The document discusses concepts related to measurement and instrumentation systems, including: 1. Measurement involves comparing a physical quantity to a standard unit using an instrument under controlled conditions. Units are needed to give measurements meaning. 2. Common systems of units include the Imperial (or English) system and the metric (SI) system which is based on fundamental units of the meter, kilogram, and second. 3. Dimensional analysis is used to determine the consistent dimensions of terms in equations and validate derivations. Physical quantities have consistent dimensional relationships regardless of the specific units used.

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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 …

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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.

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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!

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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!

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Units of Measure (3)
• Same quantity,
.. Different units

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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.

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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

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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.

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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

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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

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

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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.

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

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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!

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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.

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Conversion of Units of Measure (2)
• Not Important?!
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!

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Conversion of Units of Measure (3)
• Not Important?!
• This calculation just saved $300 million dollars!

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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

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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 Symbol
Fundamental
MKS Unit
Fundamental
Imperial Unit
Mass M kg slug
Length L m ft
Time t s s
Temperature T o
K o
R
Electric Current I Amp Amp
Luminous Intensity J cd cd

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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]

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Dimensional Analysis (3)
• Simple Dimensional Analysis Example

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Dimensional Analysis (4)
• More Complex Dimensional Analysis Example

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Dimensional Analysis (5)
• 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

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Dimensional Analysis (6)
Source: http://www.physics.uoguelph.ca/tutorials/dimanaly/dimanaly_ans7.html, Cited 12-22-06
More complex examples

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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)

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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

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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

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Another Example: Specific Impulse (2)

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More Dimensional Analysis Examples
29
MKS →
kg
m − s2
=
kg − m
m2
− s2
=
kg − m
s2
⋅
1
m2
=
N
m2
→ check!
• Pressure
Quantity Symbol
Fundamental
MKS Unit
Fundamental
Imperial Unit
Mass M kg slug
Length L m ft
Time t s s
Temperature T o
K o
R
Electric Current I Amp Amp
Luminous Intensity J cd cd

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More Dimensional Analysis Examples (2)
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V
u(y)
y
dy
τwall = µ ⋅
du
dy|y=0
Boundary Layer Wall Shearing Stress → τwall = µ ⋅
du
dy|y=0
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
µ =
τwall
du
dy|y=0
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
• Dynamic Viscosity
MKS →
kg
m − s
=
kg − m
m2
− s2
⋅ s =
kg − m
s2
⋅
1
m2
⋅ s =
N
m2
⋅ s = Pa − s

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MKS Units of µ?
• From Definition for Viscosity !
Nt − s
m2
=
kg − m
s2
⎛
⎝
⎜
⎞
⎠
⎟− s
m2
=
kg
m − s
=
1000g
100cm − s
=10 ⋅
g
cm − s
µ =
τwall
∂u
∂y
→ units ≈
Nt
m2
⋅
1
m / s
m
=
Nt − s
m2
= Pa − s
→ poise ≡1⋅ P =1⋅
g
cm − s
→ 0.10 ⋅ Pa − s
→1⋅ Pa − s =10 ⋅ P
→centipoise ≡1⋅ cP=0.001⋅ Pa − s = 0.01⋅ P

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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!

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The Measurement Process: Comparison to a
Standard
•Direct Comparison to a Standard
Length of a bar
• Use a carpenter’s Rule

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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

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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.

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

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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.

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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.

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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.