1

Transducers and Measurement systems

By: Yidnekachew Messele

1

Linear Displacement Is defined as specified distance in a specified

direction It is measured in length units such as meters,

kilometers etc. Symbol is s

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Measuring Linear Displacement Very small displacements:

Strain Gauges Capacitive Sensorsp Inductive Sensors (LVDT)

Medium displacements Slide Wire / Film Wire wound potentiometer

Large Displacements (above range of most ‘pure’ linear d )transducers)

Convert linear to angular motion and measure the angular motion with an angular displacement transducer

Measure velocity and integrate signal to obtain displacement

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Linear Displacement - Resistive Methods

Resistance is defined by thefollowing equation

Therefore if the length, thicknessor resistivity of an objectchanges with respect todi l t th

AlR

displacement we can use theresistance as a way to measure it

4

2

Linear Displacement - Resistive Methods

(Slide Wire/Film) This is the simplest way of measuring displacement between a

moving and a stationary objectg y j A piece of wire or film is connected to a stationary object A slide, which makes contact with the wire, is attached to the

moving object This acts as a very basic potentiometer

5 6

Slide Wire Range

± 1 – 300mm

Advantages Simple Good Resolution Low Cost

Disadvantages Wire does not have high resistance, film is better (±200 to 500Ω/cm) Wear Frictional Loading Inertial Loading

7

Linear Displacement - Resistive Methods (Wire

Wound Potentiometer)

Wire Wound potentiometersuse the same principle asuse the same principle asslide wire sensors exceptthat they use a coil ofinsulated resistance

The slider runs on onesurface of the coil that is notsurface of the coil that is notinsulated

8

3

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PotentiometerLinear potentiometer is a device in which the resistance varies as a function of the position of a slider.

Vex

V=0 to VexRp

Rx

maxRR

exRR

pmax

x

xx

VV

Rx

xR

x

p

x

xmax xV

maxVV

maxR

xx

xx

ex

p

X can also be the degrees of turns.

10

Potentiometers Resolution

± 1mm – 4m Advantages Advantages

Simple Robust

Disadvantages Resolution dependant on wire diameter Continuous use over portion of the wire will cause wear

F i ti l L di Frictional Loading Inertial Loading

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Linear Displacement - Resistive Methods (Strain

Gauges)

Attach the strain gauge to the objecth h bj i i i d i ill l i When the object is in tension or compressed it will result in a

change in the resistance of the strain gauge

This is used to measure the change in length of the object

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4

Strain Gauges

Advantages: Relatively easy to understand and attach Cheap

Disadvantages Need temperature compensation

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Linear Displacement - Capacitive Methods

Capacitance is defined as Therefore we could use the AC r 0

change in Plate Area Permittivity of the dielectric Distance between the plates

as a way to measure

dC

ydisplacement

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Linear Displacement - Capacitive Methods

(Variable Area)

If we have an two electrodes and one moves relative to the other in a lineardirection we will get an effective change in the area of the platesdirection we will get an effective change in the area of the plates

This results in a change in the capacitance which can be related todisplacement

d

wxAC r 0

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Linear Displacement - Capacitive Methods

(Distance Between the Plates)

If we have to electrodes, one fixed and the other movable wecan arrange it that the distance between the plates changes fora change in displacement

xAC r 0

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5

Linear Displacement - Capacitive Methods

(Distance Between the Plates)

This type of capacitive arrangementconsists of two fixed outer plates andpone central moveable plate

The central plate can move towardseither of the plates which essentiallychanges the capacitance between themoveable plate and the fixed plates

If the moveable plate is in the centreof the capacitor voltages V1 and V2of the capacitor, voltages V1 and V2will be equal

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Linear Displacement - Capacitive Methods

(Permittivity)

The dielectric moves relative to the plates and this causes a h i th l ti itti it f th di l t ichange in the relative permittivity of the dielectric

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Linear Displacement - Inductive Methods

Inductive methods use very similar principles to resistive andcapacitive methods

The inductance of a coil is given by the following equation The inductance of a coil is given by the following equation

Where N is the number of turns in the coil, µ is the effectivepermeability of the medium in and around the coil, A is thecross sectional area and l is the length of the coil in m

][ Henrys l

ANL 2

cross sectional area and l is the length of the coil in m As with the other examples if we change any one of these

parameters we get a change in the inductance

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Linear Displacement - Inductive Methods

(Linear Variable Differential Transformers LVDTs)

LVDTs are accurated hi htransducers which are

often used in industrialand scientific applicationsto measure very smalldisplacementsdisplacements

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6

Linear Displacement - Inductive Methods

(Linear Variable Differential Transformers LVDTs)

An LVDT consists of a centralprimary coil wound over the wholeprimary coil wound over the wholelength of the transducer and twoouter secondary coils

A magnetic core is able to movefreely through the coil

The primary windings are energized The primary windings are energizedwith a constant amplitude ACsignal (1 – 10kHz)

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This produces an alternating magnetic field which induces asignal into the secondary windings

The strength of the signal is dependant on the position of thecore in the coils

When the core is placed in the centre of the coil the output will When the core is placed in the centre of the coil the output willbe zero

Moving the coil in either direction causes the signal to increase The output signal is proportional to the displacement

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Linear Variable-Differential Transformer (LVDT)

Vo=V1-V2

-x

V1 V2

V1 V2 Vi

LVDTs are devices to measure displacementby modifying spatial distribution of analternating magnetic field.

Vi

V1 > V2 Vi

Vo

Oscillating excitation voltage-50 Hz to 25 kHz 23

Linear Variable-Differential Transformer (LVDT)

Vo=V1-V2

X=0

V1 V2

V2 = V1Vi

Vi

Vi

Vo24

7

Linear Variable-Differential Transformer (LVDT)

Vo=V1-V2

+x

V1 V2

V2 > V1Vi

Vi

Vi

Vo

So, the direction of displacement can be determined from the relative phase of the signal. 25

LVDTs Range: ±2.5nm - ±10cm Advantages: Advantages: Good resolution

Disadvantages: Needs shielding to prevent interference from magnetic

sourcessources

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Force, Torque and Tactile o ce, o que and actileSensors

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Force Sensors The fundamental operating principles of force, acceleration, and

torque instrumentation are closely allied to the piezoelectric andstrain gage devices used to measure static and dynamic pressures.

Piezoelectric sensor produces a voltage when it is "squeezed" by aforce that is proportional to the force applied.

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8

Difference between these devices and static force detectiondevices such as strain gages is that the electrical signal generatedby the crystal decays rapidly after the application of force.

The high impedance electrical signal generated by thepiezoelectric crystal is converted to a low impedance signalpiezoelectric crystal is converted to a low impedance signalsuitable for such an instrument as a digital storage oscilloscope.

Depending on the application requirements, dynamic force canbe measured as either compression, tensile, or torque force.

Applications may include the measurement of spring or slidingf i ti f h i t i l t h l ffriction forces, chain tensions, clutch release forces.

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Torque Sensors Torque is measured by either sensing the actual shaft deflection

caused by a twisting force, or by detecting the effects of thisdeflection.

The surface of a shaft under torque will experience compressionand tension, as shown in Figure.

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To measure torque, strain gage elements usually are mounted inpairs on the shaft, one gauge measuring the increase in length (inthe direction in which the surface is under tension), the othermeasuring the decrease in length in the other direction.

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Force/Torque Measurement Force and torque measurement finds application in many

practical and experimental studies as well as in controlapplications.F i li Wh i f i b i i l Force-motion causality. When measuring force, it can be criticalto understand whether force is the input or output to the sensor.

Design of a force sensors relies on deflection, so measurement ofmotion or displacement can be used to measure force, and in thisway the two are intimately related.

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Design of a Force Sensor Consider a simple sensor that is to be developed to measure a

reaction force at the base of a spring, as shown below.

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In the force sensor design given, no specific sensingmechanism was implied. The constraint placed on thestiffness exists for any type of force sensor

Sensor Mechanisms for Force

stiffness exists for any type of force sensor. It is clear, however, that the force sensor will have to respond

to a force and provide an output voltage. This can be done indifferent ways.

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Sensing Mechanisms To measure force, it is usually necessary to design a

mechanical structure that determines the stiffness. Thisstructure may itself be a sensing material.F ill i d l di i hi h b Force will induce stress, leading to strain which can bedetected, most commonly, by– strain gages (via piezoresistive effect)– some crystals or ceramics (via piezoelectric effect)

Force can also be detected using a displacement sensor, suchas an LVDTas an LVDT.

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Strain-gage Force Sensor Design Let’s consider now the force sensor studied earlier, and

consider a design that will use one strain gage on an axiallyl d d i lloaded material.

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Strain guages

Many types of force\torque sensors are based on strain gage measurementsmeasurements.

The measurements can be directly related to stress and force and may be used to measure other types of variables including displacement and acceleration

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What’s a strain gauge? The electrical resistance of a length of wire varies in direct

proportion to the change in any strain applied to it. That’s theprinciple upon which the strain gauge works.

The most accurate way to measure this change in resistance isby using the wheatstone bridge.

The majority of strain gauges are foil types, available in a widechoice of shapes and sizes to suit a variety of applications.

They consist of a pattern of resistive foil which is mounted ona backing material.g

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They operate on the principle that as the foil is subjectedto stress, the resistance of the foil changes in a definedway.

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Strain gauge Configuration The strain gauge is connected

into a wheatstone Bridge circuitwith a combination of fouractive gauges(full bridge),twoguages (half bridge) or,lesscommonly, a single gauge(quarter bridge).

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Guage factor

A fundamental parameter of the strain guage is its i i i i d i i l hsensitivity to strain, expressed quantitatively as the

guage factor (GF).

Guage factor is defined as the ratio of fractional h i l i l i h f i l hchange in electrical resistance to the fractional change

in length (strain).

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Strain guage contd.. The complete wheatstone brigde is excited with a stabilized

DC supply. As stress is applied to the bonded strain guage, a resistive

change takes place and unbalances the wheatstone bridgewhich results in signal output with respect to stress value.

As the signal value is small the signal conditioning electronicsprovides amplification to increase the signal.

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Ballast circuit

Assume a simple signal di i i i iconditioning circuit, a

ballast circuit, will be used to convert resistance change in strain guage to voltagestrain guage to voltage change.

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Analysis of Force sensors

The ballast circuit output is given by :output is given by :

Under strain the gage resistance change is:

Where G is the “gage factor”. The change in the output voltage is :

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Sensitivity of Force sensor

We can now express theoutput voltage change inoutput voltage change interms of sensitivity as :

Where sensitivity is givenby :

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Torque Sensor Torque is a measure of the forces that causes an object to

rotate. Reaction torque sensors measure static and dynamic torque

with a stationary or non-rotating transducer. Rotary torque sensors use rotary transducers to measure

torque.

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Technology Magnetoelastic : A magnetoelastic torque sensor detects changes

in permeability by measuring changes in its own magnetic field. Piezoelectric : A piezoelectric material is compressed andp p

generates a charge, which is measured by a charge amplifier. Strain guage : To measure torque,strain guage elements usually

are mounted in pairs on the shaft,one guage measuring theincrease in length the other measuring the decrease in the otherdirection.

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Figures showing Torque sensors

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Torque Measurement The need for torque measurements has led to several methods of

acquiring reliable data from objects moving. A torque sensor, ortransducer, converts torque into an electrical signal.

Th t t d i t i th t t t i t The most common transducer is a strain guage that converts torque into achange in electrical resistance.

The strain guage is bonded to a beam or structural member that deformswhen a torque or force is applied.

Deflection induces a stress that changes its resistance. A wheatstonebridge converts the resistance change into a calibrated output signal.g g p g

The design of a reaction torque cell seeks to eliminate side loading(bending) and axial loading, and is sensitive only to torque loading.

The sensor’s output is a function of force and distance, and is usuallyexpressed in inch-pounds, foot-pounds or Newton-meters.

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Classification of torque sensors Torques can be divided into two major categories, either static or

dynamic. The methods used to measure torque can be further divided into two

i i h i i limore categories, either reaction or in-line. A dynamic force involves acceleration, were a static force does not. In reaction method the dynamic torque produced by an engine would be

measured by placing an inline torque sensor between the crankshaft andthe flywheel, avoiding the rotational inertia of the flywheel and anylosses from the transmissionlosses from the transmission.

In-line torque measurements are made by inserting a torque sensorbetween torque carrying components, much like inserting an excitationbetween a socket and a socket wrench.

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Technical obstacles

Getting power to the gages over the tationary/rotating d i h i l b kgap and getting the signal back.

The methods to bridge the gap are either contact or non-contact.

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Contact/Non-contact methods Contact: slip rings are used in contact-type torque sensors to

apply power to and retrive the signal from strain gagesd h i h fmounted on the rotating shaft.

Non-contact: the rotary transformer couples the strain gagesfor power and signal return. The rotary transformer works onthe same principle as any conventional transformer excepteither the primary or secondary coils rotate.

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Applications of force/torque sensors In robotic tactile and manufacturing applications In control systems when motion feedback is employed. In process testing, monitoring and diagnostics applications. In measurement of power transmitted through a rotating

device. In controlling complex non-linear mechanical systems.

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Pressure Measurements

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Pressure definition Pressure is the action of one force against

th f Th P fanother over, a surface. The pressure P of a force F distributed over an area A is defined as:

P = F/A

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Pressure definition Pressure is the action of one force against another over, a

surface. The pressure P of a force F distributed over an area A isdefined as:

P = F/A

System Length Force Mass Time Pressure

MKS Meter Newton Kg Sec N/M2 = Pascalg /

CGS CM Dyne Gram Sec D/CM2

English Inch Pound Slug Sec PSI

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How Much is a Pascal (Pa) 1 atmosphere (14.7 psi, 750mmHg) is approximately

100 kPa = 1 bar 1 kPa is about 7 mmHg 1% of a gas at our altitude is about 7 mmHg

How is pressure generated? Collision of molecule with wall

M i l i Momentum is mass x velocity Sum collisions over area to get force

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Static, Dynamic, and Impact pressures

Static pressure is the pressure of fluids or gases that are stationary or not in motion.

Dynamic pressure is the pressure exerted by a fluid or gas when itimpacts on a surface or an object due to its motion or flow. In Fig.,impacts on a surface or an object due to its motion or flow. In Fig.,the dynamic pressure is (B − A).

Impact pressure (total pressure) is the sum of the static anddynamic pressures on a surface or object. Point B in Fig. depictsthe impact pressure.

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Definition Of Pressure

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Definition Of Pressure Absolute pressureThe pressure is referenced to

zero absolute. Absolutepressure can only have apositive value.

Gauge pressureThe pressure is referenced to

atmospheric pressure and byconvention is measured inthe positive direction.

Vacuum pressurepThe pressure is referenced to

atmospheric pressure and byconvention is measured inthe negative direction.

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Standard Atmospheric Pressure

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Pressure MeasurementA number of measurement units are used for pressure. They are as follows:1. Bar (1.013 atm) = 100 kPa2. Pascals (N/m2) or kilopascal (1000Pa)*3 Pounds per square foot (psf) or pounds per square inch (psi)

1 psi= 51.714 mmHg= 2.0359 in.Hg3. Pounds per square foot (psf) or pounds per square inch (psi)

4. Atmospheres (atm)5. Torr = 1 mm mercury6. Pascals (N/m2) or kilopascal (1000Pa)

Pressure Units As previously noted, pressure is force per unit area and historically a great

variety of units have been used depending on their suitability for the

= 27.680 in.H2O= 6.8946 kPa

1 bar= 14.504 psi1 atm. = 14.696 psi

variety of units have been used, depending on their suitability for theapplication.

For example, blood pressure is usually measured in mmHg becausemercury manometers were used originally.

Atmospheric pressure is usually expressed in in mmHg for the same reason. Other units used for atmospheric pressure are bar and atm.

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Wet Meters (Manometers)

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Manometer basics Characterized by its inherent accuracy and simplicity of

operation. It’s the U-tube manometer, which is a U-shaped glass tube

partially filled with liquidpartially filled with liquid. This manometer has no moving parts and requires no calibration. With both legs of a U-tube manometer open to the atmosphere

or subjected to the same pressure, the liquid maintains the samelevel in each leg, establishing a zero reference.

With a greater pressure applied to the left side of a U-tubemanometer, the liquid lowers in the left leg and rises in the rightleg.

The liquid moves until the unit weight of the liquid, as indicatedby h, exactly balances the pressure.

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Pressure in open tankA container filled with a liquid has a pressure (due to the weight of the liquid) at a point in the liquid of:

P = F/AP = W/AP = ρgV/AP = ρghA/AP = ρgh

P = pressureF = force A

h

A = AreaW = weight of the liquid V = volume above the Areag = gravitationρ = mass densityh = distance from the surface

A

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When the liquid in the tube is mercury, for example, theindicated pressure h is usually expressed in inches (ormillimeters) of mercury. To convert to pounds per squareinch (or kilograms per square centimeter), P2 = ρh

Where P2 = pressure, (kg/cm2)ρ = density, (kg/cm3)h = height, (cm)

Gauge pressure is a measurement relative to atmosphericpressure and it varies with the barometric reading.

A gauge pressure measurement is positivewhen the unknown pressure exceedswhen the unknown pressure exceedsatmospheric pressure (A), and is negativewhen the unknown pressure is less thanatmospheric pressure (B).

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Variations on the U-Tube Manometer The pressure reading is always the

difference between fluid heights,regardless of the tube sizes.

With both manometer legs open tothe atmosphere, the fluid levels arethe same (A).

With an equal positive pressureapplied to one leg of eachpp gmanometer, the fluid levels differ,but the distance between the fluidheights is the same (B).

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Reservoir (Well) Manometer In a well-type manometer, the cross-sectional area of one

leg (the well) is much larger than the other leg. Whenpressure is applied to the well, the fluid lowers only slightlyp pp y g ycompared to the fluid rise in the other leg.

In this design one leg is replaced by a large diameter well sothat the pressure differential is indicated only by the heightof the column in the single leg.

The pressure difference can be read directly on a singlescale. For static balance, If the ratio of A /A is small,

Where A1 = area of smaller-diameter leg A2 = area of well

2 1 1 2(1 / )P P A A h If the ratio of A1/A2 is smallcompared with unity, then theerror in neglecting this termbecomes negligible, and thestatic balance relation becomes

2 1P P h 69

Pressure Sensing Pressure is sensed by mechanical

elements such as plates, shells, and tubesthat are designed and constructed todeflect when pressure is applied.

Pressure

Sensing Elementp pp

This is the basic mechanism convertingpressure to physical movement.

Next, this movement must be transducerto obtain an electrical or other output.

Finally, signal conditioning may beneeded, depending on the type of sensorand the application Figure illustrates the Signal

Transduction element

displacement

electric

and the application. Figure illustrates thethree functional blocks.

Signal Conditioner

V or I output70

The main types of sensing elements are Bourdon tubes, diaphragms, capsules, and p bellows .

All except diaphragms provide afairly large displacement that isuseful in mechanical gauges andfor electrical sensors that requirea significant movement.g

The basic pressure sensing element can be configured as a C-shaped Bourdontube (A); a helical Bourdon tube (B); flat diaphragm (C); a convoluteddiaphragm (D); a capsule (E); or a set of bellows (F).

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Primary Pressure Elements Capsule, Bellows & Spring Opposed Diaphragm

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Bellows

In general a bellows can detect a slightly lower pressure than a diaphragmdiaphragm

The range is from 0-5 mmHg to 0-2000 psi Accuracy in the range of 1% span

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Bourdon Tube In “C” type Bourdon tube, a section of tubing that is closed at

one end is partially flattened and coiled. When a pressure is applied to the open end, the tube uncoils. This movement provides a displacement that is proportional to This movement provides a displacement that is proportional to

the applied pressure. The tube is mechanically linked to a pointer on a pressure dial

to give a calibrated reading.

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20

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Bourdon Tubes

(a) C-type tube.(b) Spiral tube. (c) Helical tube

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Bourdon Tubes

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Diaphragm Gauges To amplify the motion that a diaphragm capsule produces, several

capsules are connected end to end. Diaphragm type pressure gauges used to measure gauge, absolute, or

diff ti ldifferential pressure. They are normally used to measure low pressures of 1 inch of Hg, but

they can also be manufactured to measure higher pressures in the rangeof 0 to 330 psig.

They can also be built for use in vacuum service.

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Diaphragm

A diaphragm usually is designed so that the deflection-versus-(a) flat diaphragm; (b) corrugated diaphragm

p g y gpressure characteristics are as linear as possible over aspecified pressure range, and with a minimum of hysteresisand minimum shift in the zero point.

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CapsuleA capsule is formedby joining theperipheries of twodiaphragms throughsoldering or welding.

Used in some absolutepressure gages.

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Use of capsule element in pressure gage

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Potentiometric type sensor A mechanical device such as a diaphragm is used to

move the wiper arm of a potentiometer as the input pressure changes.

A direct current voltage (DC) V is applied to the topA direct current voltage (DC) V is applied to the topof the potentiometer, and the voltage that is droppedfrom the wiper arm to the bottom of the pot is sentto an electronic unit.

It normally cover a range of 5 psi to 10,000 psi. Can be operated over a wide range of temperatures.

S bject to ear beca se of the mechanical contact Subject to wear because of the mechanical contactbetween the slider and the resistance element.

Therefore, the instrument life is fairly short, andthey tend to become noisier as the pot wears out.

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Bellows Resistance Transducer Bellows or a bourdon tube with a

variable resistor. Bellow expand or contract causes the Bellow expand or contract causes the

attached slider to move along theslidewire.

This increase or decrees theresistance.Th i di ti i Thus indicating an increase ordecrease in pressure.

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Inductance-Type Transducers The inductance-type transducer consists of three parts: a coil, a

movable magnetic core, and a pressure sensing element. An AC voltage is applied to the coil, and, as the core moves,

the inductance of the coil changes.

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LVDT Another type of inductance transducer, utilizes two coils

wound on a single tube and is commonly referred to as aDifferential Transformer or sometimes as a Linear VariableDifferential Transformer or sometimes as a Linear VariableDifferential Transformer (LVDT).

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Piezoelectric Piezoelectric elements are bi-directional transducers capable of

converting stress into an electric potential and vice versa. One important factor to remember is that this is a dynamic

effect providing an output only when the input is changingeffect, providing an output only when the input is changing. This means that these sensors can be used only for varying

pressures. The piezoelectric element has a high-impedance output and

care must be taken to avoid loading the output by the interfaceelectronics. Some piezoelectric pressure sensors include aninternal amplifier to provide an easy electrical interfaceinternal amplifier to provide an easy electrical interface.

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•Piezoelectric sensors convert stress intoan electric potential and vice versa.•Sensors based on this technology areused to measure varying pressures.

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Strain Gauge Pressure Sensors Strain gauge sensors originally used a metal diaphragm with strain gauges

bonded to it. the signal due to deformation of the material is small, on the order of 0.1% of

the base resistance Semiconductor strain gauges are widely used, both bonded and integrated

into a silicon diaphragm, because the response to applied stress is an order ofmagnitude larger than for a metallic strain gauge.

When the crystal lattice structure of silicon is deformed by applied stress, theresistance changes. This is called the piezoresistive effect. Following aresome of the types of strain gauges used in pressure sensors.D i d i M lli i b f d di h Deposited strain gauge. Metallic strain gauges can be formed on a diaphragmby means of thin film deposition. This construction minimizes the effects ofrepeatability and hysteresis that bonded strain gauges exhibit. These sensorsexhibit the relatively low output of metallic strain gauges.

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Range of Elastic-Element Pressure Gages

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Dead-weight pressure gauge A cylindrical piston 1 is placed inside a stainless-steel cylinder 2. The measuring pressure is supplied through the vent 8 to the fluid 4. The gravitational force developed by calibrated weights 3 can balance this

force and the piston itself..Th b l h ld b hi d f t i iti f th i t i t The balance should be achieved for a certain position of the piston against a pointer 9 of the stainless-steel cylinder.

A manual piston pump 5 is used to achieve approximate force balance (to increase pressure in the system), whereas a wheel-type piston pump 6 serves for accurate balancing.

A Bourdon-type pressure gauge 7 is used for visual reading of pressure.3

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1

2

4

5

6

7

8

2

96

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Calibration of Pressure Sensing Devises

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Flow MeasurementFlow Measurement

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Since 1989 there were at least 23 distinct type offor technologies available the measurement offlow in closed conduit.

Flow meters selection are part of the basic art of Flow meters selection are part of the basic art ofthe instrument engineer, and while only handfulof these technologies contribute to the majority ofinstallations.

And wide product knowledge is essential to findthe most cost effective solution to any flowmeasurement application.

99

Types of Flows Reynolds Number

The performance of flow meters is also influenced by a dimensionlessunit called the Reynolds Number. It is defined as the ratio of the liquid'sinertial forces to its drag forces.

The Reynolds number is used for determined whether a flow is laminaror turbulent. Laminar flow within pipes will occur when the Reynolds number is below the critical

Reynolds number of 2300 and turbulent flow when it is above 2300. The value of 2300 has been determined experimentally and a certain range around

this value is considered the transition region between laminar and turbulent flow.g

100

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Venturi Meter

In the venturi meter velocity is increased and the pressure decreasedin the upstream cone.Th d f i F I b d hThe pressure drop from points F to I can be used to measure the rateof flow through the meter.Venturi meters are most commonly used for liquids, especiallywater.

101

Ventrui meter

Mass Balance

22

ba

bb

a

bba V

DDV

SSVV

102

Venturi MeterMechanical Energy Balance

hVVW 11ˆ 22 fabaabb hppzgVVW

2

22

0 00

abbb

ppV

224

So with Mass Balance Result

bab V

103

Venturi Meter

ba ppV 21

Solving for the neck velocity Vb

ba

ab

bppV

4

To account for small differences in a and b introduce a correction factor Cv= 0.98 – 0.99. bav

bppCV

2

bV

1 4

104

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Venturi MeterSince friction cannot be eliminated in the venturi meter a permanent loss inpressure occurs. Because of the small angle of divergence in the recoverycone, the permanent pressure loss is relatively small (about 10% of theventuri differential p –p )venturi differential pa–pb).

105

Orifice Meter

The orifice meter consists of an accurately machined and drilled plateconcentrically mounted between two flanges. The position of the pressuretaps is somewhat arbitrary.

106

Orifice MeterThe orifice meter has several practical advantages when compared to venturi meters.p• Lower cost• Smaller physical size• Flexibility to change throat to pipe diameter ratio to

measure a larger range of flow ratesDisadvantage:Disadvantage:• Large power consumption in the form of irrecoverable

pressure loss

107

Orifice MeterThe development of the orifice meter equation is similar to that of the venturi meter and gives:

2 ppC

0

40 2

1

SVq

ppCV ba

where: = ratio of orifice diameter to pipe diameter ≈ 0.5 usually p p yS0 = cross sectional area of orificeV = bulk velocity through the orificeC0 = orifice coefficient ≈ 0.61 for Re > 30,000–

108

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There is a large pressure drop much of which is not recoverable. This can be a severe limitation when considering use of an orifice meter.

109 110

111

ComparisonVenturi Orifice

High Capital Cost Low Capital Cost

Low Operating Cost(good p recovery)

High Operating Cost(poor p recovery)

Not Flexible(β fixed)

More Flexibility(interchangeable)(β fixed) (interchangeable)

Large Physical Size Compact

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RotametersRotameters fall into the category of flow measurementdevices called variable area meters.

These devices have nearly constant pressure and dependon changing cross sectional area to indicate flow rate.

Rotameters are extremely simple, robust devices that canmeasure flow rates of both liquids and gasses.

Fluid flows up through the tapered tube and suspends a‘float’ in the column of fluid. The position of the floatindicates the flow rate on a marked scale.

113

RotametersThree types of forces must be accounted for when analyzing rotameter performance:y g p

• Flow• Gravity• Buoyancy

Buoyancy

Gravity

F l i l t d ff t

Flow

For our analysis neglect drag effect

114

RotameterMass BalanceAssume Gradual Taper

SQVV

SVSV

21

21

Flow Between Float and Tube

313 S

SVSS

QVf

S3 is annular flow area at plane 3115

RotameterMomentum BalanceNote:• p = p• p3 = p2• Must account for force due to float

fff gVVzSgSppVVQ 2113

2

bf

SgV

SS

SQzgp

3

2

1

116

30

RotameterMechanical Energy Balance

hpzgVVW

221ˆ fhpzgVVW 132

0

2

23VKh Rf Assume: (Base velocity head on smallest flow

area)

22

2

3

21

2

3

21

212

1SSVK

SSVVzgp

R

117

Rotameter

222 1 SQgVSQ

Combining Momentum and Mechanical Energy Balance

33

11211

SSK

SQ

SgV

SS

SQ

Rbf

After Some Manipulation

gVSS 2

f

f

f

fR

f

SgV

SSKSS

SQ2

1 23

118

RotameterAssuming Sf ≈ S a discharge coefficient can be defined 211 RR KC

f

f

fR S

gVCSQ

23

1 RR KC

CR must be determined experimentally. As Q increases the float rides higher, the assumption that Sf = S is poorer, and the previous expression is more nearly correct.

119

Turbine Meter

Measure by determining RPM of turbine (3) via sensor (6). Turbine meters accurate but fragile.

120

31

Temperature MeasurementTemperature Measurement

121

Temperature Measurement Temperature measurement is a

crucial part of many industrialprocesses.

Examples of industries where it is Examples of industries where it isimportant are mineral processing,plastics, petrochemical, food etc.

There are a large number of differentmethods to measure temperature .

These use different physicalproperties. We will discuss some ofthese and look at some commontemperature measurement sensors

122

What is Temperature? Temperature is a measure of the

average kinetic energy of particles in amediumTh i t ti l it f t t The international unit for temperatureis Kelvin (K) or degrees Celsius (ºC)where

K = °C + 273.15

The measurement of low to medium t t ( 273 ºC 500 ºC) itemperatures (-273 ºC - ~500 ºC) is defined as thermometry while the measurement of higher temperatures it is known as pyrometry

123

Thermal Measurement Method: Linear Expansion of a Solid

Rod thermometers and bimetallicthermometers are based on this

i i lprinciple. These indicate temperature due

to the different thermalexpansion of two differentmetals.

A solid bar will change in length

Where a is the linear temperaturecoefficient, L is the length of the barand dT is the change in temperature

If the original length of the bar is L0at T the new length L at T can be A solid bar will change in length

when it experiences a change intemperature

at T0 , the new length L1 at T1 can becalculated as follows:

LdTdL

TL TTLLL

10

01001

124

32

Thermal Measurement Method: Thermal Expansion of Liquids Used in liquid glass thermometers for a

direct indication of temperaturedirect indication of temperature The principle is similar to that in solids

except that we consider a volumetrictemperature coefficient b

TVV 101

It is considered constant over a limitedrange

125

Thermal Measurement Method: Vapour Pressure of Liquids

Vapor pressure is dependant on temperaturetemperature

The equation for an ideal gas is

Where p is pressure, v is aspecific volume, T is the

d i h l Measuring the volume change at a

RTpv

temperature and R is the molargas constant

Therefore temperature can bemeasured in two ways:

Measuring the volume change at a constant pressure

Measuring the pressure difference at a constant volume

126

Temperature Measurement with Electrical Sensors Convert temperature to an electrical

i lsignal They often require some form of

power source Great advantage is that the signals

from these sensors are transmittableover long distances which makesover long distances which makesremote measurement feasible

127

Conductivity in Metals Good conductivity in metals is due to the freely mobile

electrons in the atomic lattice The number of free electrons and their kinetic energy are The number of free electrons and their kinetic energy are

functions of temperature. As the temperature increases, theamplitude and frequency of vibration increases

The free electrons’ movement is now hindered through themedium and therefore the resistance of the material increasesIf i i i i i If an increase in temperature causes an increase in resistanceof a material it is said to have a Positive TemperatureCoefficient (PTC)

128

33

The relationship between the temperature of metals and its electricalresistance is not liner but can be described by the followingequation:

....)(

32

01

01

1 TcTbTaRtR

TTT

Where R1 is the resistance at temperature T1, R0 is the resistance ofthe material at a reference temperature T0 .

a, b and c are the temperature coefficients of resistivity and aredependant on the metal. They are only constant over a specificrangeg

However, for certain materials it is possible to neglect the higherterms for specific temperature ranges without introducing too largean error

This reduces the equation to a linear relationship129

Any metal used for temperature measurement should meetthese requirements: Good long term stability in terms of resistance High temperature coefficient of resistivity a Resistant to corrosion and chemical impurities Not effected by other physical quantities such as pressure Good reproducibility of change in resistance as a function of

temperature Platinum (Pt) and Nickel (Ni) satisfy most of the above

requirements

130

Electrical Temperature Measurement: Resistance Temperature Detectors (RTDs)

Use the fact that certain materialsresistance changes in a predictable wayresistance changes in a predictable waywith a change in temperature

The are mainly made from metallicconductors and mostly of platinum

They are becoming the temperaturef h i i i d fsensor of choice in industry for

temperature measurements below 600ºC

131

The most common types of RTD are:

Wire-wound in a ceramic insulator Wires which are encapsulated in glass

Resistance often measured using a Wheatstone Bridge

)1()( 0 TRTR

g garrangement

132

34

Advantages: High accuracy and can therefore be used in precision

applications Has low drift with time Has low drift with time Wide operating temperature range

Disadvantages: Are not often used above 660ºC as it is difficult to keep the Are not often used above 660 C as it is difficult to keep the

platinum pure

133

Thomas Johan Seebeck A German-Estonian Physicist who

discovered that a voltage wasproduced across a metal bar when aproduced across a metal bar when atemperature difference existed in thebar in 1821

From this he formulated the SeebeckPrinciple which is used in sometemperature measurement devicestemperature measurement devices

134

The Seebeck Effect If two different metals are joined together to

form a continuous loop and their junctionsare at different temperatures, an e.m.f. willbe generated which cause a current to flow

If a millivoltmeter is inserted into the loop,its output reading will give us an indicationof the temperature difference between thetwo junctions of the loop

This concept forms the basis of a This concept forms the basis of athermocouple

135

Electrical Temperature Measurement: Thermocouples Are the most commonly used

electronic temperature measurementdevicesdevices

Consists of two dissimilar metalswhich are joined together at both ends

One of the conductors is broken inthe middle. A potential difference isgenerated across the break if thejunctions are held at differenttemperatures

Therefore if one end of athermocouple is held at a knownreference, the temperature of theother end can be calculated

136

35

Thermocouples Types

MAXMIUM

• Various metal combinations can be used for different temperature andvoltage ranges, the following are examples of common combinations:

ANSICODE ALLOY COMBINATION

MAXMIUMTEMPERATURE RANGE

mVOUTPUT

BEJKNR

Platinum/RhodiumChromel/ConstantanIron/ConstantanChromel/AlumelNicrosil/NisilPlatinum/Rhodium Platinum

0°C to +1700°C–200°C to +900°C

0°C to +750°C–200°C to +1250°C–270°C to +1300°C

0°C to +1450°C

0 to +12.426–8.824 to +68.783

0 to +42.283–5.973 to +50.633–4.345 to +47.502

0 to +16.741ST

Platinum/Rhodium PlatinumCopper/Constantan

0°C to +1450°C–200°C to +350°C

0 to +14.973–5.602 to +17.816

137

Thermocouples Advantages:

Wide operating temperature range can be used at high temperatures

Fairly cheap Interchangeable Have standard connectors

Disadvantages:g Lack of precision

138

Electrical Temperature Measurement: Semiconductor Sensors

Silicon Measuring Resistors (PTC)ll li i Small non-linearity

-70ºC - 160ºC gives a resistance change of 14W to 4kW Semiconductor Diodes

If supplied with a constant current, the conducting voltage is a function of absolute temperaturep

Almost linear between -50ºC - 150ºC

139

Thermistors A semiconductor used as a temperature sensor. Mixture of metal oxides pressed into a bead, wafer or other

shape.p Beads can be very small, less than 1 mm in some cases. The resistance decreases as temperature increases, negative

temperature coefficient (NTC) thermistor.

140

36

Thermistors Most are seen in medical

equipment markets. Thermistors are also used are

for engine coolant, oil, and airtemperature measurement inthe transportation industry.

141

Thermistors

High sensitivity to smalltemperat re changes

Limited temperature range

AdvantagesAdvantages DisadvantagesDisadvantages

temperature changes Temperature

measurements becomemore stable with use

Copper or nickel

range Fragile Some initial accuracy

“drift” Decalibration if usedpp

extension wires can beused

Decalibration if used beyond the sensor’s temperature ratings

Lack of standards for replacement 142

Electrical Temperature Measurement: Radiation Thermometers Also known as pyrometers They are non-contact sensorsy Used in the measurement range

-100 ºC - 3500 ºC They are used to measure the

temperature of a surface if it isvisible

Often used for objects withrapid temperature changes,moving objects and smallobjects

143

Electrical Temperature Measurement: Capacitive and Inductive Sensors

Both these types of sensorsare used in oscillating circuitsare used in oscillating circuits

The dielectric constant ofmost materials is temperaturedependant

The magnetic permeability ofVicalloy toroid coils changesVicalloy toroid coils changesas a function of temperature

144

37

Electrical Temperature Measurement: Crystal Oscillator Methods

If crystals are cut along certainaxes, their resonant frequency willbe largely affected by temperature

The crystal can then be used in anoscillating circuit

145

Electrical Temperature Measurement: Acoustic Methods

Uses the fact that the velocityof sound in a medium willchange according to thetemperature of the medium

146

Electrical Temperature Measurement: Temperature Dependant Colours

Strips which change colouraccording to the temperatureaccording to the temperatureof the surface they are attachedto

For example the strips used onh id f fi h kthe side of fish tanks

147

Infrared Thermometry Infrared thermometers measure the amount of

radiation emitted by an object. Peak magnitude is often in the infrared region Peak magnitude is often in the infrared region. Surface emissivity must be known. This can add a lot

of error. Reflection from other objects can introduce error as

wellwell. Surface whose temp you’re measuring must fill the

field of view of your camera.

148

38

Benefits of Infrared Thermometry Can be used for Moving objectsg j Non-contact applications where

sensors would affect results orbe difficult to insert orconditions are hazardousL di t Large distances

Very high temperatures

149