section 1.1: basic concepts of measurements and methods

MAE 3340 INSTRUMENTATION SYSTEMS 1

Section 1.1: Basic Concepts of Measurements and Methods ��

(Chapter 1: Beckwith Chaps. 1-2)

• Encyclopedia Encarta

In classical physics and engineering, measurement generally refers to the process of estimating or determining the ratio of a magnitude of a quantitative property or relation to a unit of the same type of quantitative property or relation.

Process of measurement involves the comparison of physical quantities of objects or phenomena …


What is a Measurement? (2) • Wikipedia

Measurement is the estimation or determination of extent, dimension or capacity, usually in relation to some standard or unit of measurement.


Comparison to a Standard (Metrology)

• Metrology is the study of measurement.

-In general, a metric is a scale of measurement defined in terms of a standard: i.e. in terms of well-defined unit.

- If one says I am 5, that person is indicating a measurement without supplying an applicable standard.

- They could mean I am 5 years old or I am 5 feet high.

- Measurements are at best ambiguous, or at worst, meaningless, with out units!


Units of Measure • What is a Unit of Measure?

-Act of measuring involves comparing the magnitude of a quantity possessed by an object with a standard unit by using an instrument under controlled conditions.

-Examples of measuring instruments include Thermometer (Deg.) Current Meter (Amps) Pressure Sensor (psi)

What are These gages Reading?

Without Prior Knowledge Of units we have No idea!


Units of Measure (3)

• Same quantity,

.. Different units


Units of Measure (4) • Systems of Units

Imperial (English)

• Before SI units were widely adopted around the world, the British systems of English units and later Imperial units were used in Britain, the Commonwealth and the United States. The system came to be known as U.S. customary units in the United States.

• Sometimes called foot-pound-second systems after the Imperial units for distance, weight (mass), and time.


Units of Measure (5) • Systems of Units

Metric (MKS) • The metric system is a decimalised system of measurement based on the Meter (M), kilogram (K), and second (S).

• The main advantage of the metric system is that is has a single base unit for each physical quantity. All other units are powers of ten or multiples of ten of this base unit.

• Unit conversions are always simple because they will be in the ratio of ten, one hundred, one thousand, etc.

• Also referred to as Systeme International (SI) Units


Fundamental Units of Measure • A system of measurement is a set of units which can be used to specify anything which can be measured. Some quantities are designated as fundamental units meaning all other needed units can be derived from them.

• Historically a wide range of units were used for the same quantity; for example, in several cultural settings, length was measured in inches, feet, yards, fathoms, rods, chains, furlongs, miles, nautical miles, leagues, with conversion factors which are not simple powers of ten or even always simple fractions.


Fundamental Units of Measure (2)

• This disagreement of units had serious military, cultural, and Fiscal impacts and eventually the British Royal Society headed by Michael Faraday adopted 3 fundamental Units, distance (ft), weight (lb), and time (sec).

• Later (1824) it was determined to be more fundamental to substitute Mass (slug) for weight (lb) as a fundamental unit of measure


Fundamental Units of Measure (3)

• In the 19th century, science developments showed that either electric charge or electric current must be added to complete the minimum set of fundamental quantities.

• Mesures usuelles (French for customary measurements) were a system of measurement introduced to act as compromise between metric system and traditional measurements.

• This system of measures would eventually lead to the Evolution of the modern SI system of measurements


Fundamental Units of Measure, SI system • The SI system is founded on 8 fundamental units. All other Units can be derived from these quantities.


Derived Units of Measure, SI system

• Derived units are algebraic combinations of the eight base units with some of the combinations being assigned special names and symbols.


Derived Units of Measure, SI system (cont’d)


Conversion of Units of Measure

• Although the Imperial System of units is gradually being Replaced by SI system, these units are still in common use Amongst U.S. defense contractors , and NASA!

• This use of the Imperial system is especially prevalent For mechanical units like distance, force, moments of inertia, pressure, and volume.

• Accurate conversion from one system to another is Essential!


Conversion of Units of Measure (1) • Not Important?!

The Mars Climate Orbiter (1998) was destroyed when a navigation error caused the spacecraft to miss its intended 150 km altitude above Mars during orbit insertion.

Instead the spacecraft entered the Martian atmosphere at about 57 km altitude.

The spacecraft was destroyed by atmospheric stresses and friction at this low altitude.



A review board found that thruster impulse data wer calculated on the ground in Imperial units (pound-seconds) and reported that way to the navigation team, who were expecting the data in metric units (newton-seconds)

Anticipating a different set of units, systems aboard the spacecraft were not able to reconcile the two systems of measurement, resulting in the navigation error and loss of spacecraft!



• This calculation just saved $300 million dollars!


Conversion of Units of Measure (4)

• Careful with English units! • Pounds-mass (lbm) is not a fundamental unit of measurement!

• Metric

• English -- pounds mass (lbm) and pounds force (lbf) do not cancel


Dimensional Analysis

• Most physical quantities can be expressed in terms of combinations of sin basic dimensions. These are

•Dimensions aren't the same as units. I.e. the physical quantity, speed, may be measured in units of meters per second, knots … ; but regardless of the units used, speed is always a distance divided a time, so we say that the dimensions of speed are distance divided by time, or instantaneously dL/dt.

Quantity SymbolFundamentalMKS Unit

FundamentalImperial Unit

Mass M kg slugLength L m ftTime t s s

Temperature T o K o RElectric Current I Amp Amp

Luminous Intensity J cd cd


Dimensional Analysis (2) • In same manner, dimensions of area are D2 …. area can always be calculated as a distance in one direction times a Perpendicular direction

…. area of a circle --> πr2 is really a result of the integral

[1/2 Length of arc] x [height of triangle]


Dimensional Analysis (3)

• Simple Dimensional Analysis Example



• More Complex Dimensional Analysis Example



• In algebraic expression, additive terms must have same dimensions.

--> each term on the left-hand side of an equation must have the same dimensions as each term on the right-hand side.

"a" must have the same dimensions as the product "bc", and "(1/2)xy" must also have the same dimensions as "a" and "bc".

Equation is dimensionally correct when terms have consistent dimensionality

Dimensional analysis is a valuable tool for validating the “correctness” of an algebraic derivation … i.e. finding algebra errors



Source: http://www.physics.uoguelph.ca/tutorials/dimanaly/dimanaly_ans7.html, Cited 12-22-06

More complex examples


Dimensional Analysis Example (1) • Relationship Between pressure, temperature, and density derived empirically in Modern form by John Dalton

John Dalton

p V = n Ru T • p - pressure acting on gas • V - volume of gas in system • n - Number of moles of gas in system • Ru - Universal gas constant • T - Temperature of gas

1-mole --> 6.02 x 1023 Avagadro's number

• Numerical Values for Universal Gas Constant Ru = 1545.40 ft-lbf/°R-(lbm-mole)

Ru = 49722.01 ft-lbf/°R-(slug-mole)

Ru = 8314.4126 J/°K-(kg-mole)


Dimensional Analysis Example (2)

• p - pascal • V - cubic meter • n - Number of moles of gas in system • Ru - Universal gas constant, Ru = 8314.4126 J/°K-(kg-mole) • T - Temperature of gas, °K

MKS units analysis


Another Example: Specific Impulse (1)

• Specific Impulse is a scalable characterization of a rocket’s Ability to deliver a certain (specific) impulse for a given weight of propellant

Mean specific impulse


Another Example: Specific Impulse (2)

MAE 3340 INSTRUMENTATION SYSTEMS

More Dimensional Analysis Examples

29

MKS→ kgm − s2

=kg −mm2 − s2

=kg −ms2

⋅1m2 =

Nm2 → check!

• Pressure

Quantity SymbolFundamentalMKS Unit

FundamentalImperial Unit

Mass M kg slugLength L m ftTime t s s

Temperature T o K o RElectric Current I Amp Amp

Luminous Intensity J cd cd

MAE 3340 INSTRUMENTATION SYSTEMS

More Dimensional Analysis Examples (2)

30

V

u(y)

y

dy

τwall = µ ⋅dudy |y=0

Boundary Layer Wall Shearing Stress →τwall = µ ⋅dudy |y=0

⎛

⎝⎜⎜

⎞

⎠⎟⎟

µ =τwalldudy |y=0

⎛

⎝⎜⎜

⎞

⎠⎟⎟

• Dynamic Viscosity

MKS→ kgm − s

=kg −mm2 − s2

⋅ s = kg −ms2

⋅1m2 ⋅ s =

Nm2 ⋅ s = Pa − s


MKS Units of µ? • From Definition for Viscosity !

Nt − sm2 =

kg −ms2

⎛

⎝⎜

⎞

⎠⎟− s

m2 =kgm − s

=1000g

100cm − s=10 ⋅ g

cm − s

µ =τwall∂u∂y

→ units ≈ Ntm2 ⋅

1m / sm

=Nt − sm2 = Pa − s

→ " poise"≡1 ⋅ P =1 ⋅ gcm − s

→ 0.10 ⋅ Pa − s

→1 ⋅ Pa − s =10 ⋅ P→ "centipoise"≡1 ⋅ cP=0.001 ⋅ Pa − s = 0.01 ⋅ P


MKS Units of µ? (2)

• Motor Oil?!

5W-30 Oil Rating?

SAW J300 Oil Classification

A 5W-30 oil is a mult-viscosity oil that behaves as 5-weight oil at low temperatures but gives the protection of 30-weight oil at the high engine operating temperatures.

Viscosity is defined as oil’s resistance to flow and shear and is expressed as centipoise (cP).

“W” is for Winter!


The Measurement Process: Comparison to a Standard

• Direct Comparison to a Standard

Length of a bar

• Use a carpenter’s Rule


Standards Any time you measure anything, you are comparing it to something whose value you think you know. You assume your ruler is 1 ft long. But who says what a foot is?

A combination of several international agencies are responsible for maintaining the primary standard measures of various quantities. The standard kilogram and the standard second are maintained by the French. Others are kept elsewhere. It extremely important that these standards do not change with time, even over hundreds of years.

The National Institute of Standards and Technology in Maryland is responsible for keeping standards for the US.

http://www.nist.gov/public_affairs/standards.htm


IST-F1 Cesium Fountain Atomic Clock • Primary Time and Frequency Standard for the United States

• The apparatus consists of counter-propagating lasers that cool and trap a gas of cesium atoms. Once trapped, two vertical lasers propel the atoms upward inside a microwave chamber. Depending on the exact frequency of the microwaves, the cesium atoms will reach an excited state. Upon passing through a laser beam, the atoms will fluoresce (emit photons). The microwave frequency which produces maximum fluorescence is used to define the second.


IST-F1 Cesium Fountain Atomic Clock (2) • Primary Time and Frequency Standard for the United States


Hierarchy of Standards • The hierarchy of measurement standards starts from the international standard at the apex, which is known with the highest precision and goes all the way down to working standards.

• International measurement standards are standards recognized by an international agreement to serve internationally as the basis for assigning values to other standards of the quantity concerned.

• The oldest standard in use today is the International Prototype of the Kilogram, kept at the Bureau International des Poids et Mesures (BIPM) in Sevres.


Hierarchy of Standards (cont’d)

These primary standards can’t be passed around to any entity that wants to take some measurements…

if we expect them to maintain their values, so secondary standards are kept which may be somewhat less accurate, but much more accessible.

These are calibrated against the primary standards. In this manner, a hierarchy of standards exist.


Hierarchy of Standards (cont’d)

A primary standard is designated or widely acknowledged as having the highest metrological qualities and whose value is accepted without reference to other standards of the same quantity.

Secondary standards are standards whose value is assigned by comparison to a primary standard of the same quantity. Primary standards are usually used to calibrate secondary standards. A working standard is a standard that is used routinely to calibrate or check material measures, measuring instruments or reference materials. A working standard is usually calibrated with reference to a secondary standard, and may be used to ensure that routine measurements are being carried out correctly - a check standard.

A reference standard is a standard generally having the highest metrological quality available at a given location or in a given organization from which the measurements made at that location are derived. Calibration laboratories maintain reference standards for calibrating their working standards.

section 1.1: basic concepts of measurements and methods

Documents