Transcript Precision Measurements PPT

Precision
Measurement
Foundations of Engineering
Precision Measurement
When measured quantities are reported, the last
significant digit in a measurement is somewhat
uncertain. ( Park, 1996)
“…the last significant digit is a carefully considered estimate
by the experimenter and represents the limit of his or her
ability to measure, given the measuring instrument being used
and the conditions under which the measurement is made.
This uncertainty carries over into the result calculated from
the measurements. Thus the number of significant figures in a
quantity is the number of trustworthy figures in it, the last
trustworthy figure being somewhat in doubt (but still
useful), because it is based upon an estimation.” ( Park, 1996)
Precision Measurement
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Therefore Precision Measurement must take
into consideration:
Significant Digits
 Units
 Measuring Power & Energy
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How many digits are significant?
Addition and Subtraction:
Any answer can be no more accurate as the LEAST
accurate number that was used to calculate it
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2.200 kg + 1.2 kg = 3.4 kg
 2.25 kg + 1.2 kg = *3.5 kg
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* - see rules for rounding.
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In multiplication and division you must count the digits.
The answer can have only have as many significant figures as the
LEAST of the numbers used to get it.
Non-zero digits are always significant.
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Any zeros between two significant digits are significant.
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523.7 has ____ significant figures
23.07 has ____ significant figures
A final zero or trailing zeros in the decimal portion ONLY
are significant.
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3.200 has ____ significant figures
200 has ____ significant figures
2.00 x 10^2 ____ significant figures
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Does 1000 ml mean exactly 1000? Not
necessarily.
100, 100, 10, and 1 all have one significant digit.
If the engineer wanted to express exactly 1000,
he/she would have to write 1.00 x 10^3.
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Rounding
Example: 3.141592653589 (What number is this?)*
Look at the number to the immediate right of the place you are rounding to:
If it is greater than 5 (i.e., 6, 7, 8, or 9), round the place of interest up.
So π to 4 decimal places is __________
If it is less than 5 (i.e., 0, 1, 2, 3, 4), leave the place of interest unchanged.
So π to 2 decimal places is __________
If it is 5 (use the round-to-even rule): round up by one if there are any nonzero digits following the 5
If there are only zeros following the 5, round up by one if the place of interest
is odd, or else leave it unchanged if it is even.
So π to 3 decimal places is __________
So π to 7 decimal places is __________
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Units of Measure
Base Units SI and EES (English Eng. System)
Quantity
Length
Mass
Time
Electric current
Thermd temp
Amount of Substance
SI
meter
kilogram
second
ampere
kelvin
mole
EES
foot
lb.
second
fahrenheit
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Units of Measure
Derived Units and Common Derived Units
Unit Conversions
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Several could be committed to memory.
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Fahrenheit to Celsius
Millimeters to inches
Kilograms to pounds
Gallons to liters
Online Conversion Sources
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www.onlineconversions.com or www.efunda.com
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Using the Engineering Solution Layout Excel
Spreadsheet, convert the following paying
attention to significant digits.
Assignment 1: Conversion Worksheet
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Measuring Power &
Energy Vocabulary
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Power
Mechanical Converter
Torque
Efficiency
Horsepower
BTU
Calorie
Force
Gravity
Metric System
Pressure
Speed
Tachometer
Weight
Work
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Energy Defined
Most energy converters such as a diesel or gasoline engine are designed to
accomplish one purpose: convert energy into useful work.
Energy: the ability to do work.
How does this take place in a gasoline engine?
Force is any push or pull on an object.
Gravity is a force that pulls down on every object on earth.
To lift the object we must exert force greater than the weight…therefore
weight is considered to be a force equal to the pull of gravity on an object.
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Work Defined:
Work is defined as the result of applying a force to move a mass a certain
distance.
This force is created by the combustion of a source of fuel, such as
gasoline.
Work is produced when the force moves a certain mass a certain distance.
WORK = FORCE X DISTANCE
Problem 1:
20 LBS. X 50 FT.=
20 LBS.
50 FEET
FORCE
1000 FT-LB.
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Torque Defined:
Torque is the twisting force on a shaft.
Torque wrench produces a twisting force, measured in ft.-lb.
Torque = Force (lbs.) x radius (ft.)
Torque is also produced on the output shaft of engines because of the
combustion of fuel/pushes pistons downward/causing crankshaft to spin.
This force (torque) causes other objects to rotate, turning transmissions and
wheels, boat props, lawn mower blades, etc.
Problem 2:
 A lug nut on a car tire is very tight. When repairing a flat tire, Jenny
has a choice between a 12 inch and 18 inch wrench. Which wrench
will produce more torque?
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Power Defined:
A measure of the work being done in a given period of time:
P (Power) = W (Work) / t (time) or P=(d * m)/t
Power is the final output of an engine after it has converted the energy in
the fuel into work.
A common term used to describe output power is horsepower.
Based on the premise of the amount of work that a horse can do in one
minute.
One horsepower is equal to the energy needed to lift 33,000 pounds 1 foot
in 1 minute. This is the same energy needed to lift 550 lbs. one foot in one
second.