1. Formulation of Characteristic Equations for Instruments P M V Subbarao Professor Mechanical Engineering Department Clues for Design of an Instrument to carry out Transient Measurements….

2. Characteristic Equation of A General Instrument The characteristic equation of n th order system:

3. Laplace Transformations for Instruments

4. Generalized Instrument System : A combination of Blocks The response analysis can be carried out to each independent block.

5. A True Instrument A true instrument should consist of only Zero-Order Blocks To investigate the response of a block, multiply its frequency domain form of characteristic equation with that of the chosen input equation. This is an interesting case because Equation shows that the zero-order block has no frequency dependent term, so the output for all given inputs can only be of the same time form as the input. What can be changed is the amplitude given as the coefficient a 0. A shift in time (phase shift) of the output waveform with the input also does not occur. This is the response often desired in instruments because it means that the block does not alter the dynamics of input signal. The final destination of research in instrumentation is to find a true zero order instrument for every measurement.

6. Description of Turbulent Flow : Lessons from Nature A Hurricane : THE VORTEX

7. Experimental Research in Turbulence The Structure of Vortex The vortical structures visualized by iso-surfaces of vorticity and Laplacian of pressure. The size of energy-containing (largest) eddies may be Estimated as: where, ω = ∇ ×u is the vorticity.

8. Distribution of Vortices in a Turbulent Field Iso-surface representations of vortical structures |ω|

9. True Structure of Turbulent Flow 1/size of vortex Non-dimensional Energy of eddy Only zero order probes can measure true Turbulence !!!

10. Zero Order Instrument: Wire Strain Gauge This is the response often desired in instruments because it means that the block does not alter the time response. All instruments behave as zero order instruments when they give a static output in response to a static input.

11. Wire Strain Gauge

12. Wire Strain Gauge Pressure Transducers In comparison with other types of pressure transducers, the strain gage type pressure transducer is of higher accuraciy, higher stability and of higher responsibility. The strain gage type pressure transducers are widely used as the high accuracy force detection means in the hydraulic testing machines.

14. Type Features and Applications Capacity Range Nonlinearity(% RO) Rated Output(m V/V) Compensated Temp.Range ( ℃ ) HVS High Accuracy type 0.5,..50 MPa0.2,0.31.0,1.5±1 % － 10 to 60 HVU General Purpose type 1,..50 MPa0.3,0.51.5,2.0±1 % － 10 to 60 HVJS Small & High Temperature type 1,..50 MPa0.51.0,1.5±20 % － 10 to 150 HVJS- JS Small & High Temperature type,Vibratio n-proof 1,..10 MPa0.51.0,1.5±20 % － 10 to 150 Micro Sensor Technology Tokyo

15. First Order Instruments A first order linear instrument has an output which is given by a non-homogeneous first order linear differential equation In these instruments there is a time delay in their response to changes of input. The time constant  is a measure of the time delay. Thermometers for measuring temperature are first-order instruments.

16. The time constant of a measurement of temperature is determined by the thermal capacity of the thermometer and the thermal contact between the thermometer and the body whose temperature is being measured. A cup anemometer for measuring wind speed is also a first order instrument. The time constant depends on the anemometer's moment of inertia.

17. Development of Characteristic Equation for Liquid–in –Glass Thermometer

18. Liquid in Glass Thermometer material volume  (10 −6 K −1 ) alcohol, ethyl1120 gasoline950 jet fuel, kerosene990 mercury181 water, liquid (1 ℃ ) −50 water, liquid (4 ℃ ) 0 water, liquid (10 ℃ ) 88 water, liquid (20 ℃ ) 207 water, liquid (30 ℃ ) 303 water, liquid (40 ℃ ) 385 water, liquid (50 ℃ ) 457 water, liquid (60 ℃ ) 522 water, liquid (70 ℃ ) 582 water, liquid (80 ℃ ) 640 water, liquid (90 ℃ ) 695

19. Development of Characteristic Equation for a Thermometer Conservation of Energy during a time dt Heat in – heat out = Change in energy of thermometer Assume no losses from the stem. Heat in = Change in energy of thermometer

20. RsRs R cond R tf T s (t) T tf (t) Change in energy of thermometer:

21. Define Time constant Step Response of Thermometers

24. Response of Thermometers: Periodic Loading If the input is a sine-wave, the output response is quite different; but again, it will be found that there is a general solution for all situations of this kind.

27. T s,max - T tf,max 