Measurements & Instrumentations
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Transcript of Measurements & Instrumentations
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Measurements & Instrumentations
Module 1
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Grading policy
• Participation 10 marks– Preparation, Promptness, Level of Engagement,
Behavior• HWs 10 marks• Quizzes 10 marks• Practical 30 marks– Lab activities and Practical exam
• IAT competency exams (practical and knowledge ) 40 marks
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Preparation marks
• Print the modules and cover it and bring it to every class with you• Calculator • Stationary • Lab coat
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Participation Marks
• Promptness: On time or Late• Level of Engagement• Behavior
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Objectives
• What is measurements• Measurements elements • Measurement methods / types
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Introduction to measurements
• All physical parameters are measurable, and the first step in any engineering process is measurement.
• Measurement of abstract quantities like intelligence.
• If we cannot measure something, we can not control it. This ‘something’ is referred to as a ‘physical quantity’.
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Measurements forms
• Physical dimensions of an object• Count of an object• Temperature of an object• Fluid pressure / flow rate / volume • Electrical voltage / current / resistors• Machine position / speed
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What we are trying to measure ?
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What is measurements ?• Measurement is the process of determining the magnitude of a physical
quantity such as length or mass, relative to a standard unit of measurement, such as the meter.
• It could be also defined as a comparison between a standard and a physical quantity to produce a numeric value
Measurements Elements
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Measuring Devices
• The measuring devices could be sensors, transducers or instruments.
• A ruler (length)
• A thermometer (temperature)
• A light dependent resistor (LDR) measures (light intensity)
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Skill 1: Identify the measurement elements
Physical quantity:
Measuring device:
Numeric value::
Standard unit:
Physical quantity:
Measuring device:
Numeric value::
Standard unit:
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Methods of measurement
• The two basic methods of measurement are– Direct measurement
– Indirect measurement.
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Direct Measurement
• In direct measurement, the physical quantity is compared directly with a standard.
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Indirect Measurement• In an indirect type of measurement, the physical quantity measured is
converted to an analog form that can be processed and presented. • For example, the mercury in the mercury thermometer expands and
contracts based on the input temperature, which can be read on a calibrated glass tube.
A bimetallic thermometer
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Question
Physical quantity: diameter of the ball
Measuring device: Vanier caliper
Numeric value: -----------
Standard unit: cm
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Recap
• Define measurements• Measurements elements • Measurement types / methods
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Warm up
• Give an example of an error that occur when you are taking a measurement.
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Objectives
• Definition of the error• Types of the errors• Error analysis – mean & standard deviation• Calibration
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Definition of the error
• Error = Instrument reading – true value
• Error types – Systematic errors– Random errors
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Systematic Errors• The zero error of the instrument• The shortcomings of the sensor• Improper reading of the instrument due to the improper
position of the person’s head/eye (Parallax error)• The environmental effect
Parallax error demonstration
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Systematic Errors
• Systematic errors can be corrected by calibration.
• Systematic errors can be traced and reduced
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Random errors
• Measuring the same quantity using the same instrument and every time you get different reading
• Example of random error is – measuring the mass of gold on an electronic scale several
times, and obtaining readings that vary in a random fashion.
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Random errors
• The reasons for random errors are not known and therefore can not be avoided
• They can be estimated and reduced by statistical operations
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Picture Measurement type
Direct Measurements
Direct Measurements
Indirect Measurements
Skill 2: Identify the type of measurement
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Error analysis
• Error analysis are done for the random error
• Average / Mean
• Standard Deviation
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Error analysis• Measuring the same input variable a number of times,
keeping all other factors affecting the measurement the same, the measured value would differ in a random way.
• The readings normally follow a particular distribution and the random error may be reduced by taking the average or mean.
• The average/mean gives an estimate of the ‘true’ value
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Error analysis
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Example 1
• A mass of gold is measured 5 times find the mean
• Mean / Average =
Reading 1 Reading 2 Reading 3 Reading 4 Reading 5
10g 10.2g 10.3g 10.1g 10.4g
g2.105
4.101.103.102.1010
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Standard Deviation
• The standard deviation, denoted by the letter ‘σ’ tells us about how much the individual readings deviate or differ from the average/mean of the set of readings.
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Example 2Reading (Reading – average) (Readings – average)2
16 -1 119 2 418 1 116 -1 117 0 019 2 420 3 915 -2 417 0 013 -4 16
Sum 40
1.2110
401
nsumSTD
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Example 3
• A diameter of a wire is measured by a group of students with a micrometer, and the reading are shown below:
• Assuming that only random errors are present, calculate the following:
a) mean / Average
b) Standard deviation
mm566.2569.249.245.265.255.2
Reading (Reading – average) (Readings – average)2 2.55 -0.016 0.0002562.65 0.084 0.0070562.45 -0.116 0.0134562.49 -0.076 0.0057762.69 0.124 0.015376
Sum 0.04192
0.10237215
04192.01
nsumSTD
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Excersice
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Recap
• Error• Systematic Error • Random Error• Mean • Standard deviation
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Warm Up
• Define measurements• Measurements type • Error• Systematic Error • Random Error• Mean • Standard deviation
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Instrument Performance Evaluation
• Any measuring instrument/device has a set of specifications that inform the user of its function.
• These characteristics are described in the catalogue or datasheet provided by the manufacturer
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Accuracy• Accuracy of an instrument is how close a measured value is to
the true value.
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Precision
• The ability of an instrument to give the similar reading when the same physical quantity is measured more than once
– The closer together a group of measurements are, the more precise the instrument.
– A smaller standard deviation result indicates a more precise measurement.
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Small STD
Large STD
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Precision
Precision of the
instrument
Measuring the same thing using the same instrument and every
time a different reading is obtained
Precision of the measurement
Measuring the same thing using different instruments and every
time a different reading is obtained
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Precision Calculation
STD = σ
It will tell you which instrument is more precise
Value
max (Avg – Min), (Max – Avg)
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What is the difference between precision and accuracy ?
Accuracy
Maximum deviation form the conventional true value
=max (CTV– Min), (Max – CTV)
Precision
Maximum deviation form the average value
=max (Avg – Min), (Max – Avg)
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Student 1 5 mm
Student 2 5.2mm
Student 3 4.5 mm
Student 4 4.7 mm
Student 1 5 mm
Student 2 5.1mm
Student 3 4.9 mm
Student 4 5 mm
STD = σ = 0.310913 STD = σ = 0.08165
Precision of the instrument
Which one is more precise ?
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Trial 1 5 kΩ
Trail 2 5.5 kΩ
Trail 3 4.5 kΩ
Trail 4 4.3 kΩ
Trial 1 5 kΩ
Trail 2 5.1 kΩ
Trail 3 4.9 kΩ
Trail 4 4.8 kΩ
Trial 1 5 kΩ
Trail 2 4 kΩ
Trail 3 6 kΩ
Trail 4 5 kΩ
STD = 0.537742
STD = 0.129099
STD = 0.816497
Which instrument is more precise ?
Precision of the instrument
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Bias
• The difference between the true value (TV) and average value (AV).
• Ideally, the bias should be zero.
• 𝑩𝒊𝒂𝒔 = − 𝑻𝑽 𝑨𝑽
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Example
• A mass of silver is measured four times and the values are shown below. If it the true value is 6 kg, find the bias
Trail 1 6.3 kgTrail 2 6.5 kgTrail 3 6 kg Trail 4 6 kg
kgAVTVBais
kgAverageMean
2.02.66
2.64
665.63.6/
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Range
• The range of an instrument defines the minimum and maximum values that the instrument can measure.
Min value = -40oFMax value = 120 oFRange = 120oF – (-40oF) = 160oF
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Min Value 0 Unit cm
Max value 15 Unit cm
Range =15-0=15 Unit cm
Min Value -40 Unit oC
Max value 50 Unit oC
Range 50-(-40)=90 Unit oC
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Sensitivity
• The sensitivity of a measuring instrument is its ability to detect small changes in the measured quantity.
• Sensitivity = Change in output (y-axis)/Change in input (x-axis)
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Linearity
• Some measuring instruments/devices output a signal that is proportional to the input physical quantity.
• These instruments are called linear devices. • Other instruments that don’t have a
proportional relationship between the output signal and the input are non-linear devices.
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Lab Activity 1
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Resistor Color Code
R = 25 * 10 1 Ω ± 5% = 25 * 10 Ω ± 12.5 ΩRmin = 237.5 ΩRmax = 262.5 Ω
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Resistor color code
Colors: Red – Violet – green – GoldR = (27 x 105) ± 5% Ω
Colors: Brown – Black – yellow – Silver R = (10 x 104 )± 10% Ω
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Unit Conversion
M 106
k 103
m 10-3
µ 10-6
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Unit Conversion Examples
27.0 x 105 2.7 x 106 = 2.7 M10.0 x 104 100 x 103 = 100 k 10.0 x 10-4 10-3 = 1m 500.0 x 10-5 5000 x 10-6 =50µ
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How to use DMM ?
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How to use DMM ?
Always must be connected
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Part 1 color code Resistance
valueTrue Value
DMM range
Measured values
% Error Within tolerance?
Yellow – violet – brown - gold
470 Ω 2kΩ 466Yes
Brown – Black – Red Gold
1 k Ω 2kΩ 1.13 kΩNO
Orange- orange – red -
gold
3.3 k Ω 20kΩ 3.31kΩYes
Orange – white – orange
- gold
39 k Ω 200kΩ 38.5 kΩYes
Brown – green – green - gold
1.5 M Ω 2MΩ 1.51 MΩYes
%85.0100*470
466470
%13100*1
13.11
%3.0100*3.3
31.33.3
%2.1100*39
5.3839
%66.0100*5.1
51.15.1
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Part 2 Resistor Reading
DMM1 1.1 kΩ
DMM2 1.2 kΩ
DMM3 1.09 kΩ
DMM4 0.99 kΩ
DMM5 0.97 kΩ
Resistor True value: Brown – Black – Red - Gold
kMAX
kAveragemaen
134.0134.0,096.0)066.12.1(),97.0066.1MAX(
R_avg)-(R_m_max, R_m_min)-MAX(R_avgPrecision
066.15
95.099.009.12.11.1/
20% within accurate is device the20%,%Accuracy2.0200/1000 accuracy Relative
200 200 ,30 ofmax accuracy Absolute2000.2k1-1.2CTV– d_MAX)(R_Measure
300.03k 0.97– 1 d_MIN)(R_Measure - CTV
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Part 3Reading Reading
(diameter in mm)Reading – Mean (Reading – Mean )2
Student 1
Student 2
Student 3
Student 4
Student 5
Mean
Standard deviation
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Recap • Define measurements • Measurements form • Measurements types • Error • Systematic Error / Random Error• Mean • Standard deviation• Accuracy• Precision• Bias• Range