2. Tutorial:Engineering metrology Topic: Measuring units Prepared by: Ing. Pavel Rožek Projekt Anglicky v odborných předmětech, CZ.1.07/1.3.09/04.0002 je spolufinancován Evropským sociálním fondem a státním rozpočtem České republiky.

3. Measuring units

4.  Main idea of metric system – unit’s system based on meter and kilogramme – it was originated during French revolution when 2 platinum referential ‘meter and kilogramme’ standards were made in 1799 - they were stored in French National Archive in Paris.  Later, they were called archive meter and archive kilogramme.

5.  The condition of quantification possibility in the made quantity system is making of corresponding measuring system.  Conference of general scales and measures (CGPM) introduced International system of units SI in 1960 as complete system of units.

6.  Nowadays, SI system is made by 7 basic units which make together with derived units complete system of units. QuantityBasic unitSign LengthMeterM WeigthKilogrammekg Timeseconds Electric currentampereA Thermodynamic temperature kelvinK Amount of substancemoleMol Luminositycandelacd

7.  Basic unit meter is the length of way through which light in vacuum travels in 1/299 792 458 second.  Basic unit kilogramme is weigth of international kilogramme prototype.  Basic unit second is the time which equals to 9 192 631 770 radiation periods, corresponding with 2 very fine structure levels transition of basic caesium 133 atom condition.  Basic unit ampere is constant electric current which, at 2 linear parallel conductors passage of infinite ways and insignificant cross-section placed in distance of 1 meter in vacuum, causes force equal to 2 x 10-7 newton to 1 meter of conductor length.

8.  Basic unit kelvine is 1/273,16 part of triple water point thermodynamics temperature.  Basic unit mole is amount of substance which contains as many elementar entities as there are atoms in 0,012 carbon isotope kilogramme 12C. It is necessary to specify elementary entities at amount of substance setting, there can be atoms, molecules, ions, electrones, other particles or more specified particles´ clusters.  Basic unit luminosity candela – it is luminosity source which in given direction transmits monochromatic radiation with frequency 540 x 1012 hertz and whose radiant capacity in this direction is 1/683 watts to steradian.

9.  Derived SI units are derived from basic SI units in accordance with physical relationships among given quantities.  Derived units are made of basic units using maths signs for multiplication and division. Examples of derived SI units expressed in basic SI units See following table.

10. Derived quantityDerived unitSign AreaSquare meterm² capacitycubic meterm³ speedMeter per secondm · s-1 accelerationMeter per square secondm · s-2 Anglular speedRadian per secondrad · s-1 Angular accelerationRadian per square secondrad · s-2 densitykilogramme to cubic meterkg · m-3 Magnetic field intensityamper to meterA · m-1 Electric field intensityamper to square meterA · m-2 Moment of forcenewton meterN · m Electric field intensityvolt to meterV · m-1 permeabilityhenry to meterH · m-1 permittivityfarad to meterF · m-1 Amount of substance concentrationmole to square metermol · m-3 luminositycandela to square metercd · m-2

11.  Units which are used together with SI units because they are commonly used or they are used in specific branches. quantityunitsignValue in SI units timeminutemin1 min = 60 s hourh1 h = 3600 s dayd1 d = 24 h Plane angledegree°1° = (π/180) rad minute´1´ = (1/60)° = (π/10 800) rad second´´1´´ = (1/60)´ = (π/ 648 000) rad gradegon1 gon = (π/200) rad areaHectareha 1 ha = 1 hm² = 10 ⁴ m² capacityLiterl ; L1 L = 1 l = 1 dm³ = 10³ cm³ = 10­³ m³ weighttonet1 t = 10³ kg

12.  Prefixes are mostly related to 10-to-power (not 2-to-power). Example: 1 kilobit represents1000 bits not 1024 bits at all  Prefixes must be written without gaps before unit sign. Example: Centimeter must be written cm not c m at all  Prefixes can not be combined. Example: 10­⁶ kg must be written1 mg not 1 μkg  We can not write prefix individually. Example: 109/m³ can not be written as G/m³

13. Explain the meaning of measuring units and SI system meaning in engineering metrology. Question 2: Name out-of-system units and explain their usage in practice.

14.  Metrologie v kostce: Třetí upravené a doplněné vydání. třetí. Praha 2009: Bořivoj Kleník, PhDr. – Q-art., 2009. Dostupné z: k volnému prohlížení a stažení  26. úvodní kurz METROLOGIE: K 381-07. 2007. Česká metrologická společnost: ČMS, Praha 1. Translation:  www.seznam.cz www.seznam.cz  www.slovnik.cz www.slovnik.cz  JANATA, Petr. Handy slovník technický anglicko-český a česko- anglický. Plzeň: Nakladatelství Fraus, 2000. ISBN 80-7238-075-3  Lingea LEXIKON 5, Technický slovník anglicko-český a česko- anglický. 2010.