by
...
the
...
energy
...
needed
...
to
...
lift
...
the
...
ball float.
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float. !3.09.10 Full Flow.png|border=2px solid black,align=center,width=500px|align=center,width=500px,height=350px! {center:class=myclass}h5.Figure 2: Full Flow Experiment #1 (3/09/10): 8 - 380 mL/min{center} \\ !3.11.10 Full Flow.png|border=2px solid black,align= |
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center,width=500px|align=center,width=500px,height=350px! {center:class=myclass}h5. Figure 3: Full Flow Experiment #2 (3/11/10): 8 - 380 mL/min{center} \\ In Figures 2 and 3 there is also a seemingly linear response in the data at low flow rates. Another experiment was performed at 8 to 40 mL/min flow rates to determine if this was indeed linear. !3.11.10 Low Flow.png|border=2px solid black,align |
In Figures 2 and 3 there is also a seemingly linear response in the data at low flow rates. Another experiment was performed at 8 to 40 mL/min flow rates to determine if this was indeed linear.
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=center,width=500px|align=center,width=500px,height=350px! {center:class=myclass}h5. Figure 4: Low Flow Experiment #1 (3/11/10): 8 - 40 mL/min{center} \\ !3.12.10 Low Flow.png|border= |
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2px solid black,align=center,width=500px|align=center,width=500px,height=350px! {center:class=myclass}h5. Figure 5: Low Flow Experiment #2 (3/12/10): 8 - 40 mL/min{center} \\ From the |
From the data,
...
it
...
seems
...
that
...
there
...
is
...
a
...
linear
...
response
...
at
...
low
...
flow
...
rates
...
until
...
about
...
25-30
...
mL/min.
...
(All
...
data
...
and
...
results
...
can
...
be
...
found
...
on
...
the
...
...
...
.
Conclusions/Future
...
Work
...
It
...
was
...
concluded
...
that
...
the
...
relationship
...
between
...
head
...
loss
...
and
...
flow
...
rate
...
in
...
the
...
rotameter
...
has
...
an
...
inconsistent
...
relationship.
...
At
...
the
...
lower
...
flow
...
rates,
...
there
...
seems
...
to
...
be
...
a
...
linear
...
relationship
...
until
...
about
...
25-30
...
mL.
...
At
...
higher
...
flow
...
rates
...
it
...
behaves
...
like
...
an
...
orifice
...
with
...
head
...
loss
...
varying
...
with
...
the
...
square
...
of
...
the
...
flow
...
rate.
...
When
...
we
...
modeled
...
the
...
rotameter
...
as
...
a
...
0.09
...
in
...
orifice,
...
the
...
data
...
fit
...
if
...
we
...
added
...
a
...
2
...
cm
...
offset
...
to
...
the
...
head
...
loss.
...
Thus,
...
there
...
seems
...
to
...
be
...
an
...
additional
...
amount
...
of
...
energy
...
needed
...
by
...
the
...
rotameter.
...
We
...
believe
...
this
...
energy
...
is
...
required
...
to
...
lift
...
the
...
ball
...
float.
...
This
...
extra
...
energy
...
needed
...
will
...
always
...
be
...
present
...
and
...
causes
...
errors
...
at
...
lower
...
flow
...
rates.
...
This
...
also
...
results
...
in
...
a
...
non-zero
...
intercept
...
for
...
the
...
flow
...
vs.
...
head
...
loss
...
relationship
...
in
...
the
...
rotameters,
...
making
...
them
...
inappropriate
...
to
...
use
...
with
...
the
...
doser
...
which
...
was
...
designed
...
using
...
a
...
flow
...
varying
...
with
...
the
...
square
...
root
...
of
...
h
...
relationship.
...
Thus,
...
we
...
recommend
...
using
...
other
...
flow
...
measurement
...
devices,
...
such
...
as
...
calibration
...
columns,
...
with
...
the
...
doser.
...