Lesson 1. Thermomechanical Measurements for Energy Systems (MENR) Measurements for Mechanical Systems and Production (MMER)

Transcription

1 Lesson 1 Thermomechanical Measurements or Energy Systems (MENR) Measurements or Mechanical Systems and Production (MMER) 1 A.A Zaccaria (Rino ) Del Prete

2 I oten say, when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is o a meagre and unsatisactory kind; it may be the beginning o knowledge, but you have scarcely, in your thoughts, advanced to the state o Science, whatever the matter may be. Lord Kelvin, 1883 THE LANGUAGE OF MEASUREMENTS 2

3 When man elt the need o «measuring» things around him??? 3

4 Some examples in antiquity : «How big» is the mammuth we have to hunt? «How ar» is the danger rom the village? «How many» walking days rom the village is the ood? TO MEASURE something = relating to the world we live in and being able to communicate knowledge to our ellow! 4

5 Since ever, man has always "measured"... the distance between himsel and the things (length), the size o things (weight) and the time it takes to do things... These are still the undamental measurements in the modern world!!! 5

6 Egyptian length units : With these units egyptian build their pyramids!!! 6

7 Roman and British length units : Milestone (pietra miliare) For romans : 1000 double steps = 1 mile The «yard» was imposed by king Henry the 1st o England in year

8 Approximate and accurate measurements! To make rough measurements everyone can use their eet and their hands! Those measurements will be "made with the eet"... Saranno misure «atte con i piedi» To make accurate measurements it is necessary to deine a sample and a measurement unit valid or everyone! These will be measurements taken with calibrated instruments Saranno misure «atte con strumenti tarati» 8

9 The metric system: The «metric system» was introduced in France in 1790 with the French Revolution. The new units o length, weight and time required about 10 years o work and the overcoming o many contrasts to be drawn. They were attended by many amous scientists including Borda, Lagrange, Laplace, Monge, Condorcet, Mechain, Delambre and Coulomb. In 1799, the irst platinum iridium samples o meter and kilogram were deposited in the archives o France! In 1875, 17 nations, including Italy, signed the "International Metre Convention". In 1889 took place the irst General Conerence on Weights and Measures (1 GFCM), which deinitively established the new units 9

10 Types and applications o Measuremet instrumentation: Why do we do measurements today? 1. To monitor technical processes and operations 2. To control technical processes and operations 3. To perorm experimental engineering analysis 10

11 Theorethical vs experimental analysis methods : Features o theorethical methods: Features o experimental methods: 11

12 We will employ the «physical approach» to measurements: What is a measurement? 1. Classiication: a) to identiy the characteristics or the properties o an object or a physical phenomenon; b) to group the objects or phenomena into classes where the identiied properties are homogeneous. It s a qualitative cognitive method! 2. Ordering: a) to consider only the properties that can be sorted according to a scale. It s a irst orm o quantiication o the properties, based on the intensity o the selected property. 3. Measurement: a) to associate to the property considered a number that represent it each time such property maniests itsel equal to itsel. This position establishes a measurement scale. This means establishing a correspondence between the physical properties o objects or phenomena and real numbers. 12

13 A B measurement o A with respect to B α always exists and it is a real number! When we choose a reerence property or unit B U then we associate uniquely a number to the physical quantity and we can introduce the measurement o the quantity A! A a U measurement o A! To express «physical properties» with numbers we have to ind and associate them with a suitable measurement unit! Examples : A m a B C Length : meters Temperature: Celsius degree b 13

14 What i I choose a new unit U or the same physical property A??? A U ' a' a The property stays the same but the number a changes in a (o course)! There is a simple rule to pass rom a to a : A U ' A U U U ' A U or a' a The ratio o the two units U and U is o course dimensionless : U U ' This rule accounts or the «change o the measurement units» in science and technology! Example: 1mm mm U U ' 1mm 1km 10 6 km 6 1km 10 14

15 Are we going to choose or every physical quantity or property an arbitrary measurement unit? NO! Then we have to establish relationships between every quantity or property that allows it. Example: Geometric Units liter Lenght [ L ] undamental unit U L = m «meter» (in the International Unit System) Area [ A ] derived unit U A = m 2 [A] = [L L] = [L 2 ] Dimensions hectare inch Volume [ V ] derived unit U V = m 3 [V] = [L L L] = [L 3 ] 15

16 Kinematic Units Time [ t ] undamental unit U t = s «seconds» (in the International Unit System) Velocity [ v ] derived unit U v = m/s [v] = [L t -1 ] Acceleration [ a ] derived unit U a = m/s 2 [a] = [L t -1 t -1 ] = [L t -2 ] Kinematic relationships! Dynamic Units Mass [ M ] undamental unit U F = kg «kilogram» (in the International Unit System) Force [ F ] derived unit U F = kg m/s 2 «newton» [F] = [M L t -2 ] Work [ J ] derived unit U J = kg m 2 /s 2 «joule» [J] = [M L 2 t -2 ] Power [ W ] derived unit U a = kg m 2 /s 3 «watt» [W] = [M L 2 t 3 ] Physical relationships! 16

17 A dimensional equation is an equation that expresses with the «Maxwell notation» every derived quantity or unit U as a unction o the undamental quantity or units U 1, U 2, U 3, with the dimensions α 1, α 2, α 3. U U U U I we concentrate only on Mechanics, we deine 10 physical quantities or units and 7 relationships between them: only 10 7 = 3 quantities or units are undamental, the others are derived rom the 3 undamental!!! L L 2 A L 3 V L t t 1 v t 2 a L t M M 2 F M Lt J M L 2 t 2 W M L 2 t 3 m (undamental) m 2 (derived) m 3 t (derived) (undamental) m/s (derived) m/s 2 (derived) kg (undamental) kg m/s 2 = N (derived) kg m 2 /s 2 = J (derived) kg m 2 /s 3 = W (derived) 17

18 Since 1978 in Italy is in orce the International System o Units (SI acronym), edited in 1976 by the 11th General Conerence on Weights and Measures". Physical quantity Unit IS Name Symbol [L] Length meter m [M] Mass kilogram kg [t] Time second s [I] Electrical current intensity ampère A [T] Thermodynamic Temperature kelvin K [m] Substabce amount mole mol [Lc] Light intensity candle cd The primary units are held by the International Metrology Laboratory (B.I.P.M.) in Sevres, France, while in Italy the secondary units are held and disseminated by the National Institute o Metrological Research (I.N.RI.M) in Turin. The National Alternative Energies Authority (E.N.E.A.) holds the nuclear units. A very peculiar problem with undamental units : I.S. T. S. [ L ] m [ L ] m [ t ] s [ t ] s [ M ] kg [ F ] kg in the two systems o units, dierent physical quantities (a mass in the IS and a orce in the TS) have the same name!

19 In hystory, engineers were always more interested in «orces» than in «mass», because their irst goal was to make constructions that had not to collapse! 2 U F 1kg 1kg 9.81m / s 9. 81N ( ST) m 1 kg is 10 times bigger than the N! U M ( ST) 1kg 1m p 2 1ms but 1kg 1kg m 9.81ms 2 thereore: 1kg 9.81ms 2 m 1m p ms kg m 1 m p is also 10 times bigger than the kg m! 19

20 Exercise: calculate the density (speciic mass) and the speciic weight o air in the two measurement unit systems We start with the speciic weight: F V kg P 3 m pv = nrt Ideal gas law kg p 2 p 1Atm m T K 3 V m T 25C 298K kg m R K kg m kg cm We now consider an amount o air that weights 1kg 1kg V 1kg p RT 1kg 29.27kg kg mk 1 m K 1.19 kg m 3 20