1 measurement and errors

Dr. Khairul Anuar Mohamad

MEASUREMENT AND ERRORS1

CONTENTS

1.1 Principles of Measurement

1.2 SI Systems

1.3 Performance Characteristic

1.4 Errors in Measurements

1.5 Statistical Analysis of Measurement Data

Electrical Measurements & Instrumentation (BEV20103) 2

1.1 Principles of Measurement


Measurement

• Measurement is the process of comparing an unknown quantity with an accepted standard quantity.

• It involves connecting a measuring instrument into the system under consideration and observing the resulting response on the instrument.


Process of Comparison(Measurement)

Standard(Known Quantity)

Measurand(Quantity to be Measured)

Result(Output)

Fundamental Measuring Process

Measurand

• The physical quantity or the characteristic condition which is the object of measurement in an instrumentation system.

• Also called:

Measurement variable

Instrumentation variable

Process variable

Electrical Measurements (BEF23903) 5

• The measurand may be: Fundamental quantity: length, mass, and time Derived quantity : speed, velocity, acceleration

Measurement Process


Before measurement• Methods/procedures of

measurement.• Characteristics of the parameter.• Quality: time and cost, instrument

capabilities, knowledge of measurement, acceptable result.

• Instrument to use.

During measurement• Quality- best instrument chosen,

suitable position when taking the data, etc..

• Safety- electric shock, overloaded, instrument limits, read instruction manual.

• Sampling – observe parameter changing, taking enough sample.

After measurement• Analyse the data

mathematically/statistically.• Full result must be reported

completely and accurately.

What is an instrument?

• Device that communicates, denotes, detects, indicates, measures, observes, records, or signals a quantity or phenomenon, or controls or manipulates another device.

• A tool or device used for a particular purpose; especially : a tool or device designed to do careful and exact work.


Instrumentation

• Instrumentation - The technology of using instruments to measure and control the physical and chemical properties of materials

• Process Instrumentation - When the instruments are used for the measurement and control of industrial manufacturing, conversion or treatment process

• Control system - When the measurement and control instruments are combined so that measurements provide impulse for remote automatic action.


The basic requirements for getting meaningful result

1. The standard employed for comparison purpose may be accurately defined and should be commonly acceptable.

2. The standard must be of the same character as the measurandand usually but not always, is prescribed and defined by a legal or recognised organisation, e.g. the International Organisation of Standards (ISO).

3. The apparatus used and method adopted for the comparison purposes must be provable.


Why do we need measurements?

• Measurement plays a very significant role in every branch of scientific research and engineering processes which include the following:

Control systems;

Process instrumentation

Data reduction.

• The whole area of automation or automatic control is based on measurements.


Cont…


Cont…

• The measurements confirm the validity of a hypothesis and also add to its understanding. This eventually leads to new discoveries that require new and sophisticated measuring techniques.

• Through measurements a product can be designed or a process be operated with maximum efficiency, minimum cost, and with desired degree of reliability and maintainability.


1.2 SI Systems


Review: Why do We Need Measurement

• Measurement is KEY to the knowledge and interaction.

• A Science & Technology of a measured understanding.

• Science is about doing and making, not just thinking.

• It is crucially an experimental activity, directed to measurement.

• In Engineering & Technology;• Responsible people seek the most measured way to understand

their situation.• Any inquiry will get ignited as Engineering only when its practitioners

become serious about the practice of measurement.• Measurement functions not simply to furnish a test of some theory,

but rather as a direct argument to a specific theoretical conclusion .

• The more the measured understanding is in practice, the more harmonizing its engagement of the evidence will be.

Review: What is An Outcome of A Measurement?

• Measurement leads to the expression of characteristics of systems in terms of numbers.

• Present culture is crazy about numbers.

• We seek standardization, we revere precision, and we aspire for control.

• If you can number it, you make it real.

• Once made real, it's yours to manage and control.

• We increasingly depend on numbers to know how we are doing for virtually everything.

• We ascertain our health with numbers.

Electrical Measurements & Instrumentation (BEV20103)

Standards

• Standard

• All measurement are based on comparison to some known quantity or reference (standard). Standards is a physical devices that have stable characteristics and accurately defined.

• Categorize to 4 type

1. international standard

2. primary standard

3. secondary standard

4. working standard


ISO 216 Paper Sizes

Standards


PS

IS

SS

WS

Diagram Traceability

SI System

International system of units (S.I) are divided into three classes:

• Unit: a set of size of physical quantities.

• Different systems of units are based on different choices of a set of fundamental units.


S.I Unit

Base units Derived unitsSupplementary

units

S.I Base Units – 7 base units

20

Base Quantity Base Unit

Name Symbol

Length Meter m

Mass Kilogram Kg

Time Second s

Electric Current Ampere A

Thermodynamic Temperature Kelvin K

Amount of substance Mole mol

Luminous Intensity Candela cd


* SI covers all areas, although certain units outside SI are so useful that they are accepted for general use together with the SI.

Derived Unit

• Derived Quantities are formed by combining two or more of the fundamental quantities.

• Examples:

• Area = length x width

• Volume = length x width x height

• Speed = distance/time

• Density = mass/volume

• Most of the units in the International System are derived units, that is units defined in terms of base units and supplementary units.

• Derived units can be divided into two groups - those that have a special name and symbol, and those that do not.

21Electrical Measurements & Instrumentation (BEV20103)

Mathematical operation

Cont…

22

With Names and Symbols

Unit Measure of Symbol Derivation

coulomb electric charge C A·s

farad electric capacitance F A·s/V

henry inductance H V·s/A

hertz frequency Hz cycles/s

joule quantity of energy J N·m

ohm electric resistance Ω V/A

tesla magnetic flux density T Wb/m2

volt voltage V W/A

watt power W J/s

weber magnetic flux Wb V·s


Cont…

23

Without Names and Symbols

Measure of Derivation

acceleration m/s2

angular acceleration rad/s2

angular velocity rad/s

density kg/m3

electric field strength V/m

magnetic field strength A/m

velocity m/s


Supplementary Units

• Third class of S.I units

• Supplementary units may be regarded either as base units or as derived units

• Example of S.I derived units formed by using supplementary units

• - Angular velocity (rad/s)

• - Angular acceleration (rad/s^2)

24

Quantity S.I Units

Name Symbol

Plane angle radian rad

Solid angle steradian Sr

Volume litre L

Pressure bar bar


Extra: SI Prefix

• A prefix that can be applied to an SI unit to form a decimal multiple or submultiples.

25

10n Prefix Symbol Long scale

1024 yotta Y Quadrillion

1021 zetta Z Trilliard

1018 exa E Trillion

1015 peta P Billiard

1012 Tera T Billion

109 Giga G Milliard

106 Mega M Million

103 Kilo k Thousand

102 hecto h Hundred

101 deca Da Ten

10n Prefix Symbol Long scale

10-1 Deci d Tenth

10-2 Centi c Hundredth

10-3 Mili m Thousandth

10-6 Micro µ Millionth

10-9 Nano n Milliardth

10-12 pico p Billionth

10-15 Fento f Billiardth

10-18 Atto a Trillionth

10-21 Zecto z Trilliardth

10-24 vocto y QuadrillionthElectrical Measurements & Instrumentation (BEV20103)

Dimensional Analysis

• Conceptual tool applied in physics, chemistry and engineering to understand physical situations that involve physical quantities and derive equation for relationship

26

Length MassTime Current

Length/time=Velocity (m s-1)

Velocity/time=Acceleration (m s-2)

Acceleration x mass = Force (kg m s-2)

Current x time = Electric charge (A s)

Force/charge = Field strength (kg m s-3 A-1)


Dimensional Analysis

• Example:

Velocity = length/time; [v] = [L]/[T] = [LT-1]

Acceleration = velocity/time; [a] = [v]/[T] = [LT-2]

27

Length MassTime Current

Length/time=Velocity (m s-1)

Velocity/time=Acceleration (m s-2)

Acceleration x mass = Force (kg m s-2)

Current x time = Electric charge (A s)

Force/charge = Field strength (kg m s-3 A-1)


END PART 1


1 measurement and errors

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