Measurements Instrumentations Module 1 Grading policy Participation 10

Measurements & Instrumentations Module 1

Grading policy • Participation 10 marks – Preparation, Promptness, Level of Engagement, Behavior • HWs • Quizzes • Practical 10 marks 30 marks – Lab activities and Practical exam • IAT competency exams (practical and knowledge ) 40 marks

Preparation marks • Print the modules and cover it and bring it to every class with you • Calculator • Stationary • Lab coat

Participation Marks • Promptness: On time or Late • Level of Engagement • Behavior

Objectives • What is measurements • Measurements elements • Measurement methods / types

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’.

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

What we are trying to measure ?

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

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)

Skill 1: Identify the measurement elements Physical quantity: Measuring device: Numeric value: : Standard unit:

Methods of measurement • The two basic methods of measurement are – Direct measurement – Indirect measurement.

Direct Measurement • In direct measurement, the physical quantity is compared directly with a standard.

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

Question Physical quantity: diameter of the ball Measuring device: Vanier caliper Numeric value: -----Standard unit: cm

Recap • Define measurements • Measurements elements • Measurement types / methods

Warm up • Give an example of an error that occur when you are taking a measurement.

Objectives • • Definition of the error Types of the errors Error analysis – mean & standard deviation Calibration

Definition of the error • Error = Instrument reading – true value • Error types – Systematic errors – Random errors

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

Systematic Errors • Systematic errors can be corrected by calibration. • Systematic errors can be traced and reduced

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.

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

Skill 2: Identify the type of measurement Picture Measurement type Direct Measurements Indirect Measurements

Error analysis • Error analysis are done for the random error • Average / Mean • Standard Deviation

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

Error analysis

Example 1 • A mass of gold is measured 5 times find the mean Reading 1 Reading 2 Reading 3 Reading 4 Reading 5 10 g 10. 2 g 10. 3 g 10. 1 g 10. 4 g • Mean / Average =

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.

Example 2 Reading (Reading – average) (Readings – average)2 16 19 18 16 17 19 20 15 17 13 -1 2 1 -1 0 2 3 -2 0 -4 1 1 0 4 9 4 0 16 40 Sum

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 Reading 2. 55 2. 65 2. 49 2. 69 (Reading – average) (Readings – average)2 -0. 016 0. 084 -0. 116 -0. 076 0. 124 0. 000256 0. 007056 0. 013456 0. 005776 0. 015376 0. 04192 Sum

Excersice

Recap • • • Error Systematic Error Random Error Mean Standard deviation

Warm Up • • Define measurements Measurements type Error Systematic Error Random Error Mean Standard deviation

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

Accuracy • Accuracy of an instrument is how close a measured value is to the true value.

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.

Small STD Large STD

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

Precision Calculation STD = σ It will tell you which instrument is more precise Value max {(Avg – Min), (Max – Avg)}

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)}

Precision of the instrument Student 1 5 mm Student 2 5. 2 mm Student 2 5. 1 mm Student 3 4. 5 mm Student 3 4. 9 mm Student 4 4. 7 mm Student 4 5 mm STD = σ = 0. 310913 STD = σ = 0. 08165 Which one is more precise ?

Precision of the instrument 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 Which instrument is more precise ? STD = 0. 816497

Bias • The difference between the true value (TV) and average value (AV). • Ideally, the bias should be zero. • ���� = ���� − ����

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 Trail 2 Trail 3 Trail 4 6. 3 kg 6. 5 kg 6 kg

Range • The range of an instrument defines the minimum and maximum values that the instrument can measure. Min value = -40 o. F Max value = 120 o. F Range = 120 o. F – (-40 o. F) = 160 o. F

Min Value 0 Unit cm Max value 15 Unit cm Range =15 -0=15 Unit cm Min Value -40 Unit o. C Max value 50 Unit o. C Range 50 -(-40)=90 Unit o. C

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)

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.

Lab Activity 1

Resistor Color Code R = 25 * 10 1 Ω ± 5% = 25 * 10 Ω ± 12. 5 Ω Rmin = 237. 5 Ω Rmax = 262. 5 Ω

Resistor color code Colors: Red – Violet – green – Gold R = (27 x 105) ± 5% Ω Colors: Brown – Black – yellow – Silver R = (10 x 104 )± 10% Ω

Unit Conversion M k m µ 106 103 10 -6

Unit Conversion Examples 27. 0 x 105 10. 0 x 104 10. 0 x 10 -4 500. 0 x 10 -5 2. 7 x 106 = 2. 7 M 100 x 103 = 100 k 10 -3 = 1 m 5000 x 10 -6 =50µ

How to use DMM ?

How to use DMM ? Always must be connected

Part 1 color code Resistance value True Value DMM range Measured values Yellow – violet – brown - gold 470 Ω 2 kΩ 466 Brown – Black – Red Gold 1 kΩ 2 kΩ 1. 13 kΩ Orangeorange – red gold 3. 3 k Ω 20 kΩ 3. 31 kΩ Orange – white – orange - gold 39 k Ω 200 kΩ 38. 5 kΩ Brown – green - gold 1. 5 M Ω 2 MΩ 1. 51 MΩ % Error Within tolerance? Yes NO Yes Yes

Part 2 Resistor Reading Resistor True value: Brown – Black – Red - Gold DMM 1 1. 1 kΩ DMM 2 1. 2 kΩ DMM 3 1. 09 kΩ DMM 4 0. 99 kΩ DMM 5 0. 97 kΩ

Part 3 Reading Student 1 Student 2 Student 3 Student 4 Student 5 Mean Standard deviation Reading (diameter in mm) Reading – Mean (Reading – Mean )2

Recap • • • Define measurements Measurements form Measurements types Error Systematic Error / Random Error Mean Standard deviation Accuracy Precision Bias Range