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ตัวตรวจวัดและเคร องบันทก

1

คณะวศวกรรมศาสตร

มหาวทยลัยธรรมศาสตร

Chapter 2Recording systems and sensors

Chapter 2Recording systems and sensors

Recording instruments are used in an electronicmeasurement system to display an output (DQ

o) that is

proportional to the quantity (DQi) being measured.

Transducer Recorder

DQo

DQi

Measurement and Instrumentation



What important?

(1) accuracy (2) easy interpretation (3) rapid process

In general, the characteristics that describe the

behavior of a recording instrument are

1. Input impedance

2. Sensitivity

3. Range

4. Zero drift

5. Frequency response


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Input impedance, ZInput impedance, ZInput impedance z controls the energy removed from the system

by the recording instrument in order to display the input voltage.


Consider a simple dc voltmeter used to measure the voltage v of

a source. The power loss p through the meter is given by

p = v2 / Zm

Transducer+ -

Zm

= R m

+ i Xm

Resistance

Capacitance / Inductance



For dc and quasi-static measurements

Z = R+i X ~ R (since X0)


vi

Zs

Zm

+

-

Transducer

voltage

Thevenin’s equivalent circuit

1+(R s/R

m)

vm

= vi

vm

~ vi

* High impedance is preferred

(R m

>>R s)

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SensitivitySensitivityThe sensitivity S of a voltage recording instrument is given by

a change in voltage being measured

a change in output reading

Example A voltmeter is used to measure the voltages ofa transducer

+ -vi

d


S = = d / viDQi

DQO

S = =DQi

DQO

High sensitivity is required to give sufficiently large d for

accurate readout



RangeRange

The range, which represents the maximum voltage that can be

recorded, is determined from

+ -vi

dr

vi,max

= dr/ S

vi

= d / S

As illustrated by the above equation, when

the sensitivity S is high, the range v i will be low ;

conversely, if

the range is high, the sensitivity will be low.


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Zero driftis a variation in the output of an instrument which is not caused by

any change in the input

Zero input

“0”

Readout

“ 0”

Instabilities in the

circuits of a recorder




Frequency responseFrequency response

Input Out put

Static

Dynamic


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Recording

instrumentvi = Ai exp(jwt) vo = Ao exp(j[wt+f])

Input signal Output indicator

A = amplitude of a signal

f = phase angle

Amplitude distortion

NdB = 20 log10(Ao/Ai)

For instance, a recorder specification indicates that the frequency response is

Within ±3 dB from 0 to 100 Hz





When NdB = +3dB,

Ao/Ai = 103/20= 1.413 Ao=1.413Ai +41%

When NdB = -3dB,

Ao/Ai = 10-3/20= 0.707 Ao=0.708Ai -29%

In general, limits of ± 0.4dB should be maintained to reduce recordererror to less than ± 5%

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Analog recording system



galvanometer

voltmeter Strip chart


Galvanometer


มหาวทยลัยธรรมศาสตร Measurement and Instrumentation

is a device that is used to detect a current.

Torque, T = N I A B sina

where N = a number of turns of the coilI = current

A = cross-sectional area of the current loop

a = angle between the normal of the

cross-sectional area and the magnetic field

Note: In general, the coil is arranged so that a = 0

Torsion spring: T = k q

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Analog Voltage meters



The galvanometer can be used as a dc voltmeter by

inserting a resistor in series with the instrument.

voltmeter

Galvanometer

R

InputDc voltage

V = I x R

Digital recording systems



Transducer

Conditioning

circuits

Amplifier

ADC A/D converter

Analog Digital

Display processing


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1 0 1 1 0 0 1 0

Digital codes


Maximum count C = 2n – 1 (numbers of comparator)

Resolution,R = Vrange / 2n

N-bit binary word permits a count of 2n



R = 10 / 24 = 0.625 v

Example A /D converter

Input ranges from 0 to 10 volts

4-bit converter

C = 24 – 1 = 15

R= 0.625 0 0000

1 0.63 C1 0001

2 1.25 C2 0010

3 1.88 C3 0011

4 2.50 C4 0100

5 3.13 C5 0101

6 3.75 C6 0110

7 4.38 C7 0111

8 5.00 C8 1000

9 5.63 C9 1001

10 6.25 C10 1010

11 6.88 C11 1011

12 7.50 C12 1100

13 8.13 C13 1101

14 8.75 C14 1110

15 9.38 C15 1111

16 10.00

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Example: 4-bit word

Code Count

0000 0

0001 1

0010 2

0011 3

0100 4

0101 5

0110 60111

1000

7

8

Convert the decimal number

3 to binary

2 ) 3 1

2 ) 1 1

0


Convert the binary 0101 to

decimal

= 23x0 + 22x1 + 21x0 + 20x1

= 0 + 4 + 0 + 1

= 5

Digital recording instrument



Digital multi-meter

Data logger

Data acquisition system

Digital oscilloscope


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Sensors and TransducersSensors and Transducers

Sensors are physical elements that employ some natural phenomenon by

which they sense the variable being measured.

Transducers are electromechanical devices that convert a mechanical

change into a change in an electrical signal.

Sensor characteristics for the selection process

1. SizeSmaller is better, because of enhanced dynamic

response and minimum interference with the process

2. Range Extended range is preferred.

3. Sensitivity Higher output devices have the advantage of

requiring less amplification




Sensor characteristics

4. Accuracy

5. Frequency response

6. Stability

Devices that exhibit errors of 1% or less is

preferred.

Wide-response (both static and dynamic

loading) sensors are preferred.

Low drift in output over extended periods of time

and with changes in T and RH is essential.


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Sensors characteristics

7. Temperature limits

8. Economy

9. Ease of application

The ability to operate under a wide

temperature range is important.

Reasonable costs are preferred.


Reliability and simplicity are

significant factors.



Sensors used in transducer designSensors used in transducer design

1. Potentiometer is the slide-wire (or wire-wrapped)

resistor that is used to measure displacements for linear

motion and angles for angular motion.

1. Potentiometer is the slide-wire (or wire-wrapped)

resistor that is used to measure displacements for linear

motion and angles for angular motion.


Vo

= (x / l) Vi

Vo

Vi

xl

slide-wire resistor

D l DV Potentiometer

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2. Differential transformers , based on a variable-

inductance principle, are also used to measure

displacement.

2. Differential transformers , based on a variable-

inductance principle, are also used to measure

displacement.

Vi

Linear Variable Differential Transformer, LVDT


Magnetic

AC

f = 50-25000, Hz

D l DV LVDT



3. Resistance strain gage is a thin metallic-foil grid used

to measure the strain of an object.

3. Resistance strain gage is a thin metallic-foil grid used

to measure the strain of an object.


The strain gage can be adhesively bonded to the surface of a structure. When the structure is

loaded, strains develop and are transmitted to the foil grid. As a result, the resistance of the foil

grid changes in proportion to the load-induced strain.

Force DL DRStrain gage

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3. Resistance strain gage3. Resistance strain gage


R = r L

A

The resistance of a uniform metallic conductor can be expressed as

where r = the specific resistance of the metal

L = the length of the conductor

A = the cross-sectional area of the conductor

Differentiating R and dividing by the resistance R gives

For the case of a uni-axial tensile stress state,

dR

R

d r

r

dL

L

dA

A= + -

e a =dL

L e t = -n

dL

L

Poisson’s ratio




The gage factor (Sg) is

[Sg ~ 2 for metallic strain gauges]

The output of a strain gage (DR) is usually converted to a voltage signal with aWheatstone bridge


Sensitivity of the conductor can be written as

S A = = + (1+2n )DR/R

e a

D r / r e

a

Wheatstone

bridge

Power

supply

DL Strain gage DVoDR

DVi

Sg =DR/R

e

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VO

Vs

Vo = Vs [ - ]

R3R3+Rg

R2R1+R2


If R1=R2=R3=R4=Rg and DR g/R g

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4. Capacitance sensors (cont.)4. Capacitance sensors (cont.)

C +DC = [pF]k K A

h+Dh


If the separation between the head and the target is

changed by an amount Dh, then the capacitance C becomes

which can be written as

However, the impedance of the capacitor is linear in h.

DC/C = -Dh/h1+(Dh/h)

nonlinear relationship

DZC

/ ZC

= Dh / h



5. Piezoelectric sensors5. Piezoelectric sensors

F

q = Sq

x A x p [pC]


A piezoelectric material produces an electric chargewhen it is subjected to a force or pressure.

Sq

= charge sensitivity, A = cross section area of the material, p = applied pressure

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5. Piezoelectric sensors (cont.)5. Piezoelectric sensors (cont.)

vo

= q / C


If the external surfaces of piezoelectric material are coated with metallicelectrodes as shown in the figure, the output voltage vo is developed and related

to the charge q by

or

where

vo

= Svhp

Sv

= voltage sensitivity of the sensor = Sq/kK



6. Resistance temperature sensors6. Resistance temperature sensors

Resistance Temperature Detectors (RTD)

Material: Metals, such as Platinum, Nickel or Copper

Thermistors

Material: Semiconducting materials, such as oxides of copper

, cobalt, manganese, nickel, or titanium

DR/R 0

= c1(T-T

0) + c

2(T-T

0)2 + … + c

n(T-T

0)n

1/T = c1

+ c2ln(R ) + c

3ln3(R ) (3rd order approximation)


The change in resistance of materials with temperature

provide the basis of resistance temperature sensors.

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TemperaturemeasurementsTemperaturemeasurements

Temperature

sensorDT DL , DR, Dv, etc


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1. Expansion methods

D L = a L0 DT

When materials are subjected to temperature changes (D T) they

expand or contract according to

a is the temp. coeff. of expansion [mm/°C]

r c h(a A –a B) (T2-T1)

Metal B

Metal A

r c

h Bimetallic strip


Automobile air conditioning system

Condenser

Evaporator

Compressor

Expansion valve

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Use of bimetallic thermostat in automobile air

conditioning system



2. Electrical Resistance

Resistance thermometers consist of a sensor element that exhibits a

change in resistance with a change in temperature

2.1 Resistance Temperature Detectors (RTD)

A typical RTD consists of a wire coil sensor with

a framework for support and a sheath for protection.

The sensor is a resistive element that exhibits a

resistance-temperature relationship given by the

expression

For a limited range of temperature,


NickelTungsten

Copper

Platinum

°CTem perature

DR/R 0

= c1(T-T

0) + c

2(T-T

0)2 + … + c

n(T-T

0)n

DR/R 0 @ c

1(T-T

0)

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PT 100 temperature probe

Note:RTDs have a high accuracy and a wide operating

range. However, they have a low response time.

PT100s are resistance thermometers which are

fabricated from platinum. The operating temperature

ranges from -200 °C to 850 °C, while the resistance

of PT100 at 0 °C is 100 ohms.




2.2 Thermistors

are fabricated from semiconducting

materials, such as oxides of nickel,

cobalt, or manganese. The resistance-

temperature relationship for a thermistor

can be expressed as

where b is a material constant [K]

T is an absolute temperature [K]

Note: b ranges from 3000 to 5000 K

R = R 0 e b (1/T – 1/T0)

Rt


“The resistance decreases

exponentially with an increase

in temperature”

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*** Thermistors have a high sensitivity, a

fast response time, and good accuracyand resolution. However, they typically

achieve a high precision within a limited

temperature range.


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3. Thermoelectric

(or thermocouple) is a temperature sensor that consists of two different

metals in thermal contact. The thermal contact, called a junction, may

be made by twisting wires together or by welding, soldering, or brazing

two material together. A junction between two metals produces a

voltage related to a temperature difference.

Material A

Material B Material Bemf

Seebeck effect

Junction 2Junction 1


Material A

Material B

Junction

Thermocouple

The operation of a thermocouple is based

on a combination of thermoelectric effects

that produce a small open-circuit voltage

vo when two thermocouple junctions are

maintained at different temperatures.

The voltage vo can be represented by an

equation having the form

where C1 and C2 are thermoelectric

constants



vo = C1(T1-T2) + C2(T12-T2

2)


Seebeck effect is a phenomena in which any

conductor will generate a voltage when it is

subjected to a thermal gradient.

Source:http://www.efunda.com/designstandards/sensors/thermoc

ouples/thmcple_theory.cfm

vo C1(T1-T2)

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Peltier effect occurs when a current flows in the thermocouple circuit.

The presence of the current I in the thermocouple circuit produces thewell-known self-heating effect, where the Joule heat transfer, q,is

However, the Peltier heat transfer, q P

,is in addition to the Joule heating

effect and is given by

q = i2 R [W]

where p AB = Peltier coeff.

Junction 2Junction 1i

Material A

Material B Material B

Peltier effect

vsqp,inqp,out


q P

= p AB

i [W]



Thermoelectric cooling uses the Peltier effect to create a heatflux between the junction of two different types of materials.


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Reference junction

Measuring Junction

T

1

T2

vo




Relationship between voltage and temperature


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Thermocouple probe

(Sheath)

Tip of a probe1. Grounded

2. Ungrounded

3. Exposed


(Thermocouple)

(Insulator)



Characteristics of probe’s tips

Ungrounded tip(separated from the sheath wall

by a layer of insulation)

Grounded tip(direct contact with the sheath wall)

Exposed tip(protrudes outside the sheath wall)

is used in corrosive fluids

where the temperature is

changing slowly.

is used in corrosive fluids

where moderate response is

required.

is used for noncorrosive

gases where rapid response

is necessary.


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4. Radiative Temperature Measurement

employs the principles of radiation to measure surface temperatures

with out contacting the body.

“Radiation” is the electromagnetic waves and particles emitted from the surface of a body.


lmax T = 2898 m m.K

E l

( l , T

)

Radiation power (El

) is related to the absolute temperatureand the wavelength as shown in the above figure

El(l,T)

h = Planck's constant (6.626 x 10-34 Js)

c = Speed of Light (3 x 108 m/s)l = Wavelength (m)

k = Boltzmann Constant (1.38 x 10-23 J/K)

T = Temperature (K)



E T

The power of the radiation Eb

from an ideal (black) surface is obtained from

where

For grey surface,

Eb

=Int[El(l,T),l] = sT4

ET

= e(T) Eb

s = is the Stefan-Boltzmann constant [5.67x10-8 W/m2-K4]

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Radiation Methods

Pyrometer

- Optical pyrometer : compares the brightness of image produced by temperature

source with that of reference temperature lamp.




Radiation Methods

Pyrometer

- Infrared pyrometer : measures a source temperature by measuring the voltageoutput from a temperature detector


Lens

Focusing mirror Temperature detector Focus spot

Surface

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Radiative Temperature Measurement

Advantages

- max temperature up to 3500 C

- non-contact measurement

- no installation

Disadvantages

- accuracy depending one

- relatively high cost




Thermocouple RTD Thermistor

Advantages - self-powered

- simple

- durable

- Wide temp. range

- Wide variety

- inexpensive

- most stable

- most accurate

- more linear

- fast response

- high sensitivity

Disadvantages - non-linear

- low voltage

- Ref. junc. required

- least sensitivity

- least stable

- expensive

- ext. power required

- self-heating

- non-linear

- ext. power required

- Self-heating

- limited temp. range

Advantages and disadvantages

of the most common temperature sensors


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Pressuremeasurements

Pressuremeasurements

Pressure

sensorD P DL , DR, Dc, etc




Pressure represents a contact force per unit area. It acts inward and

normal to the surface of any physical boundary that a fluid contacts.

F

A

F P = [ N/m

2 or Pa]

Pressure scales1. Absolute pressure scale

is the pressure that is quantified relative to the absolute

zero pressure.

2. Gauge pressure scaleis the pressure that is quantified relative to the

atmospheric pressure.


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Absolute

vacuumP

abs= 0

Pvac

Pabs

Patm

Pgage

PabsPatm= 101.325 kPa

= 14.969 psia

= 760 mm Hg abs

Relative pressure scales

absatmvac P P P =

atmabs gage P P P =




Pressure in a moving fluid

Static pressure, Ps

is the pressure exerted by a stationary fluid.The force in the static pressure is due to the

motion of fluid particles (microscopic view)

Dynamic pressure, Pd

represents fluid kinetic energy whichdepends on the fluid motion (macroscopic view).

PT

= P0

= Ps+ P

d

PT

= Total pressure

P0

= Stagnation pressure

Pd

= r V 2 / 2

where


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Automotive pressure sensors

Source: http://www.sensata.com/sensors/automotive-pressure-sensor-ap2.htm



Basic pressure measuring devicesBasic pressure measuring devices

1. Barometer consists of an inverted tube containing a fluidand is used to measure atmospheric pressure.

1. Barometer consists of an inverted tube containing a fluidand is used to measure atmospheric pressure.

h

gh P P P Hg vacuumatm r ==D

gh P Hg atm r =

6.13/2

== O H Hg Hg S r r

At 1 atm, hHg = 760 mm.


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2. Manometer is an instrument used to measure differential

pressure based on the relationship between pressure and the

hydrostatic equivalent head of fluid.

2. Manometer is an instrument used to measure differential

pressure based on the relationship between pressure and the

hydrostatic equivalent head of fluid.

)( 1212 hh g P P P ==D r

A B C

1 2

h

12 P P =Case A

Case B atm P h g P = r 1

Case C h g P P P atmvac r ==1




3. Bourdon-type pressure gage

Bourdon tube (coiled tube) is a curved metal tube having an

elliptical cross section that mechanically deforms under pressure

3. Bourdon-type pressure gage

Bourdon tube (coiled tube) is a curved metal tube having an

elliptical cross section that mechanically deforms under pressure

A-A

ความดัน

Bourdon Gage

atmabs gage P P P =

Patm

0= gage P at 1 atm

0 Pa


Bourdon tube

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Pressure transducerPressure transducer1. Displacement-type

converts a measured pressure into deformation of an

elastic element used in the transducer.

1.1 Diaphragms-type

1.2 Bellows and Capsule


Displacement-type

(elastic element)D P DL



Pressure transducer

1.1 Diaphragm-type utilizes a clamped circular plate as the

elastic element. The deformation of the diaphragm is

converted into electrical signal by either LVDT or strain

gages.

DP DL DVDiaphragm LVDT


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Pressure transducerPressure transducer1.2 Bellows and Capsule are a thin-wall flexible metal tube of which

one end is held fixed and pressure is applied internally. A pressure

difference will cause the change in length of the elastic element.

Bellow

VO

ViDP DL DV

Bellow Potentiometer




Pressure transducerPressure transducer2. Piezoelectric Crystal Elements converts pressure electric

charges. The charge amplifier is used to convert an eletric

charge, q into an output voltage.

P1

P2

Dt

Crystal

Electrode

Electrode

A

*** can be used to measure either quasi-static or dynamic response.

Max pressure up to 100,000 psi

Max temperature ~ 350 C


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Figure 1: In a typical automotive sensor application forManifold Absolute Pressure (MAP), a piezo-electric

pressure sensor and signal conditioning IC link to the

ECU via a 3-wire interconnect.

Manifold absolute pressure sensor (MAP) provides instantaneous manifold pressure informationto the engine's electronic control unit (ECU). The data is used to calculate air density and

determine the engine's air mass flow rate, which in turn determines the required fuel metering foroptimum combustion (see stoichiometry) and influence the advance or retard of ignition timing.

Source:

http://www.eetimes.com/document.asp?doc_id=1272786



Pressure transducerPressure transducer

3. Capacitive pressure sensor uses a diaphragm and

pressure cavity to create a variable capacitor to detect

strain due to applied pressure, capacitance decreasing as

pressure deforms the diaphragm. Common technologies

use metal, ceramic, and silicon diaphragms..


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Velocity

measurements

Velocity

measurements


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Fluid velocity

v(t) = V + v’

where V = mean velocity

v’ = fluctuating velocity

v(t)

t

V

v’

Laminar flow

Turbulent flow

v’ ~ 0

v’ 0

Due to surface roughness, low viscosity, change in direction, inertia




max. at CL.

Fully developed flow


Ideal flow(Uniform distribution)

Frictionless wall Real flow(Parabolic profile)

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Volumetric flow rate, Qis the volume of fluid which passes through a given surface per unit time

Mass flow rate, m

is the mass of fluid which passes through a given surface per unit time

Q = v dA = AV [m3/s]

. m = r v dA = r AV [kg/s]

A = area [m2]

V = mean velocity [m/s]

where




1. Pitot-Static tube1. Pitot-Static tube

Pd

= PT

- Ps

= r lg h

r aV 2 / 2 = r

lg h

Pd

= PT

- Ps

= r lg h

r aV 2 / 2 = r

lg h

hV = [2C

d( r

lg h)/ r

a]1/2

Cd

= dynamic pressure correction

where


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2. Thermal anemometer 2. Thermal anemometer

Hot-wire probe Hot-film probe

The rate at which energy Q is transferred between a warm body at Ts

and a cooler moving fluid at Tf is propotional both to the temperature

difference between them and to the thermal conductance of the heat

transfer path, hA. This thermal conductance increases with fluid velocity,

thereby increasing the rate of heat transfer at any given temperature

difference.




Heat transfer between a hot wire and fluid flow

Qc

= hA (Tw-T

f ) [W]

Qw

= I2R W

[W]

where A and B are constants that depend on the fluid and sensor

physical properties and operating temperature, and n is a constant that

depends on sensor dimensions (typically, 0.45 < n < 0.52)

Convection heat transfer

Heat generated in the wire

It is known that the heat transfer coefficient h is related to fluid velocity V by

h = A + B Vn


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Material used for hot-wire and hot-film sensors exhibit a change inresistance with temperature change. The relationship can be expressed as

Equating Qw with Qc, we obtain

From the above equation, it is evident that the fluid velocity V can be written

as

R w

= R 0[1 + g (T

w – T

0)]

i2R

0[1 + g (T

w – T

0)] = (a + b Vn ) A (T

w-T

f )

V = f (i, Tw, Tf )



Therefore, if Tf is known then the fluid velocity is determined by

measuring either

1) the resistance Tw

[constant–current bridge-anemometer system]

or

2) the current i [constant–temperature bridge-anemometer system]

V = f (i, Tw, T

f )

measured by

temperature transducer

kept constant

V = f (Tf,T

w)

V = f (i, Tw, T

f )

measured by

temperature transducer

kept constant

V = f (Tf, i)

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Hotwire

Variable resistor V

Q = I2R

w


Constant-current bridge

Constant –current bridge-anemometer system

In this circuit, R2

and R3

are much larger than sensor Resistance Rw; therefore,

current i is essentially independent of changes in the sensor resistance Rw.

R4

R2 R3

C

constant current

source, is

Vo @ ½ i

sR

w(DR

w/R

w)

Vo



Constant –temperature bridge-anemometer system

An adjustable current source is used in order to maintain a constant

temperature, Tw

(i.e. Rw

is constant). The fluid velocity is a function of input current

and flow temperature, Tf .

Variable

resistor

G

VQ = I

2R

w

V = C0

[(i/i0)2-1]2

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Hotwire anemometer

Advantages

1. Can be used to measure a point velocity

2. Can be used to measure fluctuating velocity (Turbulent) (up to 500 kHZ)

3. High sensitivity (Hot-film is less sensitive)

Disadvantages

1. Fragile (Hot-film is more sturdy)

2. Can not be used in conducting fluids (Hot-film can)3. Expensive


HW#4

4.1 Consider a deflection bridge, which initially has all arms ofthe bridge equal to 100 ohms, with the resistance temperature

sensor at Rg. The supply voltage is 10 V. If the temperature of

Rg is changed such that the bridge output is 0.569 V, what is

the temperature of the sensor? How much current flows

through the sensor and how much power must it dissipate?

R g= R

0[1+0.00395(T-T

0)]

DVout

= Vin

DR g/R

g

42(DR g/R

g)

where R 0

= 100 and T0= 0 C

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4.2 A piezoelectric pressure transducer as shownin figure is used to measure the pressure of air

in a tank by generating analogue signals, and

it is to be calibrated by measuring both the

pressure and the electric current

simultaneously for various settings. If the

relationship between the pressure and the

corresponding current is given by

P = 13.00 I - 51.00

where P = pressure in a tank [kPa],

I = current [mA],

Determine (a) the sensitivity of the transducer,

(b) zero offset, and (c) Dh if I = 10 mA



3. Laser Doppler Anemometer 3. Laser Doppler Anemometer

is a measuring device that utilizes the “Doppler effect” to measurethe local velocity in a moving fluid. In this technique, the light is emitted

from a source and travels toward the light detector. The light is splitted

by the beam splitter. The lights are then combined to produce the beat

signal (fringe).

fringe

l

q d

l

2 sin (q/2)d =

d = fringe spacing


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Relationship between laser frequency and fluid velocity

V = f D

d

f s= f

i± f

DLaser frequency

where f i

= frequency of incident laser

f s

= frequency of scattered light

f D

= Doppler shift

Fluid velocity

LDA


As a moving particle suspended in the fluid passes through the laser beam,

it scatters light in all directions. The light detector will perceive the

scattered light at a frequency, f s:

The velocity is related directly to the Doppler shift by



Laser Doppler Anemometer

Advantages

1. The flow is not disturbed by the presence of a probe. (non-intrusive

measurement)

2. Velocity is measured directly, and calibration is not required.

3. The method is suitable for a wide range of velocities.

4. A component of velocity in a specified direction can be measured.

5. The relationship between input and output is linear.

d


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Flowmeasurements

Flowmeasurements




1. Rotameter 1. Rotameter

Rotameter

The meter consists of a float within a vertical

tube, tapered to an increasing cross-sectional area

at its outlet. Flow entering through the bottom

passes over the float, which is free to move. The

equilibrium height of the float indicates the flow rate.

The operating principle is based on the balancebetween the drag force, the weight, and buoyancy

force acting on the float.

SF: FD + FB = mg

Cd = drag coefficient AF = cross-sectional area of a float

V = average velocity past the float

where FB = Buoyancy force

FD = Drag force = Cd r V2 AF / 2


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Volumetric flowrate, Q = V Aa(y) = K Aa(y)

where Aa(y) is the annular area between the float and the tube

V is the average velocity past the float

K is a meter constant

W

FD

FB

*** error ± 2% turndown ratio 10:1


V = [2 ( r F r ) g / (Cd r AF )]1/2



2. Pressure differential meters2. Pressure differential meters

1 2

Dh

)1(

222 b r

D=

f

d

P C AQ

1

2

A

A= b

h g P D=D m r

f r

m r

are based on the relationship between volume flow rate and the

pressure drop.

Cd = discharge coefficient

= f (Re, b)


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2. Pressure differential meters (cont.)2. Pressure differential meters (cont.)

*** simple, inexpensive, but resulting in high pressure losses.


2.1 Orifice meter

consists of a circular plate, containing a hole (orifice),which is inserted

Into a pipe such that the orifice is concentric with the pipe inside diameter.



*** require large installation space and

most expensive but least pressure losses

2. Pressure differential meters (cont.)2. Pressure differential meters (cont.)


2.2 Venturi meter

consists of a smooth converging contraction to a narrow throat

followed by a shallow diverging section as shown.

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2. Pressure differential meters (cont.)2. Pressure differential meters (cont.)2.3 Flow Nozzle

consists of a gradual contraction to to a narrow throat.


*** require less installation space than a venturi and has about 80% of initial cost.



3. Turbine meters3. Turbine meters

make use of angular momentum principles to

measure flow rate. A rotor is encased within a

bored housing through which the fluid to bemeasured is passed. The exchange of

momentum between the flow and the rotor turns

the rotor at a rotaional speed that is proportinal to

the flow rate as following

Q = K wwhere K is a meter constantw is an angular velocity

*** low pressure losses

error ± 0.25% turndown ratio 20:1


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4. Ultrasonic flow meters4. Ultrasonic flow meters

use sound waves to determine flow rate.

D V s,0

D V f,//

V f

V f, V s,o

Transmitter

receiver

)( ,o s s f V V AV AQ ==




4. Ultrasonic flow meters (cont.)4. Ultrasonic flow meters (cont.)

Advantages

1. The flow is not disturbed by the presence of a probe. (non-intrusive

measurement)

2. No pressure losses.

3. A large diameter pipe can be measured.

Sensor locationSensor location

Upstream > 10 D

Downstream > 5

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Humiditymeasurements

Humiditymeasurements

Humidity

sensorHumidity DL , DR, Dk etc




Relative Humidity, RH

is a measurement of the

amount of water vapor in a

mixture of air and water

vapor, defined as the partial

pressure of water vapor in the

air-water mixture, given as a

percentage of the saturated

vapor pressure under those

conditions

Humidity sensor

1. - Traditional hair of horse or human with

a strain gauge or a water absorbent polymer

which stretches and shrinks according to RH.

2. Capacitive RH sensor

3. Resistive RH sensor

4. Thermal conductivity

LD RH % Traditional hair

C D RH % Capacitive RH sensor

RD RH % Resistive RH sensor

k D RH %Thermal conductivity

RH sensor


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thin film of polymer or metal oxide is deposited

between two conductive electrodes



ั ศ ส

ทาจาก hygroscopic medium เชน Polymermeasure the absolute humidity by quantifying the

difference between the thermal conductivity of dry air

and that of air containing water vapor


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