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Lab 1: Measuring Air Velocity – Accuracy and Precision

byJoe Cool

5 February 2010

Department of Mechanical EngineeringUniversity of Wisconsin-Madison

1513 University AvenueMadison, WI 53706-1572

Lab 1: Measuring Air Velocity 5 February 2010J. Cool

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 4 1.1 Background 4 1.2 Objectives 6 1.3 Overview 62.0 Procedure and Apparatus 7 2.1 Experimental setup – Hardware 7 2.1.1 Experimental setup – U-Tube Manometer 7 2.1.2 Experimental setup – Electronic Diaphragm Gage 8 2.2 Experimental setup – Software 9 2.3 Experimental setup – Procedure 9 2.3.1 Procedure – U-Tube Manometer 10 2.3.2 Procedure – Electronic Diaphragm Gage 10 2.4 Analysis 10 2.4.1 Analysis – U-Tube Manometer 11 2.4.2 Analysis – Electronic Diaphragm Gage 123.0 Results 14 3.1 Results – U-Tube Manometer 14 3.2 Results – Electronic Diaphragm Gage 154.0 Discussion 185.0 Conclusions and Recommendations 19 5.1 Summary of Results 19 5.2 Recommendations 19References 20

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Nomenclature

Sym.

Definition Units

Xi Measurement --------Sx Standard Deviation --------N number of data points --------

x Average --------P Pressure Pah Height MV Velocity m/sg acceleration due to gravity m/s2

T Temperature ˚CQ Resolution mV/bitv Voltage Vx’ true value --------t ν , P variable values --------

Greek Symbols

Sym.

Definition Units

Δ change in -------ρ Density Kg/m3

ν degrees of freedom -------

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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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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:

V 22

2+gz 2+

P2

ρa=

V 12

2+gz1+

P1

ρa (1)In this experiment gravity was neglected. After removing the gravity terms and rearranging, Equation 1 becomes:

P2−P1=ΔP=ρa(V 1

2−V 22 )

2 (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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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:

V 1=√ 2 ρw ghρa (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 InstrumentationNational Instruments CompactDAQ USB 8 slot chassis

National Instruments Model 92154-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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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:

x= 1N ∑

i=1

N

x i (5)

The standard deviation of a data set was calculated with this relationship:

Sx=√ 1N −1∑i=1

N

(x i−x )2 (6)

The subsequent equation was used to contrive the precision interval of a set of measurements:

± t ν ,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:

x i=x± t ν , P Sx (% P) (8)

Some data analysis also required the precision interval for the true mean which can be calculated using the following relationship:

± t ν ,P

S x

√N(9)

The uncertainty of the true value can then be assessed using the following equation:

x '=x± t ν , 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:

ur=√∑i=1

J

(∂ r∂ x i

uxi)2

(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.

ρair=P

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=1.2 LS BRMS (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 Low- Range 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= x−x ' (15)

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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 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:

P2−P1=10−04−2.5

v−0.67=2.67 v−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 UnitsUncertainty Uncertainty Justification

g 9.807 m/s^2 0accepted experimental value

h0.015

4 m 0.00421 See Appendix A

P_ambient9579

2 Pa 149 See Appendix A

rho_air 1.082kg/m^3 0.004 See Appendix A

rho_water 997.6kg/m^3 0.35 See Appendix A

T_ambient 23 C 1.12 See Appendix AT_nozzle 35.3 C 0.206 See Appendix AVoltage_ambient

0.2423 V 0.00679 See Appendix A

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Voltage_hairdryer

0.4757 V 0.0553 See Appendix A

P_2_ambient-

0.021in. H2O 0.0181 See Appendix A

P_2_ambient-

5.121 Pa 4.51 See Appendix A

P_2_hairdryer0.601

8in. H2O 0.14 See Appendix A

P_2_hairdryer 149.9 Pa 34.9 See Appendix A3.0 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 CalculationsTrial ∆P [mmH2O] ∆P [Pa]

1 11 1082 12 1183 11.5 1124 12 1185 12.5 123

Mean 11.8 116Stdev 0.510 5.59

t (ν,P) = (4,0.95) 2.776

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Estimated Precision 95 %

xi = 1.16x102±0.115x102 Pa (P=95%)

t (ν,P) = (4,0.99) 4.604Estimated Precision 99%

xi = 1.16x102±0.257x102 Pa (P=99%)

Random Uncertainty uv = 0.71 m/sAvg. Velocity 14.2 m/s, Sx = 0.345 m/s

Table 4: Bias Data for the U-Tube Manometer

Bias CalculationsHuman observation bias

1 Reading ∆H at eye level2 Reading from bottom meniscus3 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 122Stdev 0.078 19.3

t (ν,P) = (999,0.95) 1.96Estimated Precision 95 %

xi = 1.22x102±0.379x102 Pa (P=95%)

t (ν,P) = (999,0.99) 2.58Estimated Precision 99%

xi = 1.22x102±0.499x102 Pa (P=99%)

Random Uncertainty uv = 2.27 m/s

Avg. Velocity 14.6 m/s, Sx = 5.8 m/s

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Table 6: Bias Data for the Electronic Diaphragm Gauge

Bias CalculationsTrue Voltage 0.250 VAvg. 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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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_[=diaprhagm_gage_P992.pdf>.

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http://www.iop.org/EJ/abstract/0022-3735/15/3/006

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