Mech lab manual for engg

7/29/2019 Mech lab manual for engg

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ME 310 Lab Manual

Mechanical EngineeringInstrumentation

v 1.0, Jan. 27, 2003


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ME 310 Lab Manual, Spring 2003 University of Kentucky

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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


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



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



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



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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 operational amplifiers (Integrated circuits)

A DC power supply

An O-scope

A Handheld DMM

A function generator


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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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.



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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



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.



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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)


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.


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 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).


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 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.


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.

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Mech lab manual for engg