mech lab manual for engg
TRANSCRIPT
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ME 310 Lab Manual
Mechanical EngineeringInstrumentation
v 1.0, Jan. 27, 2003
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Table of Contents
LABORATORY SAFETY 3
REPORT WRITING 4
EXPERIMENT 1: UNCERTAINTY & ERRORS 6
EXPERIMENT 2: PERIODIC WAVEFORMS 9
EXPERIMENT 3: SENSORS & SIGNAL CONDITIONING 12
EXPERIMENT 4: SIGNAL CONDITIONING 16
EXPERIMENT 5: DIGITAL DATA ACQUISITION 18
EXPERIMENT 6: STRAIN GAGES 23
EXPERIMENT 7: PRONY BRAKE 26
EXPERIMENT 8: VELOCITY AND FLOW RATE 28
APPENDIX A: BREAD BOARDS 31
APPENDIX B: RESISTORS 32
APPENDIX C: ZONIC DAQ SYSTEM 35
APPENDIX D: SPRING-MASS SYSTEMS 37
Need to add Appendices on DMM, O-SCOPE, Fn Generator, Power Supply, etc.
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Laboratory Safety
Here are several rules that you should follow while in the ME 310 lab.
1.
Follow instructions of the TAs.2. Use common sense. Most of the experiments you will be dealing with have very little chance for
encountering something dangerous, but be careful. Some examples include the following:
a. If an experiment involves high voltage and/or current, dont touch hot-wires.
b. If something is rotating rapidly, stand clear and keep any loose clothing away.c. Shield your eyes (that is, wear goggles) from lasers and other coherent light sources.
3. Never work alone.
4. Dont bring food or drink into the lab. Liquids are conductive and food can gum up the equipment.
5. Read through the lab handout thoroughly before starting on an experiment. This includes any
instrumentation specifications and MSDS.
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REPORT WRITING
Some reports in the ME 310 may require a formal laboratory report. The report should be written in such a way thatanyone could duplicate the performed experiment and find the same results as the originator. The reports should be
simple and clearly written. Reports are due one week after the experiment was performed, unless specified
otherwise.
The report should communicate several ideas to the reader. First the report should be neatly done. The experimenter
is in effect trying to convince the reader that the experiment was performed in a straightforward manner with great
care and with full attention to detail. A poorly written report might instead lead the reader to think that just as little
care went into performing the experiment. Second, the report should be well organized. The reader should be able to
easily follow each step discussed in the text. Third, the report should contain accurate results. This will require
checking and rechecking the calculations until accuracy can be guaranteed. Finally, the report should be free of
spelling and grammatical errors.
Long Report Format
The following format is to be used for formal Laboratory Reports:
Title PageThe title page should show the title and number of the experiment, the date the experiment was
performed, experimenters name and experimenter's partners' names.
Table of Contents Each page of the report must be numbered for this section.Object The object is a clear concise statement explaining the purpose of the experiment. This is one of the
most important parts of the laboratory report because everything included in the report must somehow
relate to the stated object. The object can be as short as one sentence and it is usually written in the past
tense.
Theory The theory section should contain a complete analytical development of any important equations
pertinent to the experiment, and how these equations are used in the reduction of data. The theory sectionshould be written textbook-style.
Procedure The procedure section should contain a schematic drawing of the experimental setup including
all equipment used in a parts list with manufacturer serial numbers, if any. Show the function of each part
when necessary for clarity. Outline exactly step-
Results The results section should contain a formal analysis of the data with tables, graphs, etc. Any
presentation of data that serves the purpose of clearly showing the outcome of the experiment is sufficient.
Discussion and Conclusion This section should give an interpretation of the results explaining how theobject of the experiment was accomplished. If any analytical expression is to be verified, calculate % error
and account for the sources. Discuss this experiment with respect to its faults as well the as its strong
points. Suggest extensions of the experiment and improvements. Also recommend any changes necessary
to better accomplish the object. Each experiment write-up contains a number of questions. These are to beanswered or discussed in the this section.
Bibliography A detailed listing of all references used.
Appendix
(1) Original data sheet.
(2) Show how data were used by a sample calculation.
(3) Calibration curves of instruments that were used in the performance of the experiment. Include
manufacturer of the instrument, model and serial numbers. (The instructor will usually supply Calibration
curves.)
Short Report Format
Often the experiment requires not a formal report but a short informal report. An informal report includes the Title
Page, Object, Procedure, Results, and Conclusions. Other portions may be added at the discretion of the instructoror the writer. Another alternative report form consists of a Title Page, an Introduction (made up of shortened
versions of Object, Theory, and Procedure) Results, and Conclusion and Discussion. This form might be used
when a detailed theory section would be too long. You should also include the raw data sheets used to record data in
the laboratory.
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Graphs
In many instances, it is necessary to compose a plot in order to graphically present the results. Graphs must be
drawn neatly following a specific format. The figure below shows a graph prepared using a computer. There are
many computer programs that have graphing capabilities, including Excel and MATLAB. Nevertheless an
acceptably drawn graph has several features of note and an example is given below. Note that symbols are used to
show experimental data while lines are used to denote theoretical calculations.
Tables
x/c
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Experiment 1: Uncertainty & ErrorsObjectives:In this experiment you will:
Become familiar with basic electric circuit components
Measure, classify and record different error types
Fit a set of data to a statistical distribution and make predictions based on this distribution
Estimate uncertainty due to propagation of errors in an experiment
Perform a linear least squares fit to a set of measured data
Required Hardware:
Breadboard
A selection of resistors, inductors and capacitors
Handheld Digital Multimeter (DMM)
Handheld LCR meter (1 to be shared among groups)
DC power supply
Miscellaneous connectors, clips and plugs
Required Documentation:
Table of color codes for resistors Manual or datasheet for DMM
Manual or datasheet for LCR meter
Activity #1
Procedures:
1. Select 6 resistors of the SAME resistance.
2. Using the color coded bands, determine and record the nominal value and tolerance of the resistors
3. Using the DMM, measure and record the resistance for each of the 6 resistors
4. From the DMM manual or datasheet, record the meters bias uncertainty (this can be obtained by comparing
DMM readings to the more accurate LCR meter), resolution and accuracy for measuring resistance. Also
record the resolution and accuracy for the LCR meter.
Note: Circuit elements should be selected based on the available specifications of the DMM and other such
equipment (i.e., try to select resistor sizes for which there is an accuracy rating available in the DMM manual).
Additionally, in order to avoid large uncertainties in the calculations due to a bias error in the DMM resistors oflarger nominal values should be selected.
Calculations:
1. Compute the sample mean and standard deviation for the 6 resistance measurements. Compare these to the
nominal value and tolerance of the resistors taken from the color coded bands. Is there a difference? Why
or why not?
2. Compute the uncertainty in this mean value. Include both precision and bias uncertainty. (Use t-distribution
for small # of samples with a 95% confidence level)
3.
Assuming the distribution is normal, plot the Gaussian distribution (use Matlab to do this!). Using theGaussian distribution, how many resistors (of the 6 measured) are expected to be within 25% of the mean?
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Activity #2
Background:
You will need to re-familiarize yourself with the concepts of equivalent resistance, capacitance and inductance for
parallel or series connections of each element.
Procedures:
1. Select any 2 resistors of different resistance. Record their nominal value and tolerance. Connect them in
series on the breadboard. Measure the resistance across the two resistors using the DMM.
2. Take the same 2 resistors and connect them in parallel on the breadboard. Measure the resistance across the
two resistors using the DMM. Remove the resistors from the breadboard.3. Select any 2 capacitors of differing capacitance. Record their nominal value and tolerance. Connect them
in series on the breadboard. Measure the capacitance across the two capacitors using the LCR meter.
Remove the capacitors from the breadboard.
4. Select any 2 inductors of differing inductance. Record their nominal value and tolerance. Connect them in
parallel on the breadboard. Measure the inductance across the two inductors using the LCR meter. Remove
the inductors from the breadboard.
5. Using the manual or the datasheet for the DC power supply, record the load regulation and use this value
as the uncertainty associated with the power supply.
Calculations:
1. Calculate and place in a table the overall uncertainty for each measurement (1-4) taken above. This shouldinclude the precision error (tolerance) of the passive circuit element (resistor, inductor or capacitor), the bias
error of the DMM, and the propagation of error due to multiple circuit elements. You can assume that the
LCR meter has no bias error since it is the reference for the DMM bias error, however, you should considerits precision error.
2. The power loss due to current flowing through a resistor is P=I2R, where R is the equivalent resistance of the
circuit. For circuits 1 and 2 (below), if 10 volts dc were applied to them using the DC power supply (see
circuits below), estimate the nominal value and the uncertainty for the power loss in each circuit.
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Activity #3
Background
A voltage divider is a simple circuit used to scale down an input voltage to a smaller output voltage. Such a circuit
is commonly found in signal conditioning systems for sensors. The general construct of the voltage divider consists
of two resistors in series. The input to the circuit is the DC power supply which supplies a constant voltage. The
output of the circuit is the voltage, measured across the second resistor. The circuit diagram is shown below.
Procedures:
1. Select any 2 resistors of different resistance. Record their nominal values and tolerance. Using these tworesistors and the DC power supply, construct the voltage divider circuit as shown in the diagram above.
sketch the circuit showing the nominal value of each resistor and its location. (BEFORE CONNECTINGTHE DC POWER SUPPLY, MAKE SURE IT IS TURNED OFF AND THE VOLTAGE OUTPUT
TURNED ALL THE WAY DOWN!)
2. Turn on the DC power supply. Set the voltage to 1.0 volts. (This is the input voltage to the circuit). Using
the DMM, record the output voltage. (The output voltage is across the leads of the second resistor.)
3. Create a table of input voltage vs. output voltage for input voltage values of 0.2, 0.4, 0.6, 0.8, 1.0, 1.5, 3.0,
5.0, 8.0, 10.0 volts. Label this column of the table Experimental Data.
Calculations:
1. Using Ohms law and Kirchoffs law, derive an expression for Vout/Vin in terms of R1 and R2 for the voltage
divider circuit.
2. Using this relationship and the nominal value and tolerance of the resistors R1 and R2, compute the predicted
output voltage and its uncertainty (%) for each input voltage in step #3 of the procedures. Place these in a
column next to the Experimental Data and label this column Predicted. Compute the % difference
between the experimental and predicted values of output voltage and place this in a final column next to the
others labeled % difference. Is this % difference within the predicted uncertainty? Why or why not?
3. Create a plot of Vout vs. Vin. This plot should include: a) each experimental data point, b) a best fit line
(linear least squares) through the experimental data and c) each predicted data point. Write the equation of
the best fit line. Do these match up well? Discuss.
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Experiment 2: Periodic Waveforms
Objectives:
In this experiment you will:
Use a function generator, an O-scope and a DMM (Digital Multimeter), to create and measure periodic
waveforms and their properties
Use Fourier series to construct the same periodic waveforms
Measure the response characteristics of zero, first and second order electrical and mechanical systems
Measure the frequency response (both amplitude and phase) of a second order system using the sine sweep
approach
Required Hardware:
Breadboard
A selection of resistors, inductors and capacitors
The spring-mass-damper experimental module
A hotplate, thermocouple and metal piece
Handheld DMM
Function generator Oscilloscope
DC power supply
Agilent Dynamic Signal Analyzer (or Zonic Box) (for sine sweep test)
Temperature sensor on DMM and stopwatch
Miscellaneous connectors, clips and plugs
Required Documentation:
Table of color codes for resistors
Manual or datasheet for DMM
Activity #1: Periodic Waveforms
Background: Periodic waveforms can take on any shape (sinusoidal, sawtooth, squarewave, triangle, and many
others) as long as that shape repeats itself. Periodic waveforms are very useful in the analysis and design of
dynamic systems (of which many measurement systems are). One way to introduce them into systems is to use afunction generator. The most useful way to measure them is with an Oscilloscope. Using a Fourier Series
expansion, an equation can be written for any periodic waveform. The Fourier Series is an infinite series, but in
practice only a finite number of terms in the series can be computed. How many terms that is required to accurately
reproduce a waveform is always a question. It is one that you will try to answer in this activity.
Procedures:
1. Using a BNC to BNC cable and a T connector, connect the output of the function generator (a voltage
output) to channel 1 of the O-scope (see figure 1 below).2. Connect the DMM to the T connector using a BNC to BNC cable and a banana plug to BNC connector.
3. Turn on the function generator and the O-scope. Set the output of the function generator to a sinusoidal
output with a peak amplitude of 1 volt and a frequency of 100 Hz. Capture the waveform using the O-scopeand save the data in ASCII format to disk. Now use the DMM at the T connector to measure and record
the RMS value of the voltage waveform.
4. Now play with the amplitude and the frequency inputs and observe how the waveform changes on the O-
scope. Make notes of what happens in your notebook. Is it what you expect?
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5. Re-set the peak amplitude to 1 volt and frequency to 100 Hz and change the waveform to sawtooth. Again,
capture the waveform using the O-scope and save the data to disk. Again, measure and record the RMS
value of the waveform using the DMM.
Calculations:
1. Plot the voltage vs. time data for the sinusoidal and the sawtooth waveforms. From these plots, determine
the frequency (in Hz), peak amplitude (in volts) and the RMS amplitude in volts (use eq. 4.21). Make a
small table that compares the frequency, and peak amplitude values that you put into the function generator
and measured with the DMM to the values you measured from the waveforms. Also include in this table a
comparison of the RMS voltage measured using the DMM and that you computed using eq. 4.21.
2. Write an equation for the sinusoidal and the sawtooth waveforms. (For the sawtooth use Table 4.1). Using
these equations, plot the waveforms for 1 term, 2 terms, 10 terms and 50 terms in the expansion. Compare
these plots to the measured plots and comment on the results.
Figure 1: Set-up for Activity #1
Activity 2: Response of Zeroth Order Systems
Background: Zeroth order systems are governed by equations that contain no derivatives, that is, their output is
equal to a constant times the input. Another way of looking at it is that, for a constant input, the output is
independent of time. Electrical circuits containing only resistors are zeroth order. Mechanical systems such as a
collection of levers are completely analogous to the resistance circuits and are also zeroth order because they simplyamplify a force. A voltage divider circuit is the subject of this activity.
Procedures
1. Select 2 resistors of different resistance. Record their nominal values and their tolerance.2. Using the breadboard and the function generator, construct the voltage divider circuit shown below in fig. 2.
(Be sure to record which resistor is R1 and which is R2).
3. Using a collection of alligator clips, BNC connectors and a T junction, connect the output from the
function generator directly to O-scope channel 1 (Vin), and connect O-scope channel 2 across the leads of R2(Vout). (Again, see figure 2 below.)
4. Set the output of the function generator to a squarewave with a 1 volt peak amplitude and 2 Hz frequency.5. Capture both waveforms from channels 1 and 2 on the O-scope (each in their turn) and save them to disk in
ASCII format.
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Calculations:
1. Plot the waveforms of Vin and Vout on the same plot. What are the differences between these two
waveforms? Are these waveforms consistent with a zeroth order system?
2. Using Kirchoffs and Ohms Laws, derive the relationship Vout/Vin. Are the measured results consistent
with this relationship?
Figure 2: Set up for Activity #2
Activity #3: First Order System Step Response
Background: First order systems are governed by differential equations that only contain the first derivative.
Electrical systems that contain only resistors and capacitors (no inductors) have first order responses. Vibratory
mechanical systems that contain only springs and dampers (no mass) are completely analogous to the R-C electrical
circuits and also have first order responses (see Table 5.2). The most classic of all first order system is the thermalsystem. It is the subject of this activity.
Procedures:
1. Turn the hotplate on and place the dial at a setting of 3. (Nothing should be on the hotplate yet.) Place the
temperature sensor against the hotplate and note when the equilibrium temperature is reached. It will take a
few minutes for the plate to reach a steady temperature. Record several temperatures over the surface of the
hotplate to get a good average value of the surface (this is the step input to your system).2. Leave the hotplate on. Now remove the temperature sensor from the hotplate and let the sensor cool. Apply
the thermal grease to a spot on one side of the metal washer. Place the sensor into the grease on the washer
and record the equilibrium temperature of the washer. Record this temperature (it is the initial temperature
of your system).
3. Now place the washer onto the hotplate and simultaneously start the timer.
4. Record the temperature every 5 seconds until the equilibrium is reached. (After a few minutes, you maywant to increase the time between measurements.)
Calculations:
1. Plot the temperature vs. time data that you recorded in step 3 above. Also, plot a straight line indicating the
step input temperature.
2. Describe the shape of this plot. Describe what features of this plot make it a first order response.3. Compute the time constant. Write an equation for this temperature response.
4. According to your text, It is often assumed that a process is completed during 5 time constants. Do you
agree with this statement for your system? Why or why not?
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Experiment 3: Sensors & Signal ConditioningObjectives:In this experiment you will:
Obtain a basic understanding of some of the primary mechanisms used in stage 1 (sensing) devices
Obtain a basic understanding of some simple stage 2 (signal conditioning) devices
Learn how to set-up and use some of the most common sensing schemes
Learn how to construct a calibration curve and estimate system sensitivity
Required Hardware:
Breadboard
A selection of resistors
A large manually variable 1 Ohm resistor
A potentiometer with the cover missing
A commercially available position sensing system (inductive probe)
A thermistor, strain gage
Handheld Digital Multimeter
DC power supply Hotplate, steel wafer
Miscellaneous connectors, clips and plugs
Required Documentation:
Table of color codes for resistors
Manual or datasheet for DMM
Activity #1: Resistance Varying Position Sensors with Voltage Dividing Potentiometer Circuit
Background: Many mechanical sensors (stage 1 devices) work on the principal of a change in resistance. The most
common are temperature sensors (thermistors) and position sensors (potentiometers). However, most dataacquisition systems are set up to measure and acquire voltage, not resistance. Therefore, signal conditioning (a stage
2 device) is required to convert the change in resistance to a change in voltage. A common circuit used for this
purpose is the voltage dividing potentiometer circuit (section 7.7.1).
Procedures:
1. Connect the 1 ohm manually variable resistor directly to the DMM and set the DMM to read resistance.
(refer to fig. 1 below) Make sure that 1 lead of the DMM is connected to the tab fixed to the body of the
resistor and the other is on the sliding band. (The measured resistance is that between the tab and the sliding
band.)
2. Position the sliding band at 1, 2, 4 and 6 from the tab. At each location measure the resistance. In order
to obtain consistent readings be sure to place the indentation on the sliding band directly over one of the
coils of wire on the resistor. Repeat this procedure 3 times. First going up and then coming back down.Record the data each time.
3. Remove the DMM. Then, attach a 10 ohm resistor in series with the 1 ohm variable resistor and the DC
power supply. (Make sure the DC power supply is off!) Place the DMM such that it measures voltageacross the 10 ohm resistor. This is the voltage dividing potentiometer circuit. (Refer to the sketch in Fig. 2
below.)
4. Turn on the power supply set the excitation to 1 volt. Then turn off the power supply.
5. Position the band to 1, turn on the DC power supply and measure the output voltage. Turn off the power
supply.
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6. Repeat step 6 for 2, 4 and 6. Turn off the power supply each time you change the position of the tab.
Then turn it back on to take the reading. Repeat this procedure 3 times. First going up and then coming
back down. Record the data each time.
Calculations:
1. Plot the measured resistance vs. position for all data points. (Show the points as you go up using one type of
symbol and the points as you come back using another type of symbol. Do not connect the points with a line.
Only show the symbols.)
2. Plot the best fit line through all of the data. Show this line on the same plot as the data points and write the
equation of this line on the graph (this is a calibration curve). What is the sensitivity of this sensor
(ohms/inch)?
3. Define the term hysteresis. Is there any hysteresis in your data?
4. Plot the voltage vs. position for all data points just as you did in #1.
5. Plot the best fit line through all of the data. Show this line on the same plot as the data points and write the
equation of this line on the graph (this is a calibration curve). What is the sensitivity of this sensor
(volts/inch)?
6. Assuming the DMM is a high impedance readout device, derive an expression for the sensitivity (volts/inch)
of the sensor with voltage divider using Kirchoffs and Ohms laws, and the relationship between resistanceand position found in 2. (Similar to what was done to get 7.8a, but with a twist.) Does this sensitivity match
that measured in 5? What would be the source of any errors? Are they bias or precision?
Sliding Band with Indentation
Variable 1 Ohm Resistor
Holder
DMM
Figure 1: Set-up for Activity #1
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Variable 1 Ohm ResistorDC Power
Supply
DMM
Sliding Band with IndentationHolder
Figure 2: Set up for Activity #1 with voltage dividing circuit
Activity 2: Thermistor with Voltage Sensitive Wheatstone Bridge
Background: A thermistor is a device that changes resistance as its temperature changes. It is a commonly used
temperature sensing device in industry and in laboratories. The simplest way to use a thermistor is to hook up aDMM across its leads and measure resistance directly. Thermistors come with calibration curves that relate
resistance to temperature. Alternatively, you could make your own calibration curve. As you should be aware, most
data acquisition systems accept voltage inputs, not resistance directly. Therefore, we wish to hook up the thermistor
into a signal conditioning circuit that converts temperature to resistance and then resistance to voltage. One way to
do this is to use a voltage sensitive Wheatstone bridge.
Procedures:
1. Connect the thermistor to the steel thermal wafer using thermal compound. Place the thermal wafer onto the
hotplate. (The hotplate should be off and at room temperature.)
2. Select 3 identical resistors and record their nominal value and tolerance. Using these resistors, the
thermistor, a breadboard, and the DC power supply, connect the voltage sensitive Wheatstone bridge circuitshown in figure 3.
3. Turn on the DC power supply (this is Vi in the circuit) and set it to 1 volt.
4. Make a table with 3 columns: temperature, resistance, and voltage. Using the thermal sensing device
measure the temperature of the wafer (should be room temperature). Then use the DMM to measure the
resistance across the leads of the thermistor. Finally, use the DMM to measure the output voltage, Vo, from
the Wheatstone bridge. Record these.
5. Turn on the hotplate and increase its temperature by turning the knob to 4 different positions. Each time let
the temperature reach equilibrium by waiting until the resistance reaches a steady value. Each time recordthe temperature, resistance and voltage.
6. Turn off the hotplate and the power supply. Let everything cool down and disconnect all leads.
Calculations:
1. Plot the temperature vs. resistance data points. Fit the data with the best fit curve (not necessarily linear, so
use MATLAB or Excel.)
2. Plot the temperature vs. voltage data points. Fit the data with the best fit curve (again, not necessarily linear,
so use MATLAB or Excel.)
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3. What is the sensitivity of the sensor (ohms/C) at a temperature of 50 C? What is the sensitivity of the
sensor with bridge circuit (volts/C) at a temperature of 50 C? What is the sensitivity of the bridge circuit
alone (volts/Ohm) at a temperature of 50 C? Using equation 7.18, compute the predicted value of bridge
sensitivity (volts/Ohm) and compare this to the measured value. Are they the same? Why or why not?
Vo
R2 R3
RthermR1
Vi
Figure 3: Set up for Activity #2
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Experiment 4: Signal ConditioningObjectives:In this experiment you will:
Obtain a basic understanding of the different ways to filter a sensor signal (a stage 2 operation)
Understand the difference between active and passive circuits (stage 2 devices)
Measure the frequency, attenuation and phase of dynamic signals
Required Hardware:
Breadboard
A selection of resistors, inductors and capacitors
A selection of operational amplifiers (Integrated circuits)
A DC power supply
An O-scope
A Handheld DMM
A function generator
Miscellaneous connectors, clips and plugs
Activity #1: High Pass and Low Pass Filters with Passive Circuit Elements
Background: Many sensors measure oscillatory quantities. Vibration is the classic mechanical example. A problem
occurs though when mechanical or electrical noise is also contained in the measured quantity. This noise is typically
at a very high frequency, which is introduced electrically, or at a very low frequency where sensor inaccuracies
occur. In either case one would like to filter out the noise frequencies and keep the frequencies that contain the
desired signal. This is accomplished by either low pass, high pass or band pass filtering. These filters can be
constructed using passive circuit elements (resistors, inductors, capacitors) which require no external source ofpower. This is the subject of this activity.
Procedures:
1. Using the breadboard, a resistor and a capacitor, connect the passive low pass filter circuit shown in Fig.
1a.
2. Place the function generator across the input. Using a BNC "T" connector, bring the function generatorsignal into channel 1 of the O-scope. See Fig 1a.
3. Finally, set up channel 2 of the O-scope to measure the output voltage across the capacitor.
4. Set the function generator to 1 volt peak and 10 Hz frequency. Observe the waveforms for channel 1 and
channel 2 of the O-scope. Save these waveforms to disk for plotting later.5. Using the attached frequency response plots and equations, compute the cut-off frequency for the filter. Set
the function generator to this cutoff frequency. Re-scale the O-scope to get nice waveforms for both
channels 1 and 2. Save these waveforms to disk for plotting later.
6. Finally, set the function generator to 10 times the cut-off frequency. Again, re-scale the O-scope to get
nice waveforms for both channels 1 and 2. Save these waveforms to disk for plotting later.
7. Turn off the function generator and O-scope. Now, rewire the circuit as shown in Fig. 1b. This small
change converts the circuit to a high pass filter.
8. Repeat steps 4-6.
Calculations:
1. Plot and label the O-scope data taken in steps 1-8 above.
2. For the low pass filter, use the plots and associated equations to estimate the voltage attenuation (ratio ofVout/Vin) and phase lag at all 3 frequencies (10 Hz, fc and 10fc). These are measured values.
3. Using the frequency response plots for the low pass filter (given to you in this handout), estimate the
voltage attenuation (ratio of Vout/Vin) and phase lag at all 3 frequencies (10 Hz, fc and 10fc). These are
theoretical values. Make a table that compares the measured and the theoretical values. Are they the
same? Why or why not?
4. Repeat steps 2 and 3 for the High pass filter.
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Figure 1: Set up for Activity #1
Activity 2: High Pass and Low Pass Filters with Active Circuit Elements
Background: An alternative way to construct filters is using active circuit elements (operational amplifiers). These
devices must use an external power supply and also make use of passive circuit elements. This is the subject of this
activity.
Procedures:
1. Using the breadboard, 2 resistors, capacitor, operational amplifier and DC power supply, connect the passive
low pass filter circuit shown in Fig. 2a.
2. Place the function generator across the input. Using a BNC "T" connector, bring the function generator
signal into channel 1 of the O-scope. See Fig 2a.3. Finally, set up channel 2 of the O-scope to measure the output voltage across the output from the Op-amp.
4. Set the function generator to 1 volt peak and 10 Hz frequency. Observe the waveforms for channel 1 and
channel 2 of the O-scope. Save these waveforms to disk for plotting later.
5. Using the attached frequency response plots and equations, compute the cut-off frequency for the filter. Set
the function generator to this cutoff frequency. Re-scale the O-scope to get nice waveforms for both
channels 1 and 2. Save these waveforms to disk for plotting later.
6. Finally, set the function generator to 10 times the cut-off frequency. Again, re-scale the O-scope to get nice
waveforms for both channels 1 and 2. Save these waveforms to disk for plotting later.
7. Turn off the function generator, DC power supply and O-scope. Now, rewire the circuit as shown in Fig.
2b. This small change converts the circuit to a high pass filter.
8. Repeat steps 4-6.
Calculations:
1. Plot and label the O-scope data taken in steps 1-8 above.
2. For the low pass filter, use the plots and associated equations to estimate the voltage attenuation (ratio ofVout/Vin) and phase lag at all 3 frequencies (10 Hz, fc and 10fc). These are measured values.
3. Using the frequency response plots for the low pass filter (given to you in this handout), estimate the voltage
attenuation (ratio of Vout/Vin) and phase lag at all 3 frequencies (10 Hz, fc and 10fc). These are theoretical
values. Make a table that compares the measured and the theoretical values. Are they the same? Why or
why not?
4. Repeat steps 2 and 3 for the High pass filter.
Figure 2: Set up for Activity #2
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Experiment 5: Digital Data AcquisitionObjectives:In this experiment you will:
Obtain a basic understanding of D/A and A/D conversions
Use the Zonic data acquisition system and computer to acquire signals
Use the computer based software to process and analyze those signals
Required Hardware:
Zonic DAQ system
Laptop computer with software
Function generator
Accelerometer
Spring/mass system
Miscellaneous connectors, clips and plugs
Required Documentation:
Zonic hardware and software manual (FAS Manual)
Accelerometer data-sheet
Read the Appendix given in this lab description to get a basic understanding of the DAQ system, both hardware and
software, being used in the lab.
Activity #1: A/D and D/A conversions
Background:This experiment will demonstrate simple use of the DAQ system including how to capture and analyze periodic
signals. It will also utilize the concept of Nyquist frequency discussed in class. Since most periodic signals that one
will measure in the field will have a given frequency and amplitude, an engineer must have a vague idea of the
magnitude of these values before measuring them to ensure that the proper range of the signals is being measured.
While amplitude is easily checked, frequency response must be well within the prescribed range of the DAQ
parameters (between resolution and Nyquist frequency) for accurate determination of the signals spectral content.
To explore this behavior, we will observe the response of the DAQ system by using fake input generated from a
function generator. By keeping the DAQ parameters fixed, we can examine the limitations of the DAQ by varying
the input.
Procedures:
1. The DAQ system should be ready to go. If not, ensure the following steps have been completed:
a. The PCMCIA card is connected to the Zonic DAQ box and is installed in the PC slot.
b. Both the Zonic Medallion unit and PC are plugged in.
c. Once the PC has been booted, start the FAS Medallion (Zonic) program found under the Windows
Start menu. Check with the TA if problems are encountered.
2. Hook up the output of the function generator to the input channel #1 of the DAQ box. This is shown in
Figure 1.
3.
Clicking anywhere in theAnalysis pane will bring up the Analysis parameters window. Set theexperiment to Free Run with the following Sampling settings as shown in Figure 2:
a. Number of Averages: 1
b. Frame Size: 4096
c. Bandwidth: 100 Hz1
1Note that frame size and bandwidth are other terms for number of data points and frequency range, respectively.
Do not confuse this with Nyquist frequency, however. (Youll calculate that later.)
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4. Set the amplitude of the output of the function generator to 1 VPP. Keep this amplitude throughout your
experiments.
5. Set the frequency of the function generator to 10 Hz (approximately, it need not be exact) with asine wave.
a. Click onAquire and wait. In one period, the system should acquire a signal from channel 1.
b. Examine the Time behavior of the signal. Are you capturing enough information to accurately
describe the signal?
c.
Examine the spectral content of the signal (Uspec
). Record the mode(s) of the signal calculatedby the program.
d. Export the time and spectrum information to a text file on a floppy disk as described on page 35
of the FAS Manual. Use a new file for each run. (Do not use the Save function.)
6. Now increase the frequency to 200 Hz and repeat the procedure in step #5. Do not change the settings from
step #3. Note if you are able to properly identify the signal.
7. Decrease the frequency to ~0.1 Hz and repeat the procedure in step #5 keeping the software settings the
same. Again note if you are able to properly identify the signal.
8. Finally, return the frequency to 10 Hz and repeat the procedure in step #5 for a square ware and then asaw-
tooth wave. Make special note of the frequency content of the signal.
Figure 1: Set up for Activity #1
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Figure 2: DAQ software settings.
Calculations:
1. For the Sampling parameters, calculate the frequency range of the DAQ system. That is, the lowest
frequency accurately measured (resolution) and the highest frequency accurately measured (Nyquist
frequency). Use the sampling (i.e., frame) period if needed. How does the latter compare with the
bandwidth?
2. From the software, list the measured versus the predicted values of the modes for the 5 measurementsabove: sine wave at 0.1, 10, and 200 Hz, square and saw-tooth waves at 10 Hz.
3. Analyze the 5 exported time signals in MATLAB and compare the frequency information with that
predicted by FAS.
Activity 2: Dynamic Signal Analysis (Waveform Capture and FFT)
Background:
The previous experiment explored the capabilities of the system and the limitations of the software settings when
examining particular input data. In this experiment we will acquire data from a sensor connected to a periodic signal.
An accelerometer will be used to measure the vertical acceleration of a Spring-Mass system caused by an initial
displacement. This periodic data will then be used to calculate the frequency of the system and the spring constant ofthe spring. In this case, the accelerometer is a variable capacitance sensor which operates by using the imposed
acceleration to alter the distance between the two conductors of the capacitor.
Procedures:
1. Set up the Spring-Mass system as shown in Figure 3. The spring should be suspended from the hook on the
ring stand with the mass holder hanging from one end.
2. Attach the accelerometer (using Velcro) to the mass holder. The arrow on the accelerometer should be
pointing either directly up or down, not horizontally.3. Like most sensors, the accelerometer requires an excitation voltage. This is simply the power the sensor
requires to operate. Connect the accelerometer to the power supply and then to the input channel of the
DAQ system using the following wire color scheme:
a. Green: +5V supplyb. Yellow: common (common to both power supply and sensor output return circuits)
c. Orange: output signal
4. Test the system by displacing the spring and acquiring data as discussed above. You should record a
periodic signal.
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5. Record the data for the experiment matrix listed below. In each case, export the data for later analysis.
Initial Displacement: 5.0 cm Initial Displacement: 10.0 cm
Mass: 51 g
Mass: 102 g
You do not need to Export the data for this Activity. The setup for the system is shown in Figure 4. Disconnect all
wiring and turn off the power supply when finished.
Calculations:
1. Return to Hooks law. Recall that the sinusoidal motion of the system is described by the equation
y(t) = yO cos(k
Mt) whereyo is the initial displacement of the spring, kis the spring constant, andMis
the mass of the system (assuming the mass of the spring is negligible). From this equation, determine what
the equations for the velocity and the acceleration of the system. For the matrix listed above, plot a curve ofthe acceleration of the system and predict the spring constant by matching the curve to that of your
experimental data. Did you need to calibrate the sensor for this calculation?
2. From theory, the frequency of the oscillation is predicted to be f =1
2p
kM
where kandMare defined
above. Determine the mode for each of the runs in your matrix of experiments and determine kbased upon
these measurements. Do you encounter multiple frequencies in your measurements? If so, why?
Notes: Do not forget to include the mass of the hook and the accelerometer in your calculations. Make sure you
include your error in both of your values ofkcalculated above.
Figure 3: Spring-Mass arrangement for Activity #2.
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Figure 4: Set up for Activity #2.
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Experiment 6: Strain GagesObjectives:In this experiment you will:
Use strain gages to examine the behavior of strain (and relation to stress)
Wire your own strain gage bridge circuit
Use a commercial strain gage indicator
Use the Zonic data acquisition system and computer to acquire signals
Required Hardware:
Zonic DAQ system
Laptop computer with software
DMM
Power supply
Various cantilever beams instrumented with strain gages
Various weights
Breadboard
Miscellaneous connectors, resistors, clips and plugs
Measurements Group Strain Gage Indicator (P-3500) & Switch/Balance Unit (SB-10)
Required Documentation:
Zonic hardware and software manual (FAS Manual)
Strain Gage Indicator manual (or supplement)
Read the Appendix given in the previous lab description (lab #5) to get a basic understanding of the DAQ system,
both hardware and software, being used in the lab.
Activity #1: Single Strain Gage on a Cantilever Beam
Background:
In this experiment you will use a strain gage to examine bending on a cantilever beam. The strain gage you will be
using is a quarter bridge strain gage, meaning it is intended to be 1 of 4 resistors in a circuit. You will first need to
provide the bridge circuit consisting of the other 3 resistors; you then need to provide an input voltage and measurethe output voltage when the resistance changes due to varying resistance in the strain gage part of the circuit.
For this activity, you will need to test 3 different beams, each instrumented with a single strain gage. The beams are
of different materials (weld steel, spring steel, and aluminum) and sizes. You will need to examine each one in turn.
Procedures:
1. The DAQ system should be ready to go. If not, ensure the following steps have been completed:
a. The PCMCIA card is connected to the Zonic DAQ box and is installed in the PC slot.
b. Both the Zonic Medallion unit and PC are plugged in.
c. Once the PC has been booted, start the FAS Medallion (Zonic) program found under the Windows
Start menu. Check with the TA if problems are encountered.
2. Clicking anywhere in theAnalysis pane will bring up the Analysis parameters window. Set the
experiment to Free Run with the following Sampling settings as shown in Figure 2:a. Number of Averages: 1
b. Frame Size: 4096
c. Bandwidth: 100 Hz
3. Choose 1 of the 3 beams instrumented with a single strain gage (it doesnt matter which one). Each of these
gages has two separate strain gages on it; one for longitudinal strain and one for lateral strain. You only
need to examine the former in the current activity.
4. Using the DMM, measure the resistance across the strain gage.
5. Using the breadboard, choose 3 appropriate resistors (What value of resistor should you use? Should theyall be identical?) and wire up a an appropriate bridge circuit. See Figure 12.10 of the text.
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6. Using the power supply, connect a 5V input across the bridge circuit.
7. Connect the output of the bridge circuit to the DMM in DC voltage measurement mode. Flexing the beam
should give you a variation in the output. If it does not, your circuit is not working properly.
8. Mount the beam using a c-clamp to the table. Make sure the strain gage is facing up.
9. Measure the voltage using the DMM.
10. Attach a single weight to the end of the beam and measure the voltage using the DMM.
11. Increase the weight and repeat.
12. Turn the beam over (making sure the clamp is in the same location on the beam) and repeat steps 9 through
11.
13. The above information provides enough data to calibrate the gage.
14. Hook the output of the strain gage up to the Zonic input channel 1.
15. With no weight on the end, excite the end of the beam and acquire the output response of the bridge.
Record the signal (amplitude versus time) and the frequency response (amplitude versus frequency).
16. Repeat with a single mass attached to the beam. Increase the mass and repeat.
17. Repeat the above steps (4 through 16) with the other 2 beams. (You do not need to rewire your bridge
circuit.)
Calculations:1. For each of the instrumented beams, determine and plot the calibration curve. Determine the output in
mstrain. (See Section 12.11 of the text.)
2. Determine the bridge constant for your circuit (see Table 12.4 of the text).3. For each of the beams, calculate the spring constant of the beam. (You have multiple measurements for
each beam; the output frequency is a function of the mass and spring constant, but the latter should be thesame. Thus, present your results with an appropriate error estimate.)
Activity 2: Multiple Strain Gages on a Cantilever Beam
Background:
One of the primary benefits of digital DAQ is the ability acquire multiple measurements simultaneously. In this
exercise, you will examine the output of two separate strain gages on a single beam simultaneously.
Procedures:
1. Using the procedure outlined in Activity #1, wire up two identical bridge circuits.2. Using the cantilever beam instrumented with 2 gages, test your circuits using the DMM and make sure they
are working properly.
3. Connect the output of the 2 beams to the two input channels of the Zonic DAQ. Make sure the dual inputs
are working correctly.
4. Mount the beam to the table using a c-clamp.
5. Placing mass on the end of the beam, excite the beam and record the output; export the output to a disk.
Calculations:
1. From theory, the frequency of the oscillation is predicted to be f =1
2p
kM
where kandMare defined
in the Appendix. Determine the mode for each of the two inputs in your matrix of experiments and
determine kbased upon these measurements. Are the frequencies identical? If not, why?
2. From the simultaneous measurements, find the correlation between the inputs using MATLAB.
Activity 3: Using a Strain Gage Conditioner
Background:
You will typically not need to create your own bridge circuit; most often you will use a bridge circuit in the form of
a strain gage conditioner. The benefit of this type of system is that it works with multiple types of strain gages and
does not need to be rewired each time a different gage is used. (See Figure 12.11 in the text for an example.) In this
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lab, you will use a Measurement Systems strain conditioning unit consisting of a SB-10 Switch and Balance Unit
and P-3500 Strain Indicator. (See the lab supplement describing this experiment.)
Procedures:
1. Select a quarter bridge strain gage on the beam (there are both quarter bridge and half bridge gages on the
beam). Record which strain you used.
2. Each of the quarter bridge gages has 3 wires connected to it. This will need to be connected to the strain
gage conditioner in the correct order.
3. Measure the resistance across the 3 wires. The resistance should either be high or low. This will tell you
where the resistor is located in the circuit.
4. Using the diagram on the cover of the SB-10 for the quarter bridge circuit, connect the 3 wires to the
appropriate terminals.
5. Turn the P-3500 on and ensure that all proper connections and settings are made. The display should return
a value of strain for no load conditions. The units are in mstrain.
6. Select a moment arm location of 6 in for the weights and record the strain for a load of 10, 20, 30 and 40
lbs.
7. Repeat for moment arm locations of 12 and 18 in.
Calculations:
1. Plot the mstrain reading for your experiments on a single plot versus load. You should have a single curve
for each of the moment arm locations. Are the curves significantly different? What does this tell you about
the location of the strain gage on the shaft?
2. From this plot, determine where the strain gage was placed.
3. Calculate the appropriate stress that was placed on the beam and plot versus load. (Use the supplement and
Chapter 12 of the text.)
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Experiment 7: Prony BrakeObjectives:
In this experiment you will:
Learn how to operate a Prony brake.
Measure the shaft torque of a motor.
Measure the rotation rate of a motor using a stroboscope.
Determine the effective (brake) horsepower of a motor.
Required Hardware:
Prony brake
Stroboscope
Required Documentation: This handout
Motor specs (from motor plate)
Theory: The prony brake is a devise used for measurement of torque and horsepower in machines by measuring the
force applied and the RPM. Figure 1 provides a basic schematic of a Prony brake setup.
http://www.me.psu.edu
Figure 1
The basic operation of a Prony brake is as follows:The unit under test can be anything with a rotating shaft a motor or engine for example.
The tension on the brake is adjusted to control torque due to friction on the band.
As torque is applied, the prony brake mechanism tries to rotate (counterclockwise in the sketch above).
However, a cable keeps the mechanism stationary. A force scale or other suitable force sensor measures the
tension in this cable.
The force, F, is measured at a known moment arm called the torque arm, r, to calculate the torque; i.e. T =
Fr.
Shaft rotation rate is measured simultaneously.
Input power is monitored to determine overall motor efficiency.
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The test is conducted over a range of input power (RPMs) and loads to determine motor
Shaft power is then calculated as
The advantages of a prony brake dynamometer are that it is simple, small in size, and inexpensive. The
disadvantages are that limited power can be dissipated with a prony brake, the mechanical brake is sometimes not
very stable, and the unit cannotsupply power - it can only absorb power.
Procedure:
1. Open the inlet valve located before the filter and make sure that there is a continuous water supply belowthe load cell.
2. Turn the power supply switch ON and assure that all the devises are working.
3. Make a note of the rating of the motor. This will be available on a plate on top of the motor. Note that this
is the rating of the motor and not the max power output by the shaft since there are always some losses
involved.
4. The two input variables are the RPM, varied by turning the knob on the motor control unit, and the loadapplied on the load arm. The knob on the control unit to the motor can be rotated for varying the speed of
the motor. Start with the knob at the zero position.
5. On the control unit of the motor, turn the Wbutton ON , which gives you the power INPUT to the motor at
that particular speed.
6. By turning the lever on the load arm clockwise, we can increase the load and vice-versa. BE CAREFUL
NOT TO STOP THE MOTORby over tightening it. This could result in motor failure. ProceedSLOWLY and carefully observe your power input to the motor. The point of identification of the stoppage
of load is left at the discretion and skill of the engineer. You can notice that the motor speed considerably
drops, some noise is heard, and that the power input reading increases. This should be enough indication to
stop the load application.
7. Turn the Stroboscope ON and note the RPM of the shaft. Note the load reading in pounds on the meter
below the control unit.
8. Repeat these steps for various speeds and note the shaft RPM, applied load, and the input power to the
motor.
9. Turn the motor control knob to zero, turn off the water supply, and finally the power switch key.
WARNING! Make sure you observe the following precautions.1. The motor is spinning at a high rate with a large torque. Make sure you keep the protective cover over the
shaft at all times and avoid getting too close to the motor shaft.
2. Remove any loose clothing before running the experiment (but dont run the experiment naked, either).
3. Make sure there is continuous water supply throughout the operation of the experiment. If you observe any
leaks in the system, shut down the experiment immediately.
4. Never allow the motor to stop rotating by increasing the load or cable tension as this will result in
overheating the motor and could permanently damage it.
Calculations:
Perform the following calculations.1. Calculate the breaking torque of the shaft of the motor by using suitable formula. Plot this over the range of
motor RPM.2. For a single input power setting, calculate the output power for different load settings (varied RPM and
applied load). Is the output power constant for a single value of input power? Why or why not?
3. Calculate the overall motor efficiency and plot as a function of RPM and input power (same or separate
graphs). Determine if there is a peak (maximum) efficiency and where this occurs.
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Experiment 8: Velocity and Flow RateObjectives:In this experiment you will:
Measure pressure, velocity, and flow rate of a fluid
Calibrate a flowmeter
Examine the difference between various types of fluid measurements
Required Hardware:
Various flow loops
Various meters, including rotameters, orifice meters, manometers, bourdon tubes, etc.
Stop watch, ruler, etc.
Required Documentation:
This manual
Appendices
A Fluids Mechanics text (you did keep your fluids text, didnt you?)
These activities do not need to be completed in the order listed.
Activity #1: Velocity and Flow Rate Measurement Using a Pitot-Static Tube and Inclined Manometer
Background:
In this experiment you will use a Pitot-static tube to measure the velocity profile in a circular duct and use this
information to determine the flow rate, head loss, and whether the flow is laminar or turbulent.
Procedure:
1. Examine the fan and Pitot-static tube/manometer system. Make sure the tube is placed in the end of the
duct before the exit. The Pitot-static tube should line up on the centerline.
2. Measure the inside diameter and length of the duct.
3. Zero out the manometer if necessary. It should read a pressure difference of 0 inches at the meniscus.
4. Turn on the fan and make sure the Pitot-static tube/manometer system is responding properly.
5. Turn off the fan and place the tube in the center of the duct. Use the knob on the linear traverse to move thetube up and down.
6. Using the stop watch, turn on the fan and record/estimate how long it takes the fluid in the manometer to
reach steady state. (Note: there is a time lag in the fan response and how long it takes the fluid to reach
steady velocity, but this should be much smaller than the manometer response time.) You will use this laterto estimate the time constant of the manometer.
7. Using the linear traverse, move the Pitot-static completely to the bottom of the duct just barely touching the
walls.
8. Beginning at this point, record the pressure difference, and if available, the velocity, from the manometer in
5 mm steps.
9. When finished, turn off the blower and return the manometer to its initial position.
Calculations:
1.
Using the time data in step 6 of the procedures, estimate the response time and time constant of themanometer. How confident are you of this value?
2. From step 8, plot the pressure difference and the velocity profiles in step 7 versus the duct radius. (If a
velocity scale was not available on the manometer, calculate the velocity directly from the pressure usingBernoullis equation.) Convert the pressure data to Pascals and velocity to m/s before graphing and use
these units in all further calculations.
3. From the velocity data determined in step 2, evaluate the statistics of the data. Find the mean, median, and
standard deviation of the velocity. At what radial location are the mean and median velocities located?
4. Based upon the mean velocity, calculate the Reynolds number. Is this flow laminar or turbulent?
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5. Plot the ideal (theoretical) velocity profiles for laminar and turbulent pipe flow (Hagen-Poiseuille flow)
along with the observed data. How well does the data compare? (The equations for laminar and turbulent
pipe flow velocity profiles are in any undergraduate fluid mechanics text.)
6. Determine the flow rate Q by integrating the measured velocity profile over the duct area, dA.
7. Calculate the head loss of the duct in meters.
8. What is the spatial resolution of the Pitot-static tube? Is this larger or smaller than your step size?
Activity #2: Calibration of a Flow Rate Meter in Air
Background:
In this experiment you will calibrate a variable area flow meter in air with an unknown scale using the pressure drop
in a pipe.
Procedure:
1. Examine the system. There are at least 3 valves that can be used to control the amount of air in the
experiment; the valve on the air supply, the inlet shut-off valve, and the metering valve. Use one or a
combination of these valves to control the flow rate.
2. Measure the length of the pipe L between the two pressure gages and record this and the diameter of thepipe D=2R (it is labeled on the pipe in meters).
3. With no flow of air, note where the float is located in the flow meter and what reading it is giving. This
zero value is your first calibration point.4. Turn on the air supply, a little at first.
5. Record the pressure reading on the two gages, upstream and downstream.
6. Record the reading on the flow meter.
7. Repeat steps 5 and 6 for at least 5 readings total (not including the zero reading).
Calculations:
1. Determine the pressure drop, Dp=p1-p2, for each of your measurements.
2. Plot flow rate Q versus pressure drop for your measurements and determine the power of the exponent in
the relation: Dp=Qn.
3. If n1, then the flow is laminar. If n1.75, then the flow is turbulent. In the former case, the pressure drop
flow rate relation is given by Dp = 8mLQ (pR4) which can be determined exactly from the Navier-
Stokes equations. In turbulent flow, the relation between pressure drop and flow rate is given by
Dp 0.241Lr0.75
m0.25Q
1.75D
-4.75which is determined using Blasius boundary layer theory. Determine
which equation is more appropriate for your data (or both if your curve has more than one trend) and recast
this equation in terms of Q as a function ofDp. Using your experimental parameters, calculate Q in cubic
meters per second for each datum.
4. Plot your flow meter observed Q versus your Q determine the from the pressure drop.
5. These equations were determine assuming the flow is incompressible. Is this true for the flow you
examined? Why?
6. What units is scale on the flow meter given in?
Activity #3: Calibration of Flow Meters in Water
Background:In this experiment, you will measure the flow rate in an open water loop using 4 different meters; a turbine flow
meter, orifice meter, and nozzle (venturi) meter as well as a variable area flow-meter (float-type rotameter). The
turbine flow meter is read using a frequency counter (to measure the rotation rate of the turbine) while the two
obstruction meters are read using U-tube manometers. The flow rate is measured using a mass scale and stopwatch.
Procedure:
1. Close the control valve located on the bottom of the safety valve.
2. Zero out the mass scale (use units of kg).
3. Turn on the frequency counter as follows:
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a. Turn counter on with SAMPLE RATE control.
b. Set FAST/NORM/HOLD switch to NORM.
c. Set TIME BASE/MULTIPLIER to 1 second.
d. Press FREQ A button.
e. Set COM/SEP switch to SEP.
f. Set CHANNEL A ATTEN to X100 or X1.
g. Set AC/DC switch to AC.
h. Set CHANNEL A LEVEL to PRESET.
i. As flow rate is varied, decrease attenuation with CHANNEL A ATTEN until a stable count is
displayed.
4. Turn all the valves fully open and ensure continuous flow of water in the loop.
5. Open the safety knob slowly at the bottom end of the rotameter such that fluid from the manometers
doesnt flow out. Set your desired flow rate.
6. Close the valve of the reservoir (holding tank) and allow water to collect. Begin timing.
7. Note the readings of the two manometers, rotameter, and turbine flow meter, and also the time it takes for
the tank to collect up to the given mark.
8. Repeat for at least 3 different flow rates.
Calculations:
1. From the mass flow rate measurements (kg/s), determine the volumetric flow rates (m3/s).
2. Determine the calibration curve for each of the 4 flow meters. List on a separate graph. Using the flow ratedetermined from the mass scale as your x-axis in each case.
3. Calculate the discharge coefficients of the two obstruction meters using the specifications provided in the
handout.
4. What units is the flow rate on the rotameter given in?
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Appendix A: Bread BoardsA bread board is a device used for testing and prototyping circuit designs. It can be used to quickly connect varioustypes of circuit elements without permanent connections (i.e., soldered). A typical bread board is shown below.
The bread board has many strips of metal (copper usually) which run underneath the board. The metal strips are laid
out as shown below. The long top and bottom row of holes are usually used for power supply connections.
These strips connect the holes on the top of the board. This makes it easy to connect components together to build
circuits. To use the bread board, the legs of components are placed in the holes (the sockets). The holes are made
so that they will hold the component in place. Each hole is connected to one of the metal strips running underneath
the board.
Each wire forms a node. A node is a point in a circuit where two components are connected. Connections between
different components are formed by putting their legs in a common node. On the bread board, a node is the row of
holes that are connected by the strip of metal
underneath.
Placing components and connecting them together
with jumper wires build the rest of the circuit. Then
when wires and components from the positive supply
node to the negative supply node form a path, we can
turn on the power and current flows through the path
and the circuit becomes hot.
For chips with many legs (ICs), place them in themiddle of the board so that half of the legs are on one
side of the middle line and half are on the other side.
A completed circuit might look like the one shown at
right. This circuit uses two small breadboards.
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Appendix B: ResistorsResistors are coded with a series of colored stripes used to represent the value of the resistor, tolerance, and and
sometimes the reliability or temperature coefficient. The above chart is probably the largest you will see, because I
tried to include every possible resistor type there is. If you look at a few different books and websites and compare
their charts, chances are that they will be different, and may even contradict one another in areas. The chart I have
provided is somewhat more confusing than most, but once you understand it you will see that it contains every
possible meaning to a code on a resistor, whereas another chart may give the wrong reading to some resistors.
The first two bands on a resistor are always the first two digits of the resistance. The third band contains the thirddigit, but may not be included in some resistors. After the first two or three digits comes the multiplier. This number
represents the power of 10 that is then multiplied with the first digits to give the resistance. Note that a gray or white
band used as the multiplier has two possible meanings. The bands usually represent 10^8 and 10^9, but in someoddballs they may actually mean 10^-2 and 10^-1. More often you will see a silver or gold stripe used to represent
10^-2 and 10^-1. The next band, and most often the last, is the tolerance band. This band indicates what the actualvalue of the resistor may be. The actual resistance of the resistor must be within this percentage of the rated value, or
else it is considered no good.
The reliability and temperature coefficient bands are not included on many resistors, and they will never both be on
the same resistor. A reliability band indicates the failure rate per 100 hours. The temperature coefficient bandspecifies the maximum change in resistance with change in temperature, measured in parts per million per degree
Centigrade (ppm/C). You will see reliability bands more often on older resistors, and temperature coefficient bands
on newer ones.
If a resistor has four bands total (or three bands if the tolerance is 20%), it will contain two digits, a multiplier, and
a tolerance band. If a resistor has five bands and is a newer one, it most likely has three digits, a multiplier, and atolerance band. If an older resistor contains five bands, it is probably one containing two digits, a multiplier,
tolerance, and reliability band. You will probably only ever see newer resistors with six bands, and they will include
three digits, multiplier, tolerance, and temperature coefficient bands.
Lets say you have a resistor with a yellow, violet, red, and gold band. The first band represents the first digit, and a
yellow band means 4, so the first digit in the value of the resistor is 4. The next band is violet, meaning 7 is our next
digit. The next band is our multiplier, and will tell us to what power of 10 we must multiply the first two digits by. A
red band in the multiplier means 10^2, so to get the value of the resistor we must multiply 47 by 10^2. This gives us
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4,700 ohms, or 4.7 kiloohms. The last band is the tolerance, a gold band meaning the actual value must be 5% of
the value on the resistor. So the actual value of the resistor may be anywhere from 4,465 ohms to 4,935 ohms. If we
were to then measure the resistance of the resistor with a DMM and found that it was 4,935 ohms
it would be defective.
Sometimes figuring out what end is what can be difficult. Some resistors will have the bands close to one end,
indicating the starting point. On others, the last band will be larger than any of the others. But in many resistors it iscommon for all stripes to be evenly distributed and equal in width. If you have a gold or silver stripe, the end that
stripe is furthest from is your starting point, because we know gold and silver cannot be used for any of the digit
values. But sometimes you might have a resistor such as brown, green, black, red, brown. It could be either be read
as a 15k ohm 1% or 12M ohm 1% resistor. If you are stuck in a situation where you cannot figure out what end is
what, the next best thing is to just get a DMM and measure it.
Resistors are manufactured in standard values, known as the E series. The most common series is the E12, where
there are 12 resistors in a decade (1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, and 8.2). Other series include the
E6, E24, E48, and E96 series. The values in the series are spaced similar to how notes in an instrument are. To getthe approximate value of a resistor in one of the series, the equation v=10^((n-1)/E) can be used, where v is the
value of the resistor, n is the number of the resistor, and E is the series. For example, say you want the approximate
value of the 3rd resistor in the E12 series. The value will be v=10^((3-1)/12)=1.467799268, or 1.5 when you round
up the value.
Several examples follow.
Example 1:
You are given a resistor whose stripes are colored from left to right as brown, black, orange, gold. Find the
resistance value.
Step One: The gold stripe is on the right so go to Step Two.
Step Two: The first stripe is brown which has a value of 1. The second stripe is black which has a value of
0. Therefore the first two digits of the resistance value are 10.
Step Three: The third stripe is orange which means x 1,000.
Step Four: The value of the resistance is found as 10 x 1000 = 10,000 ohms (10 kilohms = 10 kohms).
The gold stripe means the actual value of the resistor mar vary by 5% meaning the actual value will be
somewhere between 9,500 ohms and 10,500 ohms. (Since 5% of 10,000 = 0.05 x 10,000 = 500) .
Example 2:
You are given a resistor whose stripes are colored from left to right as orange, orange, brown, silver. Find
the resistance value.
Step One: The silver stripe is on the right so go to Step Two.
Step Two: The first stripe is orange which has a value of 3. The second stripe is orange which has a value
of 3. Therefore the first two digits of the resistance value are 33.
Step Three: The third stripe is brown which means x 10.
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Step Four: The value of the resistance is found as 33 x 10 = 330 ohms.
The silver stripe means the actual value of the resistor mar vary by 10% meaning the actual value will be
between 297 ohms and 363 ohms. (Since 10% of 330 = 0.10 x 330 = 33) .
Example 3:
You are given a resistor whose stripes are colored from left to right as blue, gray, red, gold. Find the
resistance value.
Step One: The gold stripe is on the right so go to Step Two.
Step Two: The first stripe is blue which has a value of 6. The second stripe is gray which has a value of 8.
Therefore the first two digits of the resistance value are 68.
Step Three: The third stripe is red which means x 100.
Step Four: The value of the resistance is found as 68 x 100 = 6800 ohms (6.8 kilohms = 6.8 kohms).
The gold stripe means the actual value of the resistor mar vary by 5% meaning the actual value will be
somewhere between 6,460 ohms and 7,140 ohms. (Since 5% of 6,800 = 0.05 x 6,800 = 340).
Example 4:
You are given a resistor whose stripes are colored from left to right as green, brown, black, gold. Find the
resistance value.
Step One: The gold stripe is on the right so go to Step Two.
Step Two: The first stripe is green which has a value of 5. The second stripe is brown which has a value of
1. Therefore the first two digits of the resistance value are 51.
Step Three: The third stripe is black which means x 1.
Step Four: The value of the resistance is found as 51 x 1 = 51 ohms.
The gold stripe means the actual value of the resistor mar vary by 5% meaning the actual value will be
somewhere between 48.45 ohms and 53.55 ohms. (Since 5% of 51 = 0.05 x 51 = 2.55).
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Appendix C: Zonic DAQ SystemThe Zonic Medallion and FAS (Fundamental Acquisition Software) system is a data acquisition system (DAQ) thatis specifically designed to measure and analyze periodic signals. The unit used in the ME 310 lab is capable of
measuring two analog input channels simultaneously and provides 1 output channel (not needed here).
The system is relatively sophisticated but finicky during use. It will take a little time to get used to the format and
operation of the software, but once it is setup, it is fairly straightforward to use.
A sample screen is shown below. Here the data is a sine wave presented in the time domain.
To record data, click on the Acquire button. The status bar in the upper right corner of the window will indicate if
a signal has triggered the system and is being recorded. To change the analyzer setup or channel setup, click in the
respective window and a new window will appear. To change the limits of the plot, click on the value of the limit
you wish to change and type in the desired value. You can change the type of plot using the menus in the lower left
corner.
Once the data has been recorded, FAS automatically calculates the frequency spectrum of the signal. To examine the
frequency content or other information, click in the selection bar located immediately above the plot. We are
interested primarily in two plots, Time and Uspec, which are defined as follows:
TIME: Displays a time domain waveform of filtered, sampled data scaled in Volts.
USPEC: A display function of the magnitude of the instantaneous unaveraged spectrum.
Additional information is available in the FAS manual.
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The plots below represent samples of the time and spectral domain plots from typical experiment.
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Appendix D: Spring-Mass Systems
A simple mass-spring system (Figure 1) will be the basis of this laboratory investigation. The spring is a cantilever
beam, and the mass is fixed to the free end.
Figure 1: Simple Mass-Spring System.
To develop a mathematical model for this system we will redraw the mass-spring system as shown in Figure 2. Inthis case the cantilever spring is replaced by a helical coil spring.
Figure 2: Simplified Schematic Diagram.
If we remove the weight from the system and replaced the spring with a force vector we now have a free-body-
diagram (FBD). A free-body-diagram shows an isolated body with all of the applied and body forces note as
vectors. Figure 3 shows the FBD.
Figure 3: FBD of Mass-Spring System.
From the FBD and using Newtons Second Law, we can write the following equation,
M
M
M y
Mg
Fs
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sFMgMa -=
where Fs is the force exerted by the spring (N);Mgis a body force as a result of the gravitational field (N); and a is
the resulting acceleration of the body. Please note that downward forces are positive. Utilizing Hookes Law, we
can write an equation that describes the spring force. This equation is,
kyFs =
where k is the spring constant (N/mm). Realizing that shortly after we attach the mass to the spring, the spring
undergoes a deformation where the spring force is equivalent to the gravitational force. We can now rewrite the
previous equation as,
)( statics yykF +=
where ystatic is the displacement of the spring that balances the gravitational force associated with the mass. Since
this initial displacement of the spring balances the gravitational force, we can rewrite the equation derived using
Newtons Second Law and the FBD as,
)()(
2
2
tkydt
tydM -=
Please note that we have replaced a differential notation fory. We have also replaced y with y(t) to denote a time-
varying function. Moving all of the terms withy to the left side of the equation resulting equation is termed a
differential equation. To solve this equation we must turn to Calculus the language of engineers. An alternative
notation to that used above is shown next.
0)()(
2
2
=+ tkydy
tydM
The resulting equation is termed a second order differential equation. While it may be some time before you get to
Calculus IV, and learn how to solve these types of equations, we will propose a solution, and then see if it works!
Lets assume that one possible solution to the above equation is
)2sin()2cos()( ftBftAty pp +=
The solutiony(t) implies the that y is a function of time that is y varies with time. Unfortunately we do not know
the values ofA andB. To solve forA andB we must look at the initial conditions.
Prior to looking at the initial conditions we must first differentiate the solution. The first derivative is,
)2cos(2)2sin(2)(
ftfBftfAdt
tdypppp +-=
Please recall that,
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)sin()cos( axaaxdx
d-=
)cos()sin( axaaxdx
d=
Differentiating the previous function a second time we have the following,
)2sin(4)2cos(4 22222
2
ftBfftAfdt
ydpppp --=
Another handy trick is to make a substitution for frequency. While it may not be obvious at first, the following
substitution simplifies our efforts.
M
kf
p2
1=
With this substitution, the second derivative ofy(t) becomes
)sin()cos()(
2
2
tM
kB
M
kt
M
kA
M
k
dt
tyd--=
It should be clear at this point that our assumed solution is valid. However, we must evaluate the constantsA andB.
To do this we will look at the initial conditions. At t=0 new know that the position isyi (the position of our initial
displacement) and therefore A must be equal toyi. If we look at the first derivative ofy(t) the velocity at t=0 we
find thatB=0. Our final solution becomes,
= t
M
kyty i cos)(
At last a valid solution! Also we must remember that the frequency of the excited system will follow the
substitution that we made above,
M
kf
p2
1=
Now, the only thing left to do is prove this analysis is appropriate by collecting some system response data.