Lab 1: Measuring Air Velocity – Accuracy and Precision
by
Joe Cool
5 February 2010
Department of Mechanical Engineering
University of Wisconsin-Madison
1513 University Avenue
Madison, WI 53706-1572
Lab 1: Measuring Air Velocity
J. Cool
5 February 2010
Executive Summary
In this experiment, two measurement procedures were used to assess the velocity of air
expelled by a hairdryer. The first method utilized a U-tube monometer and the second
used an electronic diaphragm gage (EDG). The precision and accuracy of the
measurement systems were evaluated to determine the advantages and disadvantages of
each system.
Much of this lab involved identifying the difference in accuracy and precision between
the various measurements. Each measurement involved a level of uncertainty that had to
be quantified. The respective uncertainties of each measurement were propagated
through all of the calculations to give a final uncertainty value for the velocity of the air
exiting the hairdryer. The velocity of the air stream generated by the hairdryer
determined from each of the devices was:
U-Tube Manometer:
10.4 ± 2.8 (m/s)
Electronic Diaphragm Gage: 9.15 ± 1.16 (m/s)
The average velocity measured by the manometer was 13.6% higher than the velocity
measured by the EDG. In addition, the uncertainty interval of the manometer was 2.7
times larger than the uncertainty interval of the EDG. The confidence limits of the
manometer exhibit a wider spread than that of the EDG. This indicated the EDG
produced more precise measurements than the manometer.
The simple principle of operation for a U-Tube Manometer is more accurate because it
does not rely on indirect measurements, because pressure is measured directly. The
Electronic Diaphragm Gauge, on the other hand, relies on the indirect measurement of
voltage which is converted into pressure by a calibration equation. Less direct
measurements have a higher potential for inaccuracy than measurements that are more
direct.
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Table of Contents
Section
Page
1.0 Introduction
1.1 Background
1.2 Objectives
1.3 Overview
2.0 Procedure and Apparatus
2.1 Experimental setup – Hardware
2.1.1 Experimental setup – U-Tube Manometer
2.1.2 Experimental setup – Electronic Diaphragm Gage
2.2 Experimental setup – Software
2.3 Experimental setup – Procedure
2.3.1 Procedure – U-Tube Manometer
2.3.2 Procedure – Electronic Diaphragm Gage
2.4 Analysis
2.4.1 Analysis – U-Tube Manometer
2.4.2 Analysis – Electronic Diaphragm Gage
3.0 Results
3.1 Results – U-Tube Manometer
3.2 Results – Electronic Diaphragm Gage
4.0 Discussion
5.0 Conclusions and Recommendations
5.1 Summary of Results
5.2 Recommendations
References
ii
4
4
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Lab 1: Measuring Air Velocity
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5 February 2010
Nomenclature
Sym.
Xi
Sx
N
𝑥̅
P
h
V
g
T
Q
v
x’
𝑡𝜈,𝑃
Definition
Measurement
Standard Deviation
number of data points
Average
Pressure
Height
Velocity
acceleration due to gravity
Temperature
Resolution
Voltage
true value
variable values
Units
----------------------------Pa
M
m/s
m/s2
˚C
mV/bit
V
---------------
Greek Symbols
Sym.
Δ
ρ
𝜈
Definition
change in
Density
degrees of freedom
iii
Units
------Kg/m3
-------
Lab 1: Measuring Air Velocity
J. Cool
5 February 2010
1.0 Introduction
The motivation of this experiment was to record and evaluate measurements of air velocity from
a blow dryer stream. The two devices used in this lab to experimentally determine air velocity
were a U-tube Manometer and an Electronic Diaphragm Gauge. The U-Tube Manometer and
Electronic Diaphragm Gauge were used to calculate velocity by means of their output
measurements of pressure and voltage respectively. In order to determine an experimental value
of the hairdryer velocity stream, the concepts of accuracy and precision of the measurements
were evaluated.
1.1 Background
The measurement of pressure to determine a fluid’s velocity can be important in many
engineering applications. For instance, many airplanes use Pitot-Static Tubes. These tubes use
the same fundamental concepts (explained below) used in this lab to determine the speed of the
aircraft relative to the air around it.
Determining velocity via pressure measurement is common in aircraft and marine applications,
but for other applications it may be advantageous to measure velocity using other methods. One
device for measuring fluid velocity, commonly used by weather stations, is the Cup Anemometer
[1]. This device consists of evenly spaced hemispherical cups cantilevered out from a vertical
central axis. Fluid travelling past the cups creates a moment about the central axis and the device
begins to spin. A measurement of revolutions per time is then used to compute the fluid’s
average velocity over that time. A much simpler device for measuring fluid velocity is a sphere
hung from a string. If the density and drag coefficient of the sphere are known, then one can
measure the angle that the string deviates from the vertical direction, and determine the fluid
velocity using simple fluid mechanics concepts [2].
Figure 1: Accuracy vs. Precision [3]
The difference between accuracy and precision was also carefully considered in this laboratory.
Accuracy represents how close a data point is the the true value not relative to any other data
points. Precision is the extent to which a data point can be reproduced by the same process
independent of it’s accuracy. See figure 1 for an illustration distinguishing accuracy and
precision. The image on the left shows accuracy because the average of the data points lies close
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Lab 1: Measuring Air Velocity
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5 February 2010
to the center of the bull’s eye. The image on the right shows precision because the data points
can easily be reproduced.
1.2 Theory
Pressure-based velocity measurements originate from fluid mechanics, and more specifically the
Bernoulli equation. The Bernoulli equation states that for inviscid flow, along a streamline, with
no externally applied work, and an incompressible fluid (or compressible fluid at low Mach
number) mechanical energy is conserved. The Bernoulli equation between two states is
commonly written:
V22
P
V2
P
(1)
 gz 2  2  1  gz1  1
2
a
2
a
In this experiment gravity was neglected. After removing the gravity terms and rearranging,
Equation 1 becomes:
 (V 2  V22 )
(2)
P2  P1  P  a 1
2
Equation 2 directly relates a change in pressure between two states (ΔP) to a change in the square
of the velocity at each respective state.
Figure 2: U-Tube Manometer
In this experiment, the pressure difference between states was found using a U-tube manometer
(figure 2, above). U-tube manometers utilized the fact that fluid pressure varies linearly with
depth, and that all fluids at the same depth must share the same pressure. Consider the
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Lab 1: Measuring Air Velocity
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5 February 2010
manometer shown. Using fluid statics principles it is known that:
P2 = P0 + ρwgh
(3)
The air stream leaving the hairdryer is at atmospheric pressure (P1 = P0) and travels at some
velocity V1. When the stream reaches the air/water interface the velocity of air is reduced to zero
(V2 = 0) and pressure increases to P2. Substituting Equation 3 into Equation 2, along with the
given information, then rearranging yields:
V1 
2 w gh
a
(4)
This is the equation used to calculate the velocity of the stream leaving the hairdryer as a
function of the manometer height reading.
1.3 Objectives
The objectives of this experiment were to:
 Measure pressure and voltage from a U-tube Manometer and Electronic
Diaphragm Gauge, respectively, and relate these outputs to pressures and
velocities
 Analyze the pressure and velocity measurements by evaluating accuracy and
precision of each measurement device
 Quantify both systematic and random uncertainties of the measured pressure
 Determine the random and systematic uncertainties of the calculated velocities
through propagation
1.4 Overview
In the following pages, experimental procedure and a description of the apparatus is given,
followed by an analysis of the collected data and interpretation of the results. Finally, the results
are discussed and then conclusions and recommendations for the experiment are given.
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2.0 Procedure and Apparatus
2.1 Experimental Setup – Hardware
Table 1: Electronic Instrumentation Used in the Experiment
Instrumentation Used
Attributes of Instrumentation
National Instruments CompactDAQ
USB 8 slot chassis
National Instruments Model 9215
4-Channel, 100 kS/s, 16-bit, ±10 V Simultaneous Sampling
Analog Input Module
Electronic diaphragm gage
Attributes outlined above
Tenma 72-7660
DC power supply
Tenma digital multimeter
72-410A
Vidal Sassoon 1875 W hairdryer
nozzle attached, high fan, low heat
2.1.1 Experimental Setup – U-Tube Manometer
As seen in figure 3 (below), a cold air stream was produced by a hairdryer on high outset setting
and blown into a U-Tube Manometer made from a plastic hose. The hairdryer used in the lab
Figure 3: U-Tube Manometer set-up used to measure Pressure
was an 1875 W Vidal Sassoon hairdryer with a nozzle attachment, a variable fan setting, and
variable heat setting. When the hairdryer air stream was blown into the U-Tube Manometer, a
height difference between the right and left sides of the device occurred. The height difference
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5 February 2010
was measured using a ruler with millimeter graduations. The measured height difference is the
differential pressure measured in inches of water. Using this experimentally measured pressure
differential, the initial velocity of the air stream from the hairdryer was calculated using
Bernoulli’s Equation.
2.1.1 Experimental Setup – Electronic Diaphragm Gage
The Electronic Diaphragm Gage, in figure 4 (below), was used to measure velocity in a manner
similar to the manometer.
Figure 4: Electronic Diaphragm Gauge Setup
In order to measure pressure using the Electronic Diaphragm Gauge, a data acquisition program
was created using LabView 8.6 (see figure 5, below). In the Diaphragm Gauge setup, a BNC
connector was connected from the EDG to the NI-9215 DAQ module and another connection
was made between the DC power supply and the digital multi-meter. The hairdryer stream was
directed into a clear tube in order to produce the pressure difference that the data acquisition
system read as a voltage. This voltage was converted to a pressure measurement using a linear
calibration provided by the manufacturer.
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The Electronic Diaphragm Gauge has several design conditions that need to be considered in the
uncertainty calculations. In particular, the span (3.75 V ± 60 mV), the voltage ratiometricity
(1.5% * 3.75 V), and the offset (0.25 VDC ± 60 mV) are three systematic uncertainties
associated with the gauge specifications [4]. The dominant of these three device specifications is
by far the voltage ratiometricity. This can be characterized how far the device deviates from the
voltage-pressure linear relationship of 0.25V-4V is equivalent to 0 inH2O - 10 inH2O. Another
Electronic Diaphragm Gauge specification of particular interest is the conversion between
voltage and pressure.
2.2 Experimental setup – Software
The software packages used for this lab were National Instruments LabVIEW 8.6 and Microsoft
Excel 2007 for data acquisition and analysis, respectively. The block diagram used to collect
data for the Electronic Diaphragm Gauge is shown in figure 5 (below).
Figure 5: LabVIEW 8.6 Block Diagram used to collect Diaphragm Gauge Voltage
2.3 Experimental setup -- Procedure
A mercury barometer was used to measure the ambient air pressure. A mercury thermometer was
used to measure the ambient air temperature and the hairdryer outlet temperature. These
measurements were used to calculate the density of air and water.
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2.3.1 Procedure – U-Tube Manometer
The first velocity measurement was obtained using the U-tube manometer. One group member
held the manometer tubing parallel (±5°) to the hairdryer’s air stream and centered the tubing
inside the hairdryer nozzle (±5 mm from center). The hairdryer was then turned on high fan, low
heat while another group member read and recorded the height difference of the water in the
manometer. This was performed six times, while alternating the dryer operator and manometer
reader between each run.
2.3.2 Procedure – Electronic Diaphragm Gage
The second velocity measurement was obtained using the Electronic Diaphragm Gage. The
overall procedure was very similar. One group member held the sensor tubing parallel to the
hairdryer’s air stream, while another group member recorded the data using LabVIEW. In
LabVIEW 1000 samples were collected using a sample rate of 1000 Hz. Another measurement
was taken of ambient air using the same method.
2.4 Analysis
After data was collected the accuracy and precision of the measurements was assessed. The
following equations were used to generate the statistics needed for data analysis.
The average value of observed data was calculated using the following equations where xi is the
ith sample and N is the number of samples:
1
𝑥̅ = 𝑁 ∑𝑁
𝑖=1 𝑥𝑖
(5)
The standard deviation of a data set was calculated with this relationship:
1
2
𝑆𝑥 = √𝑁−1 ∑𝑁
𝑖=1(𝑥𝑖 − 𝑥̅ )
(6)
The subsequent equation was used to contrive the precision interval of a set of measurements:
±𝑡𝜈,𝑃 𝑆𝑥
(7)
In equation (5) the correct value of t was selected based on the specified confidence level, P, and
the degrees of freedom for the set, ν, which is equal to N-1.
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After the average and precision of the collected data is determined the uncertainty of the next
data point can be expressed as:
𝑥𝑖 = 𝑥̅ ± 𝑡𝜈,𝑃 𝑆𝑥 (% 𝑃)
(8)
Some data analysis also required the precision interval for the true mean which can be calculated
using the following relationship:
±𝑡𝜈,𝑃
𝑆𝑥
(9)
√𝑁
The uncertainty of the true value can then be assessed using the following equation:
𝑥 ′ = 𝑥̅ ± 𝑡𝜈,𝑃
𝑆𝑥
√𝑁
(% 𝑃)
(10)
In this experiment the desired value of air stream velocity was derived from equation (1). In
order to determine the uncertainty of the air stream velocity, the combined uncertainty needed to
be evaluated. The combined uncertainty can be calculated using the following equation:
𝜕𝑟
𝑢𝑟 = √∑𝐽𝑖=1 (𝜕𝑥 𝑢𝑥𝑖 )2
𝑖
(11)
In equation (11) ur is the resulting uncertainty of a function r and uxi is the uncertainty associated
with an independent variable in r. J is the number of independent variables.
2.4.1 Analysis – U-Tube Manometer
When experiment was conducted five measurements of Δh were obtained. Equation (9) was
used to determine and the uncertainty of the height was found to be Δh=0.0061 ± 0.0032m
(P=95%) and Δh=0.0061 ± 0.0053m (P=99%). Please see Appendix A (not included in this
example report) for all calculations performed for experiment 1.
The pressure difference between the air stream and ambient was calculated using equation (3).
The water in the manometer was modeled as an incompressible liquid so its density, ρH2O, was
assumed to be a constant 998 kg/m3. The combined uncertainty was of the air velocity
Using equation (3) the differential pressure between the flow from the hairdryer and atmospheric
was calculated. The pressure differential was determined to be P2-P1=59.7 ± 31.3 Pa (P=95%)
and P2-P1=59.7 ± 51.0 Pa (P=99%) using equation (11).
The desired value of velocity was calculated using equation (4). First though, the temperature of
the air stream was measured in order to determine the density of the air. Equation (8) was used
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and the temperature of the air stream was found to be uncertainty T=32.9 ±7.7˚C (P=95%) and
T=32.9 ±17.9˚C (P=99%).
Knowing the temperature of the air stream, its density, ρair, was calculated by modeling air as an
ideal gas. The following equation was used to calculate the density of air where atmospheric
pressure P=95805.5 Pa, the ideal gas constant R=287.06 J/kgK.
𝑃
𝜌𝑎𝑖𝑟 = 𝑅𝑇
(12)
The density of the air stream was found to be ρair=1.09 ± .02 kg/m3 (P=95%) and ρair=1.09 ± .04
kg/m3 (P=99%) using equation (11).
The velocity of the air stream was then determined to be V1=10.4 ± 2.8 m/s (P=95%) and
V1=10.4 ± 4.5 m/s (P=99%) using equations (4) and (11).
2.4.2 Analysis – Electronic Diaphragm Gage
Two pieces of equipment were analyzed in order to gain a better understanding of the error
involved in the data. First, the National Instruments Model 9215 4-Channel A/D converter was
analyzed. The A/D converter measures a voltage range of 10.4V and operates with 16 bits. The
resolution, Q, of the A/D converter was determined using the subsequent equation where EFSR
was twice the voltage range and M is the number of bits:
𝑄=
𝐸𝐹𝑆𝑅
2𝑀
(13)
The resolution was found to be Q=0.317 mV/bit. Please see Appendix B (not included in this
example report) for all calculations performed for experiment 2. The precision of the A/D
converter was calculated using the following equation where LSBRMS=Q:
𝑅𝑀𝑆 = 1.2𝐿𝑆𝐵𝑅𝑀𝑆
(14)
The precision of the A/D converter is thus ±0.269mV. In addition, the offset error and the gain
error from the A/D converter were determined to be ±40mV and ±1mV respectively.
The second piece of equipment assessed was the electronic diaphragm gage model P992 LowRange Differential Pressure Sensor. The first test performed with the pressure gage measured
the velocity of ambient air. The true value of the voltage generated due to ambient air pressure
was known to be 0.25V which corresponds to a differential pressure of 0 inH2O. This test
revealed a bias of 2.482mV, using equation (15), which is within the specified precision range of
±60mV for zero/null readings.
𝑏𝑖𝑎𝑠 = 𝑥̅ − 𝑥′
(15)
The pressure gage was then used to measure the differential pressure between the air stream of
the hairdryer and the ambient air. The bias 2.482mV was subtracted from the collected data to
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eliminate offset error. The gage’s span error was evaluated to ±2.24mV by taking the ratio of the
span of data collected to the maximum span of the gage and multiplying it by the maximum
allowable span error of 120mV. In addition, the ratiometricity of the gage was found by
multiplying the data max span and 1.5%. The ratiometricity was found to be ±1.047mV.
Next the voltage reading for the air stream evaluated at v=0.3198 ± 0.0174V (P=95%) and
v=0.3198 ± 0.0228V (P=99%) using equation (8). From here the voltage readings were
converted to pressure values. The following relationship was used to determine the differential
pressure of the readings in inH2O:
10−0
𝑃2 − 𝑃1 = 4−2.5 𝑣 − 0.67 = 2.67𝑣 − 0.67
(16)
After converting the pressure from inH2O to Pa, the differential pressure was determined to be
P2-P1=45.784 ± 11.556 Pa (P=95%) and P2-P1=45.784 ± 15.167 Pa (P=99%) using equation (11).
Then equation (4) was used to calculate the velocity of the air stream. The air density remained
the same as in experiment 1, ρair=1.09 ± .02 kg/m3 (P=95%) and ρair=1.09 ± .04 kg/m3 (P=99%),
so please refer to calculations in Appendix A (not included in this example report) for the
determination of ρair.
The velocity of the air stream was then determined to be V1=9.15 ± 1.16 m/s (P=95%) and
V1=9.15 ± 1.53 m/s (P=99%) using equations (4) and (11).
Table 2: Summary of Uncertainties used in Calculations
(Appendices not included in this example report)
Uncertainty Analysis and Justification
Variable
Value Units
Uncertainty Uncertainty Justification
accepted experimental
g
9.807 m/s^2
0 value
h
0.0154 m
0.00421 See Appendix A
P_ambient
95792 Pa
149 See Appendix A
rho_air
1.082 kg/m^3
0.004 See Appendix A
rho_water
997.6 kg/m^3
0.35 See Appendix A
T_ambient
23 C
1.12 See Appendix A
T_nozzle
35.3 C
0.206 See Appendix A
Voltage_ambient 0.2423 V
0.00679 See Appendix A
Voltage_hairdryer 0.4757 V
0.0553 See Appendix A
in.
P_2_ambient
-0.021 H2O
0.0181 See Appendix A
P_2_ambient
-5.121 Pa
4.51 See Appendix A
in.
P_2_hairdryer
0.6018 H2O
0.14 See Appendix A
P_2_hairdryer
149.9 Pa
34.9 See Appendix A
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3.0 Results
3.1 Results – U-Tube Manometer
Summary tables for the precision and accuracy results are shown below. See Appendix A (not
included in this example report) for detailed calculations.
Figure 6: U-Tube Manometer Raw Pressure Data
Table 3: Precision Data for the U-Tube Manometer
Precision Calculations
Trial
∆P [mmH2O]
1
∆P [Pa]
11
108
2
12
118
3
11.5
112
4
12
118
5
12.5
123
Mean
11.8
116
Stdev
0.510
5.59
t (ν,P) = (4,0.95)
2.776
Estimated Precision
95 %
xi = 1.16x102±0.115x102 Pa
(P=95%)
t (ν,P) = (4,0.99)
Estimated Precision
99%
4.604
xi = 1.16x102±0.257x102 Pa
(P=99%)
Random
Uncertainty
uv = 0.71 m/s
Avg. Velocity
14.2 m/s, Sx = 0.345 m/s
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Table 4: Bias Data for the U-Tube Manometer
Bias Calculations
Human observation bias
1
Reading ∆H at eye level
2
Reading from bottom meniscus
3
Ruler & Manometer not parallel
Result
± 0.5 mmH2o BIAS
Bias (Human
observation)
4.9 Pa
Systematic
Uncertainty
uv = 0.30 m/s
3.2 Results – Electronic Diaphragm Gage
Figure 7: Electronic Diaphragm Gage Raw Voltage Data for Ambient Air
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Figure 8: Electronic Diaphragm Gage Raw Voltage Data for Ambient & Hairdryer Air
Table 5: Precision Data for the Electronic Diaphragm Gauge
Electronic Diaphragm Gauge Precision Calculations
∆P [mmH2O]
∆P [Pa]
Mean
0.492
122
Stdev
0.078
19.3
t (ν,P) = (999,0.95)
Estimated Precision
95 %
1.96
xi = 1.22x102±0.379x102 Pa
(P=95%)
t (ν,P) = (999,0.99)
Estimated Precision
99%
Random
Uncertainty
2.58
xi = 1.22x102±0.499x102 Pa
(P=99%)
Avg. Velocity
14.6 m/s, Sx = 5.8 m/s
uv = 2.27 m/s
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Table 6: Bias Data for the Electronic Diaphragm Gauge
Bias Calculations
True Voltage
0.250
V
Avg. Ambient
0.249
V
Avg. Blower
0.433
V
Offset Error
0.00121
V
Span
0.00586
V
Voltage Ratiometricity
0.0563
V
Total Gage Uncertainty
0.0621
V
Bias (device specs)
41.1 Pa
Systematic Uncertainty
uv = 2.46 m/s
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4.0 Discussion
There were many sources of variability in this experiment. For instance, the density of the air
stream, which is needed to calculate velocity, was dependent on the temperature of the air
stream. The temperature of the air stream was found to be precise only within ±7.7˚C at 95%
confidence. This alone is a very large error which then propagates into the precision of the
density calculation. An inaccurate temperature measurement of the air stream would generate
error in the calculated pressure value which would then create error in velocity measurements.
In this experiment the hairdryer did heat up the temperature of the air stream. This caused the air
density to decrease and thus the velocity of the air flow to decrease as well.
The pressure measurements in experiment 1 and experiment 2 were obtained using two different
techniques. In the first experiment the pressure was dependent on human evaluation of a change
in liquid height where as in experiment 2 the pressure measurements were dependent upon the
performance of electronic equipment. It was found that the first experiment led to a pressure
measurement 30% higher than in the second experiment. In addition, the precision interval in
experiment 1 was roughly three times larger than in experiment 2 indicating that the electronic
equipment could yield more precise results.
When using electronic equipment, such as in experiment 2, the capability of the equipment to
deliver precise and accurate results needs to be considered. For instance, it was determined that
the National Instruments Model 9215 4-Channel A/D converter has a resolution of 0.317mV/bit.
This resolution should be smaller than the precision of the equipment in combination with it.
This is the case in experiment 2 since the pressure gage was found to have a precision of over 1
mV in all cases. However, it is important to keep in mind that with every piece of equipment
added to an experimental set-up will increase the results uncertainty.
The effects of adding additional variables on measurement spread and precision can be seen in
Figure 8 which compares the data distribution of the ambient pressure to the pressure generated
by the air stream. With the ambient air the only sources of variability is due to the electronic
equipment set up to take the readings. However, when the hairdryer is introduced to generate the
air stream other sources of variability such as air stream temperature have been added. The plot
shows that with an added number of variables, measurement precision will decrease.
In experiment 2, the bias of the pressure gage was able to be eliminated as it was determined for
the test of the ambient air. Figure 7 illustrates the bias of the pressure gage. The precision of
experiment 2 was improved since this bias was eliminated from the pressure measurements used
to calculate velocity.
In the end the average velocity, as measured by the manometer, was 13.6% higher than the
velocity measured by the electronic diaphragm pressure gage. The uncertainty interval of the
manometer was 2.7 times larger than the uncertainty interval of the manometer. The confidence
limits of the manometer are much wider spread about the measurements. This indicated the
electronic set-up, utilizing the pressure gage, produced more precise measurements.
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5.0 Conclusions and Recommendations
This laboratory experiment consisted of measuring velocity at the exit of the nozzle of a hair
dryer. Two experimental setups were used to measure the velocity, a manometer and a pressure
sensor interfaced with a computer. The manometer gave a height difference, and using the basic
hydrostatic pressure equation (equation 3), the height difference was converted to a pressure.
Since the hair dryer created a streamline directly into the tube of the manometer, Bernoulli's
relationship (equation 2) was used to convert the pressure measurements to air velocity
measurements. Voltage needed to be converted to a pressure using a linear calibration for the
pressure sensor interfaced with a computer and then Bernoulli’s equation was used to find
velocity.
Throughout the experiment, many measurements introduced uncertainty into the statistical
analysis. Engineering Equation Solver was used to propagate the uncertainty. As for the
specific uncertainty of each variable, Appendix A (not included in this example report) gives a
strong argument for each.
5.1 Summary of Results
Upon analyzing the data and propagating the uncertainty, the following results were obtained:
 The velocity of air exiting the hairdryer using a manometer was 16.69 ± 2.82 m/s.
 The velocity of ambient air in the laboratory using the Electronic Diaphragm Gage was
3.077 ± 10.48 m/s.
 The velocity of air exiting the hairdryer using the Electronic Diaphragm Gage was
16.65 ± 1.94 m/s.
5.1 Future Recommendations
Recommendations include collecting more measurements with the U-Tube Manometer is order
to increase the precision of measurement data. Obtain more uncertainty information on the
ambient room temperature and pressure. This would lead to a better estimate of the uncertainty
of the density of water and air at these conditions. Another recommendation would be use an
Electronic Diaphragm Gauge that with a lower span. The average voltage readings were very
low compared to the ambient voltage readings of approximately 0.25 V. The Electronic
Diaphragm Gage works properly when receiving a 5Vdc ± 2mV input from the power supply.
The power supply and multi-meter combination used was not accurate enough to meet this
specification, and therefore a higher quality multi-meter and power supply is desired.
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Lab 1: Measuring Air Velocity
J. Cool
5 February 2010
References
[1] Beidler, A. (2008). Measuring Temperature, Humidity, Precipitation, Wind Speed. Weather
Instruments and Gauges. Retrieved February 1, 2010, from
http://meteorologyclimatology.suite101.com/article.cfm/weather_instruments_gauges
[2] Carrington, C. G., Marcinowski, A., & Sandle, W. J. (1982). A simple volumetric method
for measuring air flow. Journal of physics E: Scientific Instruments. Retrieved February 1,
2010, from http://www.iop.org/EJ/abstract/0022-3735/15/3/006
[3] Wikipedia contributors. "Accuracy and precision." Wikipedia, The Free Encyclopedia.
Wikipedia, The Free Encyclopedia, 13 Mar. 2010. Web. 26 Mar. 2010.
[4] P992 Low Range Differential Pressure Sensor. RoHS. February 4, 2010
<http://me368.engr.wisc.edu/lab_handouts/lab_equipment_datasheets/electronic_[=diaprhag
m_gage_P992.pdf>.
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