# measurements in instrumentation

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Mediciones en instrumentacion

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• INSTRUMENTATION MAINTENANCE

MEASUREMENTS IN INSTRUMENTATION

TRAINING MANUAL

Course EXP-MN-SI020 Revision 0

• Field Operations TrainingInstrumentation Maintenance

Measurements in Instrumentation

Training manual EXP-MN-SI020-EN Last revised: 17/10/2008 Page 2 / 114

INSTRUMENTATION MAINTENANCE

MEASUREMENTS IN INSTRUMENTATION

CONTENTS 1. OBJECTIVES ..................................................................................................................6 2. PHYSICAL QUANTITIES.................................................................................................7

2.1. PRESSURE AND RELATIVE UNITS ........................................................................7 2.1.1. Definition of pressure.........................................................................................7 2.1.2. The units of pressure.........................................................................................7 2.1.3. Pascals law.......................................................................................................8 2.1.4. Exercises...........................................................................................................9 2.1.5. The various types of pressure .........................................................................11

2.1.5.1. Atmospheric pressure ................................................................................11 2.1.5.2. Vacuum......................................................................................................13 2.1.5.3. Relative pressure .......................................................................................14 2.1.5.4. Absolute pressure ......................................................................................14 2.1.5.5. Differential pressure ...................................................................................15

2.1.6. Pressures related to fluid circulation................................................................16 2.1.6.1. Static pressure ...........................................................................................16 2.1.6.2. Dynamic pressure ......................................................................................17 2.1.6.3. Total pressure ............................................................................................18

2.1.7. Relation between the various pressure types..................................................18 2.2. LEVEL MEASUREMENT: BUOYANCY ..................................................................19 2.3. FLOWRATE MEASUREMENT: FLUIDS IN MOTION.............................................21

2.3.1. General points .................................................................................................21 2.3.2. Volume Forces and Surface Area Forces........................................................21 2.3.3. Definitions........................................................................................................21

2.3.3.1. Mass flowrate .............................................................................................22 2.3.3.2. Volume flowrate .........................................................................................22 2.3.3.3. Relation between Qm and Qv......................................................................22 2.3.3.4. Steady flows...............................................................................................22

2.3.4. Equation of conservation of mass ...................................................................22 2.3.4.1. Definitions ..................................................................................................22 2.3.4.2. Conservation of flowrate.............................................................................23 2.3.4.3. Expressing flowrate as a function of velocity..............................................23 2.3.4.4. Mean velocity .............................................................................................24

2.3.5. Bernoulli's theorem..........................................................................................24 2.3.5.1. The steady flow theorem in an incompressible fluid...................................24 2.3.5.2. Case of flow without work exchange ..........................................................26 2.3.5.3. Case of flow with energy exchange............................................................26

2.3.6. Application of Bernoullis theorem ...................................................................26 2.3.6.1. Pitot Tube...................................................................................................26 2.3.6.2. Venturi phenomenon..................................................................................27

2.3.7. Liquid flow contained in a tank ........................................................................28 2.3.7.1. Torricellis theorem.....................................................................................28

2.3.8. The difficulty of measuring gases ....................................................................28

• Field Operations TrainingInstrumentation Maintenance

Measurements in Instrumentation

Training manual EXP-MN-SI020-EN Last revised: 17/10/2008 Page 3 / 114

2.3.8.1. General points............................................................................................28 2.3.8.2. Perfect gas law...........................................................................................28 2.3.8.3. The perfect gas equation............................................................................29 2.3.8.4. Calculating a volume of gas in standard cubic metres ...............................31 2.3.8.5. Application..................................................................................................31 2.3.8.6. Gas density ................................................................................................31

2.3.9. Fluid flow conditions ........................................................................................32 2.3.10. Head losses...................................................................................................33 2.3.11. Systematic head losses.................................................................................34

2.3.11.1. Case of laminar flow Re < 2000 ...............................................................35 2.3.11.2. Poiseuilles law.........................................................................................35 2.3.11.3. Case of turbulent flow Re>3000...............................................................35

2.3.12. Accidental head losses..................................................................................36 2.4. DENSITY.................................................................................................................37 2.5. VISCOSITY .............................................................................................................37

2.5.1. The phenomenon ............................................................................................37 2.5.1.1. Observations ..............................................................................................37 2.5.1.2. Conclusion .................................................................................................37

2.5.2. Kinematic and dynamic viscosity.....................................................................38 2.5.2.1. Velocity profile............................................................................................38 2.5.2.2. Dynamic viscosity.......................................................................................38 2.5.2.3. Kinematic viscosity.....................................................................................39 2.5.2.4. Influence of temperature ............................................................................39

2.5.3. Measuring viscosity .........................................................................................40 2.5.3.1. Ostwald viscometer....................................................................................40 2.5.3.2. Rotary viscometer or Couette viscometer ..................................................40

2.6. TEMPERATURE .....................................................................................................41 2.6.1. From referencing to measurement ..................................................................41 2.6.2. Thermometric scales .......................................................................................44 2.6.3. Units ................................................................................................................46

2.6.3.1. Degree Fahrenheit .....................................................................................46 2.6.3.2. Degree Celsius...........................................................................................46 2.6.3.3. Kelvin .........................................................................................................47 2.6.3.4. Degree Rankine .........................................................................................47 2.6.3.5. Degree Raumur........................................................................................47

2.6.4. The relations between temperature scales......................................................48 2.6.4.1. The Celsius scale.......................................................................................48 2.6.4.2. The Fahrenheit scale .................................................................................48

2.6.5. Correspondence between sc