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Lecture 4

BIOE3270 Lecture 4: BIOE3270-Notes4.pdf

5 Pages

Biosystems Engineering
Course Code
BIOE 3270

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Dynamic Response of Measuring Instruments Transducer:  A device that converts a signal from one physical form to a corresponding signal having a different physical form Physical form: mechanical, thermal, magnetic, optical, electrical  Transducers are energy modifiers or converters Sensor: receives a stimulus and responds Dynamic Characteristics: The properties of the system transient response to an input. y=f(x)  The dynamic response is typically modeled by a constant – coefficient linear differential equation k 2 a d y(t) K a d y(t) a dy(t)a y(t)  x(t) x dtk 2 d t 1 dt o  I practice, these models are limited to zero, first, and second order Zero Order Instruments: have an output that is proportional to the input at all times  Static gain of the instrument (measure of its sensitivity) L o Example would be a strain gage where R   (output is proportional to the length of the wire. A  No delays  The sensor only changes the amplitude of the signal Unit Step Function:  x(t)=0, t 0 x(t)=1, t>0 o For a zero order instrument, y(t)=Kx(t) y(t)=0, fort 0; and y=K for t>0 therefore response of a zero  order instrument to a unit step function with height k, would be K First Order Instruments: output is given by a non-homogeneous first-order differential equation d   y(t) y(t)  Kx(t) dt o  is called the time constant of the instrument o The response of a first order instrument to the unit step function  d   y(t) y(t) K x(t)=1 dt Initial condition y(0)=0 t y(t) K(1e )  When t=  y()  K(1e)  0.632K  Second Order Instrument: second order non-homogenous differential equation   2 d d 2 2 2y(t)2 y(t) y(t) K x(t) dt dt  - constant, damping factor if the instrument  - angular frequency of the instrument  Temperature Measurement  Two necessities for temperature measurement:  o Reference temperature o Rule for measuring the difference between a certain temperature from the reference point Temperature Scales: Fahrenheit: Devised by Gabriel Fahrenheit o Earliest standard scale o Wanted to fix human body temperature at 100 degrees + he wanted whole numbers for the freezing and boiling points 32 F – freezing pt. of water 212 F – boiling pt. of water 98.6 F – human body temperature Celsius: devised by Andres Celsius o Set out to fix the boiling point o2 H O @ 0 an freezing pt. @ 100(this was later reversed) o It became popular because if the 100 division o The unit called ‘centigrade’ o In 1947 the general committee on Weight & Measures ruled that the unit be called ‘Celsius’ Kelvin: William Kelvin o Discovered the principle of energy as it related to the heat of the matter o This led to the idea of ‘absolute zero’, a temperature below which it is impossible to go since the matter would have zero energy at this point. o 1 C difference in temperature = 1 K temperature difference 273.16 K = 0.01 C & 611 Pa (Triple point of water) o A unique combination of temperature and pressure at which the solid, liquid and vapor phases co- exist at equilibrium Four Basic temperature measurement methods: 1. Thermal expansion: e.g. Hg thermometer 2. Thermoelectricity: e.g. thermocouple 3. Resistance: e.g. thermistor 4. Radiation: e.g. pyrometers Choice of a particular thermometer depends on: o Accuracy o Recording requirements o Control o Requirements o Temperature range o Location (ambient temperature) Thermal Expansion: Liquid-in-glass thermometer: o Based on expansion/contraction of liquid in a glass tube o Hg  freezes @ -39 C  Range: -35 C to 500 C o Alcohol  Range: -70 to 120 C Partial immersion: immersed to an indicated level Complete/Full immersion: entire thermometer is
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