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Section 1.1: Basic Concepts of Measurements and Methods

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Section 1.1: Basic Concepts of Measurements and Methods 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 … MAE 3340 INSTRUMENTATION SYSTEMS 1 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. MAE 3340 INSTRUMENTATION SYSTEMS 2 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! MAE 3340 INSTRUMENTATION SYSTEMS 3 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 What are under controlled conditions. These gages Reading? -Examples of measuring instruments include Thermometer (Deg.) Current Meter (Amps) Without Pressure Sensor (psi) Prior Knowledge Of units we have No idea! MAE 3340 INSTRUMENTATION SYSTEMS 4 Units of Measure (3) • Same quantity, .. Different units MAE 3340 INSTRUMENTATION SYSTEMS 5 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. MAE 3340 INSTRUMENTATION SYSTEMS 6 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 MAE 3340 INSTRUMENTATION SYSTEMS 7 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. MAE 3340 INSTRUMENTATION SYSTEMS 8 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 MAE 3340 INSTRUMENTATION SYSTEMS 9 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 MAE 3340 INSTRUMENTATION SYSTEMS 10 Fundamental Units of Measure, SI system • The SI system is founded on 8 fundamental units. All other Units can be derived from these quantities. MAE 3340 INSTRUMENTATION SYSTEMS 11 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. MAE 3340 INSTRUMENTATION SYSTEMS 12 Derived Units of Measure, SI system (cont’d) MAE 3340 INSTRUMENTATION SYSTEMS 13 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! MAE 3340 INSTRUMENTATION SYSTEMS 14 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. MAE 3340 INSTRUMENTATION SYSTEMS 15 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! MAE 3340 INSTRUMENTATION SYSTEMS 16 Conversion of Units of Measure (3) • Not Important?! • This calculation just saved $300 million dollars! MAE 3340 INSTRUMENTATION SYSTEMS 17 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 MAE 3340 INSTRUMENTATION SYSTEMS 18 Dimensional Analysis • Most physical quantities can be expressed in terms of combinations of sin basic dimensions. These are Fundamental Fundamental Quantity Symbol MKS Unit 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 •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. MAE 3340 INSTRUMENTATION SYSTEMS 19 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] MAE 3340 INSTRUMENTATION SYSTEMS 20 Dimensional Analysis (3) • Simple Dimensional Analysis Example MAE 3340 INSTRUMENTATION SYSTEMS 21 Dimensional Analysis (4) • More Complex Dimensional Analysis Example MAE 3340 INSTRUMENTATION SYSTEMS 22 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 MAE 3340 INSTRUMENTATION SYSTEMS 23 Dimensional Analysis (6) More complex examples Source: http://www.physics.uoguelph.ca/tutorials/dimanaly/dimanaly_ans7.html, Cited 12-22-06 MAE 3340 INSTRUMENTATION SYSTEMS 24 Dimensional Analysis Example (1) • Relationship Between pressure, temperature, and density derived empirically in Modern form by John Dalton • 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) 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 John Dalton 1-mole --> 6.02 x 1023 MAE 3340 INSTRUMENTATION SYSTEMS Avagadro's number 25 Dimensional Analysis Example (2) • p - pascal MKS units analysis • 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 MAE 3340 INSTRUMENTATION SYSTEMS 26 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 MAE 3340 INSTRUMENTATION SYSTEMS 27 Another Example: Specific Impulse (2) MAE 3340 INSTRUMENTATION SYSTEMS 28 More Dimensional Analysis Examples Fundamental Fundamental Quantity Symbol MKS Unit Imperial Unit Mass M kg slug Length L m ft Time t s s Temperature T o K o R • Pressure Electric Current
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