Calibrate Flow Meters Lab, CM3215 F.
Morrison
CM3215
Fundamentals of Chemical Engineering Laboratory
Calibrate Rotameter and
Orifice Meter and Explore
Reynolds #
Professor Faith Morrison
Department of Chemical Engineering
Michigan Technological University
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© Faith A. Morrison, Michigan Tech U.
Orifice Flow Meters
• Obstruct flow
• Build upstream pressure
• Δ is a function of
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Image source: www.cheresources.com/flowmeas.shtml
© Faith A. Morrison, Michigan Tech U.
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Calibrate Flow Meters Lab, CM3215 F.
Morrison
Orifice Flow Meters
Orifice plate:
(view straight-on)
Flowrate,
1
2
Pressure drop across the orifice is
correlated with flow rate
(mechanical energy balance)
Δ
Δ
Δ
2
(SI-SO, steady,
const., no rxn, no
phase chg, const,
no heat xfer)
,
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© Faith A. Morrison, Michigan Tech U.
Orifice Flow Meters
MEB: Apply MEB between
upstream point (1) and a point in
the vena contracta (2):
Δ
Δ
2
D
,
Δ
0
2
Mass balance:
Combine and eliminate
4
4
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© Faith A. Morrison, Michigan Tech U.
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Calibrate Flow Meters Lab, CM3215 F.
Morrison
Orifice Flow Meters
Apply MEB between upstream
point and a point in the vena
contracta; combine with mass
balance:
D
2
4
1
Q: What should
you plot versus
what to get a
straight line
correlation?
(answer in prelab)
Reference: Morrison, An Introduction to Fluid
Mechanics, Cambridge, 2013, page 837, problem 43.
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© Faith A. Morrison, Michigan Tech U.
Orifice Flow Meters
CM3215 Lab
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© Faith A. Morrison, Michigan Tech U.
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Calibrate Flow Meters Lab, CM3215 F.
Morrison
Rotameter Flow Meters
Reading on the
rotameter
(0-100%) is linearly
correlated with flow rate
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www.alicatscientific.com/images/rotameter_big.gif
© Faith A. Morrison, Michigan Tech U.
Rotameter Flow Meters
Think of the
float cap as
a pointer
Reading on the
rotameter
(0-100%) is linearly
correlated with flow rate
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www.alicatscientific.com/images/rotameter_big.gif
© Faith A. Morrison, Michigan Tech U.
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Calibrate Flow Meters Lab, CM3215 F.
Morrison
Reynolds Number
Re 
 vz D

This combination of experimentally
measureable variables is the key number that
correlates with the flow regime that is
observed. In a pipe:
•Laminar (Re < 2100)
•Transitional
•Turbulent (Re > 4000)
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© Faith A. Morrison, Michigan Tech U.
O. Reynolds’
Dye Experiment, 1883
Transitional flow
Turbulent flow
Images: www.flometrics.com/reynolds_experiment.htm
accessed 4 Feb 2002
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© Faith A. Morrison, Michigan Tech U.
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Calibrate Flow Meters Lab, CM3215 F.
Morrison
Flow Regimes in a Pipe
Dye-injection needle
Laminar
Re
2100
2100 Re
Re
4000
4000
•smooth
•one direction only
•predictable
Transitional
Turbulent
•chaotic - fluctuations within fluid
•transverse motions
•unpredictable - deal with average motion
•most common
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© Faith A. Morrison, Michigan Tech U.
Data may be organized in terms of two
dimensionless parameters:
density
average velocity
true pipe inner diameter
viscosity
pressure drop
pipe length
Reynolds Number
Flow
rate
Re 
 vz D

(This is a
definition)
Fanning Friction Factor
Pressure
Drop
1
P0  PL 
4
f 
2
 L  1
   v z 
 D  2

(This comes from applying
the definition of friction
factor to pipe flow)
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© Faith A. Morrison, Michigan Tech U.
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Calibrate Flow Meters Lab, CM3215 F.
Morrison
Data may be organized in terms of two
dimensionless parameters:
density
average velocity
true pipe inner diameter
viscosity
pressure drop
pipe length
Reynolds Number
Flow
rate
For now, we
(This is a
measure
definition) this
 vz D
Re 

Fanning Friction Factor
Pressure
Drop
1
P0  PL 
4
f 
2
 L  1
   v z 
 D  2

(This comes from applying
the definition of friction
factor to pipe flow)
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© Faith A. Morrison, Michigan Tech U.
Data may be organized in terms of two
dimensionless parameters:
density
average velocity
true pipe inner diameter
viscosity
pressure drop
pipe length
Reynolds Number
Flow
rate
 vz D
Re 

Fanning Friction Factor
Pressure
Drop
1
P0  PL 
4
f 
2
 L  1
   v z 
 D  2

For now, we
(This is a
measure
definition) this
In a few
(This
comes from
weeks,
weapplying
the definition of friction
measure
this
factor
to pipe flow)
as well
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© Faith A. Morrison, Michigan Tech U.
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Calibrate Flow Meters Lab, CM3215 F.
Morrison
Experimental Notes
• Measure orifice pressure drop with DP meter (low
pressures) or Bourdon gauges (high pressures)
• Determine uncertainty for both measurements (reading
error, calibration error, error propagation)
• DP meter has valid output only from 4-20mA – above
20mA it is over range
• What is lowest accurate Δ that you can measure with the
Honeywell DP meter? With the Bourdon gauges?
Consider your uncertainties.
• True triplicates must include all sources of random error
(All steps that it takes to move the system to the operating condition
must be taken for each replicate. Thus, setting the flowrate with the
needle valve and the rotameter must be done for each replicate.)
• Watch level of Tank-01 (there is no overflow protection)
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© Faith A. Morrison, Michigan Tech U.
Report Notes
• Design your graphs to communicate a point clearly (chart
design)
• The axes of your graphs must reflect the correct number of
significant figures for your data
• Calculate averages of triplicates (needed for replicate error)
• Do not use the averages in calibration-curve fitting (use
unaveraged data and LINEST).
• Use LINEST to determine confidence intervals on slope and
intercept
• True inner diameter of type L copper tubing may be found in
the Copper Tube Handbook (see lab website). The sizes ¼,
½, and 3/8 are called nominal pipe sizes.
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© Faith A. Morrison, Michigan Tech U.
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Calibrate Flow Meters Lab, CM3215 F.
Morrison
CM3215 Fundamentals of Chemical Engineering Laboratory
Lab: Calibrate Rotameter and Explore Reynolds Number
•Pump water through pipes of various diameters
•Measure flow rate with pail-and-scale method
•Calibrate the
rotameter
•Calibrate the orifice
meter (measure
Δ
)
•Calculate Re for
each run
•Determine if flow is
laminar, turbulent,
transitional
•Use appropriate
statistics, sig figs
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© Faith A. Morrison, Michigan Tech U.
PreLab Assignment
• Familiarize yourself with Reynolds number, rotameters,
and orifice meters.
• Find a good estimate of the calibration curve for the DP
meter at your lab station and have the equation in your lab
notebook.
• Prepare a safety section
• Prepare data acquisition tables
• Answer these questions in your lab notebook:
1. What should you plot (what versus what) to get a straight line
correlation out of the orifice meter calibration data?
2. In this experiment we calibrate the rotameter for flow directed
through ½”, 3/8”, and ¼” pipes (nominal sizes); will the calibration curve
be the same for these three cases or different?
3.
What is “dead heading” the pump?
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© Faith A. Morrison, Michigan Tech U.
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Calibrate Flow Meters Lab, CM3215 F.
Morrison
Comments on DP Meter
calibration curves
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www.honeywellprocess.com/
ST 3000 Smart Pressure Transmitter Models Specifications 34-ST-03-65
© Faith A. Morrison, Michigan Tech U.
Station 1 Archive (uncorrected)
4.0
historical average
3.5
3.0
p, psi
2.5
2.0
First, look
carefully at
the data.
1.5
1.0
0.5
0.0
4.0
6.0
8.0
10.0
12.0
current, mA
14.0
16.0
18.0
20.0
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© Faith A. Morrison, Michigan Tech U.
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Calibrate Flow Meters Lab, CM3215 F.
Morrison
Station 1 Archive (corrected for obvious errors)
4.0
historical average
3.5
We are
permitted to
correct or omit
“blunders”
3.0
p, psi
2.5
2.0
22
0.2308
1.5
0.0011
,
1.0
/
/
0.982
0.027
,
0.5
0.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
current, mA
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© Faith A. Morrison, Michigan Tech U.
Station 1 Archive (corrected for obvious errors)
4.0
large guarantees that the
means , are historical average
good estimates
3.5
of the true values (assuming
only random
errors are present)
3.0
p, psi
2.5
Small standard errors
2.0
22
0.2308
1.5
1.0
/
0.0011
,
/
0.982
0.027
,
0.5
0.0
4.0
6.0
8.0
10.0
12.0
current, mA
14.0
16.0
18.0
20.0
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© Faith A. Morrison, Michigan Tech U.
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Calibrate Flow Meters Lab, CM3215 F.
Morrison
Station 1 Archive (corrected for obvious errors)
4.0
historical average
3.5
3.0
p, psi
2.5
Historical, 95% CI:
2.0
1.5
0.2308 0.0022
0.98 0.05
/
1.0
0.5
0.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
current, mA
We are 95% confident that the true
values of the slope and intercept are
within these intervals.
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© Faith A. Morrison, Michigan Tech U.
Historical, 95% CI:
0.2308 0.0022
0.98 0.05
Station 1 Archive
Note that the
historical average
almost goes
through the point
,Δ
4,0
/
4.0
historical average
3.5
3.0
p, psi
2.5
2.0
1.5
1.0
Can you
comment on
that?
0.5
0.0
4.0
6.0
8.0
10.0
12.0
current, mA
14.0
16.0
18.0
20.0
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© Faith A. Morrison, Michigan Tech U.
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Calibrate Flow Meters Lab, CM3215 F.
Morrison
Historical, 95% CI:
0.2308 0.0022
0.98 0.05
Station 1 Archive
/
4.0
historical average
3.5
3.0
Δ equation: Δ ;
;
p, psi
2.5
2.0
1.5
1.0
0.5
0.0
4.0
slope
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
current, mA
(4.0,0)
If we know this point is on our correlation line, we can solve for a
value of , independent of the systematic offset in the data.
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© Faith A. Morrison, Michigan Tech U.
Summary
• We can omit “blunders” from data sets
• We are always looking for possible sources of systematic error
• When a systematic error is identified (leftover water in unequal
amounts on the two sides of the DP meter), we are justified in
making adjustments to our correlations
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© Faith A. Morrison, Michigan Tech U.
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