MEC316 Lab#3
Mass-Flow Measurement
Group #9:
Kanchan Bhattacharyya – Writer; Synthesizing Paper
Matthew Stevens – Graphs & Error Analysis
Ting Zhang – Abstract and Introduction
Xie Zheng – Principle of Operation and Experimental Procedure
A. Abstract
The general goal of this experiment is first to measure the flow rates of gases with
Rotameter and Electronic Mass Flow Meter and estimate the accuracy of Rotameter compared
with Electronic Mass Flow Meter. Basic principle of Rotameter is based on the variable area
principle. The basic principle of Electronic mass flow meter is measuring the temperature of
heat transfer in the liquid. (Variables introduction: Q represents flow rate measured with
Rotameter. Q2 represents flow rate measured with Electronic Mass Flow Meter. U1 stands for
voltage which is measured by DAQ. H stands for the float height in Rotameter.) Variables height
H and voltage U1 are required to be measured in this experiment. As long as height H is known,
we can calculate the flow rate Q1 which is measured with rotameter because Q1 is proportional
height H. Flow rate Q2 which is measured with Electronic Mass Flow Meter can also be
obtained as long as we know voltage U1. After find out Q1 and Q2 at same heights h, we can
estimate the accuracy of Rotameter and Electronic Mass Flow Meter.
The second goal of this experiment is to measure flow rate of liquids to estimate the
accuracy of one method when compared to the other method. We use two equipments Vortexshedding flow meter and Ultrasonic flow meter in measuring liquid flow-rate. The operation of
the vortex-shedding flow meter is sensing the frequency of vortex shedding behind a bluff-body
which is directly proportional to the velocity of the fluid. The basic operation principle of
Ultrasonic flow is depending on the ultrasonic pressure signals and their reflections to measure
the velocity. (Variables introduction: Q3 represents flow rate measured with Vortex-shedding
flow meter. Q4 represents flow rate measured with Ultrasonic flow meter. U2 stands for voltage
which is measured by DAQ.). Liquid flow rate Q3 with can be directly measured with Ultrasonic
flow meter. Q4 can also be obtained as long as we get U2 which is measured with DAQ
because Q4 is proportional to U2. After mapping graph Q3-U and Q4-U, we can estimate the
accuracy of Vortex-shedding flow meter compared to Ultrasonic flow meter.
B. Introduction
In gas flow-rate measurement, we use air as a representative gas. Both the rotameter
and Electronic Mass Flow Meter are used to measure the gas flow rate under the same
condition. We keep outlet pressure on the air tank at 10psig. Next, we begin to change the float
height H in rotameter. Then, we started to measure the float height H in the Rotameter and
voltage U1 with DAQ. After we get the H and U1, we can calculate the gas flow rate Q1 and Q2
respectively because Both H, Q1and U1, Q2 are proportional respectively. Let me mention
something of Rotameter. Rotameter is an industrial flowmeter used to measure the flow rate of
liquids and gases. Rotameter is popular because it has a linear scale, a relatively long
measurement drop. It’s simple to install and maintain. It may be manufactured in a variety of
materials of construction, and for a wide range of pressures and temperatures. The rotameter
can be easily sized or converted from one particular service to another. In general, it owes it
wide use to its versatility of construction and applications.
In liquid flow-rate measurement, we use water as a representative fluid. Both the Vortexshedding flow meter and Ultrasonic flow meter are used to measure the fluid flow rate under the
same condition. By adjusting Valve 1 (see Figure 3-3), we can change the liquid flow rate. Each
change of Valve 1, we record two data. One of them is voltage U2 that is acquired by DAQ. The
other data the liquid flow rate Q4 that is directly measured by Ultrasonic flow meter. We can
obtain Q3 if we know U2 because they are proportional.
C. Theory - Principles of Operation for Flow Meters
Rotameter:
Rotameter is an industrial flow meter used to measure the flow rate of gases and liquids. Its
operation is based on the variable area principle, where the fluid flow raises a float in a tapered
tube, increasing the area of passage of the fluid. The greater the flow, the higher the float is
raised. The height of the float is directly proportional to the flow rate. The float moves up or
down in the tube in proportion to the fluid flow rate and the annular area between the float and
the tube wall. It reaches a stable position in the tube when the upward force exerted by the
flowing fluid equals the downward gravitational force exerted by the weight of the float. A
change in flow rate upsets this force balance. The float then moves up or down, changing the
annular area until it again reaches a position where the forces are in equilibrium. With liquids,
the float is raised by a combination of the buoyancy of the liquid and the velocity head of the
fluid. With gases, the buoyancy is negligible, and the float responds to the velocity head alone.
Since there are specific disadvantages when use the rotameter to read the liquid flows, the
rotameter is mainly used for gases.
Electronic mass flow meter:
The gas flows through a precision sensing tube where a constant heat rate is applied by
electrical resistance heating coils. The heat transfer to the liquid upstream and downstream of
this heating coil is a function of the temperature of gases at these points as well as the mass
flow rate. We can accurately determine the mass flow rate of the gas by knowing the
temperature of the gas at these two points.
Vortex-shedding flow meter:
At low Reynolds numbers (velocity), the frequency of vortex shedding behind a bluff-body is
directly proportional to the velocity of the fluid. The frequency of vortex shedding is sensed by a
piezoelectric transducer which then gives us the velocity of the liquid.
Ultrasonic flow meter:
This is an advanced technique for measurement of flows in pipes and depends on the ultrasonic
pressure signals and their reflections for the measurement of velocity
D. List of Equipment and Experimental Procedure
Air Mass Flow Rate Experiments
1) Electronic Mass Flowmeter
2) Rotameter (Omega Engineering, Inc)
(Model FMA1728ST; Omega Engineering, Inc. FMA 1700/1800 Series)
3) Compressed Air Tank (Model DOT-3AA2400)
4) Harris Pressure Regulator (Model 35-500C-560)
5) Polyethylene Tubing & Connection Fittings
6) National Instruments DAQ Board
7) DC Power Supply
8) Laptop Computer
Water Flow Rate Experiments
1) Ultrasonic Flowmeter Omega Engineering, Inc. FD-7000)
2) Vortex Shedding Flowmeter (Omega Engineering, Inc. A100F50)
2) Lightweight Laboratory Cylindrical Tank
(Norton Plastics 54102-0015 HDPE 57L, with Cover and Spigot)
4) Leeson AC Motor (Model C6C34FK61A)
5) PVC Piping, Elbows, and Couplers.
6) Plastic Valves
6) National Instruments DAQ
7) DC Power Supply
8) Laptop Computer
Experimental Procedure
Gas flow-rate measurement (air)
1. Rotameter and the electronic mass flow meter are connected in series to measure the
flow rate of air. We set the outlet pressure on the air tank to 10 psig. Flow through both
meters is controlled by turning knob on the bottom front of the rotameter (By turning the
knob counterclockwise, we can increase the flow rate).
2. Since we are using the duplicate sets of equipment, we do not need to setup the
electrical flow meter except adjust the knob to make the excitation voltage of 17 volts.
Also, we do not need to worry about the current which should not be exceeded 250mA in
old equipment. Check all connections and then turn on the power supply.
3. Turn on the laptop and start the data acquisition program by loading WINDOWS,
execute LABVIEW. Then open exp3a.vi in the \labview directory.
4. Keeping the outlet pressure on the air tank to 10 psig, we start to make measurement
corresponding to each height of the float. First, we start with the height equals to 15mm
(the top of the sphere lined up with the scalar on the ruler in rotameter). Record the
setting of height and click on the run icon on the tool bar. We get a reading of voltage
from the program and record that value. Then, we take increment of 15mm and take
another 8 sets of data while repeating the recording.
5. Close the valve of the air tank and reset the height of the float in the rotameter back to
the original position.
Liquid flow-rate measurement (Water)
1. Since the equipment is configured already in the lab, we turn on the power supply and
set the voltage to 24V. Configure the system as shown in Fig 3.3 and make sure the
valve 1 is closed and valve 2 is open.
2. Turn on the pump and run the system for at least 5 minutes to purge the air out of the
piping system.
3. Open file exp3b.vi in LABVIEW and then turn on the ultrasonic flow meter which is
already configured to measure the flow velocity.
4. After approximately 6 minutes doing step 2, we start to make the sets of measurements
by changing valve 1. Since we decide to take 10 sets of measurements, we start with
turning the valve about 9 degree (it is hard to make sure the angle is close to 9, but we
try to make the increments even).
5. Then, record the reading shows up on the ultrasonic flow meter and also click on the run
icon on the tool bar to read the output current of the vortex meter which is measured
using LABVIEW named exp3b.vi.
6. By adjusting valve 1, make the increment is approximately 9 degrees and repeat the
step 5. After repeating the steps, we get 10 sets of data in total.
7. Close the valve 1 and turn off the power supply, pump and also the ultrasonic flow
meter.
E. Results and Discussion
Part I: Air Flow Rate Experiments
Table 1: Experimental Data & Corresponding Flow Rates (Air)
Trial (i)
Rotameter
Reading (mm)
EMFM Output
Voltage (Volts)
EMFM Flow Rate
(L/min) [Reference]
Rotameter Flow
Rate (L/min)
+/- Error in
Absolute
Rotameter
Deviation of
Measurements Rotameter Flow
[2% Reading
Rate from
Acc. + ¼%
Reference
Repeatability]
EMFM Flow
Rate
1
20.000
0.567
5.670
5.025
0.1131
0.6450
2
35.000
1.250
12.500
11.970
0.2693
0.5300
3
50.000
1.800
18.000
18.915
0.4256
0.9150
4
65.000
2.492
24.920
25.861
0.5819
0.9410
5
80.000
3.284
32.840
32.806
0.7381
0.0340
6
95.000
3.997
39.970
39.752
0.8944
0.2180
7
110.000
4.614
46.140
46.697
1.051
0.5570
8
125.000
5.562
55.620
53.642
1.207
1.9780
9
135.000
5.728
57.280
58.272
1.311
0.992
Caption: This table shows the rotameter readings and the EMFM output voltages as water flow
was changed, in Columns 2 & 3 respectively. In Column 4 we have the EMFM flow rates, which
we assume to be our reference and in Column 5, we have the rotameter flow rates. Columns 6
& 7 show the error in rotameter measurements as per the manufacturer who gives a 2% reading
accuracy and ¼% repeatability uncertainty range, as well as the absolute deviation of rotameter
flow from the reference. These two can be compared to see the differences in the rotameter
from the actual as determined by the manufacturer and the differences from the rotameter to the
EMFM flow rate, which we assume as the reference and thus the actual value.
Discussion & Analysis Part 1: Maximum Error of Rotameter
Sample Standard Deviation:
Maximum Error Formula:
Maximum Error in Rotameter Flow Rate Measurement: 0.9422 (95% Confid. Int.)
Maximum Error in Rotameter Reading (mm): 11.2 mm
How Maximum Error Was Determined:
The formula for calculating maximum error from probability & statistics is listed above, as
the sample standard deviation (s) divided by the square root of the total sample space,
multiplied by a t-value, which will vary depending on the number of samples (specifically the
degree of freedoms (DOF), n-1) and the confidence interval desired.
Using the electronic mass flow meter (EMFM) as the reference, the deviations between
the EMFM and the rotameter for each measurement 1-9 were found. These were then squared
and added, multiplied by 1/DOF, and then the square root of the result was taken. The last step
was to multiply by the desired confidence interval which we took as 95%, multiplying our result
by 2.896. Our final maximum error in the rotameter flow rate measurement came out to be
0.9422. This maximum error value covers the spread of deviation values in Column 7 of Table
1, aside from one outlier.
In order to obtain a more useful maximum error to the user of the rotameter, we used the
linear regression curve to calculate what change in rotameter reading (mm) would cause this
maximum error value in flow rate. By backtracking and solving for x, we find that this comes out
to 11.2 mm.
Why The Maximum Error Seems So Large: (Sample Size & EMFM Reading Acc.)
This may seem to be a staggering amount, but it is very important to keep in mind that
this is the result of having to ensure such a large confidence interval of 95%, which requires
multiplying by a larger t-value. If we had a larger sample size, then according to the t-score
table, we would have had to use a smaller t-value as our multiplier and this would bring our
maximum error for rotameter reading (mm) to a more sensible value.
It is also important to point out, that the EMFM was treated as an absolute reference –
that it was the exact value of the flow rate. However, the EMFM has it’s own reading accuracy
error of 2%. Looking at Column 6 of Table 1, where the +/- error that the manufacturer says
there is between the rotameter flow rate measurement and the actual flow rate (we assume to
be from the EMFM) – which was calculated by taking 2.25% of each rotameter flow rate
measurement (rotameter reading accuracy + repeatability), we see that this error is far less than
the actual deviation of the rotameter flow rate measurement from the EMFM. Thus, it is not a
good assumption to say that the EMFM is 100% exact. If we include the 2% from the EMFM and
do a rough estimate of the manufacturer’s error assurance and we simply double the error
values in Column 6, we see that they will come quite close to the actual deviation. This would
result in smaller variances when calculating our sample standard deviation which would
ultimately lead to a far smaller maximum error.
Table 2: Rotameter Calibration: Linear Regression and Uncertainty Analysis
Trial (i)
x
y
xy
x x,
a+bx
1
20.000
5.670
113.400
400.000
5.025
0.416
2
35.000
12.500
437.500
1225.000
11.970
0.281
3
50.000
18.000
900.000
2500.000
18.915
0.838
4
65.000
24.920
1619.800
4225.000
25.861
0.885
5
80.000
32.840
2627.200
6400.000
32.806
0.001
6
95.000
39.970
3797.150
9025.000
39.752
0.048
7
110.000
46.140
5075.400
12100.000
46.697
0.310
i
i
i
i
i
i
(y - (a+bx ))
i
i
2
8
125.000
55.620
6952.500
15625.000
53.642
3.912
9
135.000
57.280
7732.800
18225.000
58.272
0.985
Sx
Sy
Sxx
Sxy
a
b
theta
u
715.000
292.940
69725.000
29255.750
-4.236
0.463
7.676
0.600
a
u
b
0.007
Caption: This table shows the rotameter readings (mm) and rotameter flow rates in x
and y, and how these are transformed into a linear regression curve that minimizes the
objective error function and provides the closest linear fit to the data. This is assumed to
be the curve that models the rotameter’s reading to the actual flow rate.
Graph 1: Mass Flow Rate (Rotameter & EMFM) vs. Rotameter Position
MASS FLOW RATE VS. ROTAMETER POSITION
70
MASS FLOW RATE (L/MIN)
60
y = 0.463x - 4.236
50
40
30
20
10
0
0
20
40
60
80
100
120
140
ROTAMETER POSITION (MM)
Electronic Mass Flowmeter Flow Rate (L/min)
-4.235+0.463x
Rotameter Flow Rate (L/min)
Discussion & Analysis Part II – Manufacturer’s Accuracy of Rotameter:
Is the rotameter as accurate as the manufacturer claimed?
As stated before in our analysis of maximum error, the 2.25% measurement assurance
that the manufacturer gives, between the rotameter measurements and the actual value, results
in error values far less than the actual deviations between the rotameter flow rate
measurements and the reference (assumed to be actual) standard EMFM. So by only going by
the “tolerance” of the rotameter measurement, it is not as accurate as it should be. However, we
make a big assumption by saying that the EMFM is a viable reference standard since it has 2%
reading accuracy uncertainty of its own and if added to the 2.25% measurement assurance from
the rotameter manufacturer, it is enough to make the manufacturer’s error assurance equal the
observed deviation.
Part II: Water Flow Rate Experiments
Table 3: Experimental Data & Corresponding Flow Rates (Water)
+/- Error in
Vortex
Shedding
Measurements
[0.8% Rate
Accuracy]
Absolute
Deviation of
Vortex
Shedding
Flow Rate
from
Reference
Trial
(i)
Output Voltage
(Volts)
Ultrasonic Meter Flow
Rate [Reference]
(G/min)
Vortex Shedding Flow
Meter Flow Rate (G/min)
1
1.846
9.070
8.964
0.0717
0.106
2
1.820
8.790
8.724
0.0698
0.066
3
1.724
7.830
7.840
0.0627
0.010
4
1.633
7.010
7.002
0.0560
0.008
5
1.580
6.340
6.513
0.0521
0.173
6
1.527
5.900
6.025
0.0482
0.125
7
1.468
5.420
5.482
0.0439
0.062
8
1.392
4.750
4.782
0.0383
0.032
9
1.334
4.370
4.247
0.0340
0.123
10
1.253
3.600
3.501
0.0280
0.099
Caption: This table shows the readings and the EMFM output voltages as air flow was
changed, in Columns 1 & 2 respectively. In Column 3 we have the EMFM flow rates, which we
assume to be our reference and in Column 4, we have the rotameter flow rates. Columns 6 & 7
show the error in rotameter measurements as per the manufacturer who gives a 2% reading
accuracy and ¼% repeatability uncertainty range, as well as the absolute deviation of rotameter
flow from the reference. These two can be compared to see the differences in the rotameter
from the actual as determined by the manufacturer and the differences from the rotameter to the
EMFM flow rate, which we assume as the reference and thus the actual value.
Table 4: Vortex Shedding Flowmeter Calibration: Linear Regression and Uncertainty Analysis
Trial (i)
xi
yi
xiyi
xixi
a+bx
(y - (a+bx ))
1
1.846
9.070
16.74322
3.407716
8.963795
0.011279604
2
1.820
8.790
15.9978
3.3124
8.724285
0.00431849
3
1.724
7.830
13.49892
2.972176
7.839941
9.88261E-05
4
1.633
7.010
11.44733
2.666689
7.001657
6.96048E-05
i
i
2
5
1.580
6.340
10.0172
2.4964
6.513426
0.03007646
6
1.527
5.900
9.0093
2.331729
6.025194
0.015673605
7
1.468
5.420
7.95656
2.155024
5.481691
0.003805829
8
1.392
4.750
6.612
1.937664
4.781586
0.000997676
9
1.334
4.370
5.82958
1.779556
4.247295
0.015056502
10
1.253
3.600
4.5108
1.570009
3.50113
0.009775255
Sx
Sy
Sxx
Sxy
a
b
theta
u
15.577
63.080
24.629
101.623
-8.041
9.212
0.091
0.277
a
u
b
0.177
Caption: This table shows the rotameter readings (mm) and rotameter flow rates in x
and y, and how these are transformed into a linear regression curve that minimizes the
objective error function and provides the closest linear fit to the data. This is assumed to
be the curve that models the rotameter’s reading to the actual flow rate.
Graph 2: Mass Flow Rate vs. Vortex Shedding Output Voltage
MASS FLOW RATE VS. VORTEX SHEDDING OUTPUT VOLTAGE
10
FLOW RATE (GALLONS/MIN)
9
y = 9.2119x - 8.0414
8
7
6
5
4
3
2
1
0
1.125
1.25
1.375
1.5
1.625
1.75
1.875
2
VORTEX SHEDDING OUTPUT VOLTAGE (VOLTS)
Ultrasonic Flow Rate (G/min)
Vortex Shedding Flow Rate (G/min)
-8.904+9.212x
Caption: This plot shows both the vortex shedding flow rate and the ultrasound flow rate as a
function of voltage. As can be seen the differences in terms of whole gallons of flow rate per
minute, is marginally small.
Discussion & Analysis Part III – Maximum Error for Vortex Shedding Flow Meter
Sample Standard Deviation:
Maximum Error Formula:
Maximum Error in Vortex Shedding Flow Rate Measurement: 0.0971 G/min
Maximum Error in Vortex Shedding Meter Reading: 0.2945 V
The formula for calculating maximum error from probability & statistics is listed above, as the
sample standard deviation (s) divided by the square root of the total sample space, multiplied by
a t-value, which will vary depending on the number of samples (specifically the degree of
freedoms (DOF), n-1) and the confidence interval desired.
Using the ultrasound meter as the reference, the deviations between the ultrasound and
the vortex shedder flow meter for each measurement 1-10, were found. These were then
squared and added, multiplied by 1/DOF, and then the square root of the result was taken. The
last step was to multiply by the desired confidence interval which we took as 95%, multiplying
our result by 2.896. Our final maximum error in the vortex shedder flow rate measurement came
out to be 0.0971. This maximum error value covers most of the spread of deviation values in
Column 6 of Table 3.
In order to obtain a more useful maximum error to the user of the vortex shedder, we
used the linear regression curve to calculate what change in vortex shedder reading (V) would
cause this maximum error value in flow rate. By backtracking and solving for x, we find that this
comes out to 0.2945.
Explaining Maximum Error:
Again, like for the rotameter, the sample size is quite small, so to have a 95% confidence
interval, means multiplying by a significant 2.896, almost 3x. If we were to have a larger sample
size, such as more than 60 samples, then our t-score value multiplier would be far less and
would result in the end, as a smaller maximum error for our vortex shedder flow meter.
Evaluating Manufacturer Specifications Against Calibration Curve:
The manufacturer of the vortex shedder ensures a rate accuracy of 0.8% while the
manufacturer of the ultrasound meter ensures an accuracy of 1%. Taking a look at the last two
columns in Table 3, which show the error in the vortex shedding flow meter and the absolute
deviation between it from the reference ultrasound, respectively, we see that the deviations are
extremely small and for the most part are covered by the manufacturer’s tolerance.
F. Error Analysis
Sources of error include improper calibration, inaccuracy in measurement, and
malfunctions in the system. During calibration of the electronic flow meter we may have chosen
a current value too far from 0.25 ampere before selecting the 24 V range, and similarly we may
have chosen an inaccurate value when trying to achieve the 17 V required excitation voltage.
This would directly correlate to inaccurate measurements for flow rate as any given position
would always give a variant flow rate, depending on the degree to which the calibration
current/voltage varies. For the liquid flow-measurements, we may have incorrectly calibrated
the system by not allowing the pump to run for long enough before taking our measurements. In
giving the system adequate time to circulate the previously stagnant water, we are ensuring that
that the flow will be consistent throughout the system while simultaneously verifying the integrity
of the system. Specifically, in allowing the liquid to flow for an extended period of time we are
giving ourselves an opportunity to identify any leaks in the system or other mechanical failures.
While we did not observe any of these failures during the trials, taking measurements
prematurely may prevent us from identifying these sources.
Sources for error during measurement include inaccurate readings of rotameter float
position as well as inaccurate electronic mass/vortex shedding flow meter output voltage
readings and ultrasonic flow meter flow rate readings. While we waited for the float to settle into
position during each flow measurement, it is possible that we could have misjudged the actual
position of the float. Observing actual flow rates which correspond to the various float positions
we find that these flow rates depend linearly on the position, implying that any error in float
position would give an inaccurate approximation for the flow rate. Similarly, we can consider our
electronic mass flow meter output voltages to be potential sources for error. Like we did with the
rotameter float, we waited for the output voltage to ‘settle’ before we recorded our final value at
each given flow rate. However, it is possible that we recorded our values either prematurely or
too late. Inaccuracies in these measurements could result in both high/low voltages for a given
flow, which in turn would affect the calibration curve and subsequently our approximation for the
accuracy of the rotameter. A similar assessment can be made for inaccurate ultrasonic meter
flow rate readings and the calibration of the vortex shedding flow meter.
We can also consider defects in the experimental setup; specifically those which exist
within the respective tubing systems and flow meters themselves. While we thoroughly
inspected all experiment materials before each respective trial (gas, liquid), we must consider
leaks in the tubing/ducts assembled to transport the fluids, leaks in the joints connecting the
tubing and ducts together, as well as failure in connections to the DAQ and power supplies. For
the liquid water measurements our system was comprised of threaded ducts, couplers, and
valves interconnected with a pump. We can consider losses due to losses in these joints, as
well as those that may result from using basic stainless steel worm clamps to connect the
reservoir to the pump. These losses have the propensity to propagate, and may affect other
properties of the system in addition to the flow rate. Similarly, we can consider losses in the gas
trials, as our meters were connected via polyethylene tubing. While the tubing is connected
between the meters by threaded fittings, there may be losses which exist at these joints. Also,
one of the tubing connections to the Rotameter was held in place by simple “Scotch” Tape,
hardly a guaranteed method to keep the gas contained with the system. Finally, we can
consider any inaccuracies that might have existed in the applied gage pressure (10 psig) during
the gas trials. We assume that our estimation for an applied 10 psig pressure is accurate as
measured by both our eye as well as the pressure gage indicating the output pressure. Before
each individual trial we were sure to accurately set the pressure to 10 psig, however rapid
fluctuation makes this very difficult to measure both accurately and precisely. Subsequently, any
variance in pressure is going to have a direct correlation on the resulting flow rate through the
system.
Using Linear Regression Analysis; we found uncertainties of ua = 0.600/ub = 0.007 in
the Rotameter and ua = 0.277/ub = 0.177. These values can be attributed to any of the above
considered sources for error.
G. Conclusion
As we can see from our data plots, for both the gas flow measurements using air and for
the liquid flow measurements using water, both instruments used in either type of measurement
scale fairly well. However, absolute deviations exist and the manufacturing tolerance given is
usually quite tight as we saw for the rotameter which was only 2.25% when you consider both
reading accuracy and repeatability accuracy. Matching the data to this sort of tolerance works
well when you have a large sample size. Unfortunately, since we have only 9-10 values for our
data, any outliers can have a significant effect on the maximum error we calculate for the
rotameter and for the vortex shedder. This is because, for smaller sample sizes, the t-score
value grows enormously in order to ensure the same 95-99% confidence interval. To ensure an
uncertainty to that confidence requires a larger breadth when you have smaller sample size,
because you cannot be sure your sample data is enough to reflect the entire population. If we
had say 60 samples, to the point where we could say our data is continuous, the t-score values
would be far lower resulting in more reasonable maximum errors.
But overall, as we can see from the graphs with respect to the scaling of L/min for the
rotameter or G/min for the vortex shedders, the differences that these measurements are from
our reference, is quite small all in all and would make these instruments a good test for various
kinds of fluid flows.
Reference:
J.M. Kincaid, David Hwang, T.Y. Hsu. Laboratory Manual for MEC316