Transducers and Measurement systems

Transcription

1 Transducers and Measurement systems Dimension Measurement By: Yidnekachew Messele Rules and Tapes Rules and tapes are the simplest way of measuring larger dimensions. teel rules are generally only available to measure dimensions up to m. Beyond this, steel tapes (measuring to 30 m) oranultrasonic rule (measuring to 0 m) is used. The steel rule is the measurement accuracy is much dependent upon the skill of the human measurer and, at best, the inaccuracy is likely to be at least 0.5%. The ultrasonic rule consists of an ultrasonic energy source, an ultrasonic energy detector, andbattery-powered, electronic circuitry housed within a handheld box. Both source and detector often consist of the same type of piezoelectric crystal excited at a typical frequency of 40 khz. Energy travels from the source to a target object and is then reflected back into the detector. The time of flight of this energy is measured and this is converted into a distance reading by the enclosed electronics. Maximum measurement inaccuracy of % of the full-scale reading is claimed. 3 4

2 Calipers Calipers are generally used in situations, where measurement of dimensions with a rule or tape is not accurate enough. Determination of the point, where the two scales coincide enables very accurate measurements to be made, with typical inaccuracy levels down to 0.0%. Micrometers Micrometers provide a means of measuring dimensions to high accuracy. Measurement is made between two anvils, one fixed and one that is moved along by the rotation of an accurately machined screw thread. One complete rotation of the screw typically moves the anvil by a distance of 0.5 mm. The most common measurement ranges are either 0-5 mm or 5-50 mm, with inaccuracy levels down to 0.003%. 5 6 Position and Displacement ensors Displacement sensors are basically used for the measurement of movement of an object. Position sensors are employed to determine the position of an object in relation to some reference point. One method of determining a position, is to use either "distance", which could be the distance between two points such as the distance travelled or moved away from some fixed point, or by "rotation" (angular movement). For example, the rotation of a robots wheel to determine its distance travelled along the ground. Either way, Position ensors can detect the movement of an object in a straight line using Linear ensors or by its angular movement using Rotational ensors. 8

3 The most commonly used of all the "Position ensors", is the potentiometer because it is an inexpensive and easy to use position sensor. The potentiometer can be of linear or angular type. It works on the principle of conversion of mechanical displacement into an electrical signal. The sensor has a resistive element and a sliding contact (wiper). The slider moves along this conductive body, acting as a movable electric contact. The object of whose displacement is to be measured is connected to the slider by using a rotating shaft (for angular displacement) a moving rod (for linear displacement) 9 0 Application These are typically used on machine-tool controls, elevators, liquid-level assemblies, forklift trucks, automobile throttle controls. In manufacturing, these are used in control of injection molding machines, woodworking machinery, printing, spraying, robotics, etc. These are also used in computercontrolled monitoring of sports equipment. Measuring Linear Displacement Very small displacements: train Gauges Capacitive ensors Inductive ensors (LVDT) Medium displacements lide Wire / Film Wire wound potentiometer Large Displacements (above range of most pure linear transducers) Convert linear to angular motion and measure the angular motion with an angular displacement transducer Measure velocity and integrate signal to obtain displacement

4 Linear Displacement - Resistive Methods Resistance is defined by the following equation l R A Therefore if the length, thickness or resistivity of an object changes with respect to displacement we can use the resistance as a way to measure it Linear Displacement - Resistive Methods (lide Wire/Film) This is the simplest way of measuring displacement between a moving and a stationary object 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 A potentiometer is an electromechanical device containing an electrically conductive wiper that slides against a fixed resistive element according to the position or angle of an external shaft. 3 4 lide Wire Range ± 300mm Advantages imple Good Resolution Low Cost Disadvantages Wire does not have high resistance, film is better (±00 to 500Ω/cm) Wear Frictional Loading Inertial Loading 5 6

5 Linear Displacement - Resistive Methods (Wire Wound Potentiometer) Wire Wound potentiometers use the same principle as slide wire sensors except that they use a coil of insulated resistance The slider runs on one surface of the coil that is not insulated 7 8 Potentiometer Linear potentiometer is a device in which the resistance varies as a function of the position of a slider. Vex x max x Rp V=0 to V ex Rx V R V x x x R x R p R x R p V Vex x x max x V x ex max max R p Potentiometers Resolution ± mm 4m Advantages imple Robust Disadvantages Resolution dependant on wire diameter Continuous use over portion of the wire will cause wear Frictional Loading Inertial Loading X can also be the degrees of turns. 9 0

6 Linear Displacement - Resistive Methods (train Gauges) train gauge: it is an electrical conductor whose resistance changes as it is strained. Attach the strain gauge to the object 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 train Gauges Advantages: Relatively easy to understand and attach Cheap Disadvantages Need temperature compensation Linear Displacement - Capacitive Methods Capacitance is defined as A C 0 r d Therefore we could use the change in Plate Area Permittivity of the dielectric Distance between the plates as a way to measure displacement 3 Linear Displacement - Capacitive Methods (Variable Area) If we have two electrodes and one moves relative to the other in a linear direction we will get an effective change in the area of the plates This results in a change in the capacitance which can be related to displacement. A wx r C 0 d 4

7 Linear Displacement - Capacitive Methods (Distance Between the Plates) If we have two electrodes, one fixed and the other movable we can arrange it that the distance between the plates changes for a change in displacement C A 0 r x 5 Linear Displacement - Capacitive Methods (Distance Between the Plates) This type of capacitive arrangement consists of two fixed outer plates and one central moveable plate. The central plate can move towards either of the plates which essentially changes the capacitance between the moveable plate and the fixed plates. If the moveable plate is in the center of the capacitor, voltages V and V will be equal. 6 Linear Displacement - Capacitive Methods (Permittivity) The dielectric moves relative to the plates and this causes a change in the relative permittivity of the dielectric Linear Displacement - Inductive Methods Inductive methods use very similar principles to resistive and capacitive methods The inductance of a coil is given by the following equation L N A l [ Henrys Where N is the number of turns in the coil, µ is the effective permeability of the medium in and around the coil, A is the 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 ] 7 8

8 Linear Displacement - Inductive Methods (Linear Variable Differential Transformers LVDTs) Linear Displacement - Inductive Methods (Linear Variable Differential Transformers LVDTs) LVDTs are accurate transducers which are often used in industrial and scientific applications to measure very small displacements An LVDT consists of a central primary coil wound over the whole length of the transducer and two outer secondary coils A magnetic core is able to move freely through the coil The primary windings are energized with a constant amplitude AC signal ( 0kHz) 9 30 This produces an alternating magnetic field which induces a signal into the secondary windings The strength of the signal is dependent on the position of the core in the coils. When the core is placed in the center of the coil the output will be zero. Moving the coil in either direction causes the signal to increase The output signal is proportional to the displacement Linear Variable-Differential Transformer (LVDT) V > V V V -x Vo=V-V LVDTs are devices to measure displacement by modifying spatial distribution of an alternating magnetic field. Vi Vi Oscillating excitation voltage-50 Hz to 5 khz Vo 3 3

9 Linear Variable-Differential Transformer (LVDT) Vo=V-V V V X=0 Linear Variable-Differential Transformer (LVDT) Vo=V-V V V +x V = V Vi V > V Vi Vi Vo 33 Vi o, the direction of displacement can be determined from the relative phase of the signal. 34 Vo LVDTs Range: ±.5nm - ±0cm Advantages: Good resolution Disadvantages: Needs shielding to prevent interference from magnetic sources Pressure Measurements 35

10 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 is defined as: P = F/A ystem Length Force Mass Time Pressure MK Meter Newton Kg ec N/M = Pascal CG CM Dyne Gram ec D/CM English Inch Pound lug ec PI How Much is a Pascal (Pa) atmosphere (4.7 psi, 750mmHg) is approximately 00 kpa = bar kpa is about 7 mmhg % of a gas at our altitude is about 7 mmhg How is pressure generated? Collision of molecule with wall Momentum of mass with x velocity um collisions over area to get force tatic, Dynamic, and Impact pressures tatic 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 it 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 and dynamic pressures on a surface or object. Point B in Fig. depicts the impact pressure. 39 Definition Of Pressure Absolute pressure The pressure is referenced to zero absolute. Absolute pressure can only have a positive value. Gauge pressure The pressure is referenced to atmospheric pressure and by convention is measured in the positive direction. Vacuum pressure The pressure is referenced to atmospheric pressure and by convention is measured in the negative direction. 40

11 Pressure Measurement A number of measurement units are used for pressure. They are as follows:. Bar (.03 atm) = 00 kpa. Pascals (N/m ) or kilopascal (000Pa) 3. Pounds per square foot (psf) or pounds per square inch (psi) 4. Atmospheres (atm) 5. Torr = mm mercury 6. Pascals (N/m ) or kilopascal (000Pa) Pressure Units psi= 5.74 mmhg =.0359 in.hg = in.ho = kpa bar= psi atm. = psi 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 application. For example, blood pressure is usually measured in mmhg because mercury manometers were used originally. Atmospheric pressure is usually expressed in mmhg for the same reason. Other units used for atmospheric pressure are bar and atm. 4 Wet Meters (Manometers) 4 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 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 same level in each leg, establishing a zero reference. With a greater pressure applied to the left side of a U-tube manometer, the liquid lowers in the left leg and rises in the right leg. The liquid moves until the unit weight of the liquid, as indicated by h, exactly balances the pressure

12 Pressure in open tank A container filled with a liquid has a pressure (due to the weight of the liquid) at a point in the liquid of: P = F/A P = W/A P = ρgv/a P = ρgha/a P = pressure P = ρgh F = force A = Area W = weight of the liquid V = volume above the Area g = gravitation ρ = mass density h = distance from the surface A h 45 When the liquid in the tube is mercury, for example, the indicated pressure h is usually expressed in inches (or millimeters) of mercury. To convert to pounds per square inch (or kilograms per square centimeter), P = ρh Where P = pressure, (kg/cm ), ρ = density, (kg/cm 3 ), h = height, (cm) Gauge pressure is a measurement relative to atmospheric pressure and it varies with the barometric reading. A gauge pressure measurement is positive when the unknown pressure exceeds atmospheric pressure (A), and is negative when the unknown pressure is less than atmospheric pressure (B). 46 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 to the atmosphere, the fluid levels are the same (A). With an equal positive pressure applied to one leg of each manometer, the fluid levels differ, but the distance between the fluid heights is the same (B). 47 Reservoir (Well) Manometer In a well-type manometer, the cross-sectional area of one leg (the well) is much larger than the other leg. When pressure is applied to the well, the fluid lowers only slightly compared to the fluid rise in the other leg. In this design one leg is replaced by a large diameter well so that the pressure differential is indicated only by the height of the column in the single leg. The pressure difference can be read directly on a single scale. For static balance, P P ( A/ A) h If the ratio of A /A is small compared with Where unity, then the error in neglecting this term A = area of smaller-diameter leg becomes negligible, and the static balance A = area of well P relation becomes P h 48

13 Pressure ensing Pressure is sensed by mechanical elements such as plates, shells, and tubes that are designed and constructed to deflect when pressure is applied. This is the basic mechanism converting pressure to physical movement. Next, thismovement must be transduced to obtain an electrical or other output. Finally, signal conditioning may be needed, depending on the type of sensor and the application. Figure illustrates the three functional blocks. displacement electric Pressure ensing Element Transduction element ignal Conditioner V or I output 49 The main types of sensing elements are Bourdon tubes, diaphragms, capsules, and bellows. All except diaphragms provide a fairly large displacement that is useful in mechanical gauges and for electrical sensors that require a significant movement. The basic pressure sensing element can be configured as a C-shaped Bourdon tube (A); a helical Bourdon tube (B); flat diaphragm (C); a convoluted diaphragm (D); a capsule (E); or a set of bellows (F). 50 Primary Pressure Elements Capsule, Bellows & pring Opposed Diaphragm 5 5

14 Bellows In general a bellows can detect a slightly lower pressure than a diaphragm The range is from 0-5 mmhg to psi Accuracy in the range of % span 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 the applied pressure. The tube is mechanically linked to a pointer on a pressure dial to give a calibrated reading

15 Bourdon Tubes (a) C-type tube. (b) piral tube. (c) Helical tube Bourdon Tubes 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 differential pressure. They are normally used to measure low pressures of inch of Hg, but they can also be manufactured to measure higher pressures in the range of 0 to 330 psig

16 Diaphragm (a) flat diaphragm; (b) corrugated diaphragm A diaphragm usually is designed so that the deflection-versuspressure characteristics are as linear as possible over a specified pressure range, and with a minimum of hysteresis and minimum shift in the zero point. 6 6 Capsule A capsule is formed by joining the peripheries of two diaphragms through soldering or welding. Used in some absolute pressure gages. Use of capsule element in pressure gage 63 64

17 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 top of the potentiometer, and the voltage that is dropped from the wiper arm to the bottom of the pot is sent to an electronic unit. It normally cover a range of 5 psi to 0,000 psi. Can be operated over a wide range of temperatures. ubject to wear because of the mechanical contact between the slider and the resistance element. Therefore, the instrument life is fairly short, and they tend to become noisier as the pot wears out. Bellows Resistance Transducer Bellows or a bourdon tube with a variable resistor. Bellow expand or contract causes the attached slider to move along the slidewire. This increase or decrees the resistance. Thus indicating an increase or decrease in pressure 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. LVDT Another type of inductance transducer, utilizes two coils wound on a single tube and is commonly referred to as a Differential Transformer or sometimes as a Linear Variable Differential Transformer (LVDT)

18 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 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 interface electronics. ome piezoelectric pressure sensors include an internal amplifier to provide an easy electrical interface. Piezoelectric sensors convert stress into an electric potential and vice versa. ensors based on this technology are used to measure varying pressures train Gauge Pressure ensors train 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.% of the base resistance emiconductor strain gauges are widely used, both bonded and integrated into a silicon diaphragm, because the response to applied stress is an order of magnitude larger than for a metallic strain gauge. When the crystal lattice structure of silicon is deformed by applied stress, the resistance changes. This is called the piezoresistive effect. Following are some of the types of strain gauges used in pressure sensors. Deposited strain gauge. Metallic strain gauges can be formed on a diaphragm by means of thin film deposition. This construction minimizes the effects of repeatability and hysteresis that bonded strain gauges exhibit. These sensors exhibit the relatively low output of metallic strain gauges. 7 7

19 Range of Elastic-Element Pressure Gages Dead-weight pressure gauge A cylindrical piston is placed inside a stainless-steel cylinder. 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.. 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 Calibration of Pressure ensing Devises Mass, Force and Torque 75

20 Mass (Weight) Measurement The mass of a body is always quantified in terms of a measurement of the weight of the body, this being the downward force exerted by the body when it is subject to gravity. The first method of measuring the downward force exerted by a mass subject to gravity involves the use of a load cell. The load cell measured the downward force F, and then the mass M is calculated from the equation: ince the values of g vary by small amounts at different points around the earth s surface, the value of M can only be calculated exactly if the value of g is known exactly. 77 everal different forms of load cells are available. Most load cells are now electronic, although pneumatic and hydraulic types also exist. Within an electronic load cell, the gravitational force on the body being measured is applied to an elastic element. This deflects according to the magnitude of the body mass. Mass measurement is thereby translated into a displacement measurement task. The elastic elements used are specially shaped and designed. 78 The design aims to obtain a linear output relationship between the applied force and the measured deflection and to make the instrument insensitive to forces that are not applied directly along the sensing axis. Elastic force transducers based on differential transformers (linear variable differential transformers (LVDTs)) to measure defections are used to measure masses up to 5 tonne. Piezoelectric device used to measure masses in the range of tonne. Piezoelectric crystals replace the specially designed elastic member normally used in this class of instrument, allowing the device to be physically small

21 Pneumatic and hydraulic load cells translate mass measurement into a pressure measurement task, though they are now less common than the electronic load cell. Mass-Balance (Weighing) Instruments 8 8 Force ensors Force is a quantity capable of changing the size, shape, or motion of an object. There are four basic forces in nature: gravitational, magnetic, strong nuclear, and weak nuclear forces. The weakest of the four is the gravitational force. It is also the easiest to observe, because it acts on all matter and it is always attractive, while having an infinite range. Its attraction decreases with distance, but is always measurable. Force ensors The fundamental operating principles of force, acceleration, and torque instrumentation are closely allied to the piezoelectric and strain gage devices used to measure static and dynamic pressures. Piezoelectric sensor produces a voltage when it is "squeezed" by a force that is proportional to the force applied

22 Difference between these devices and static force detection devices such as strain gages is that the electrical signal generated by the crystal decays rapidly after the application of force. The high impedance electrical signal generated by the piezoelectric crystal is converted to a low impedance signal suitable for such an instrument as a digital storage oscilloscope. Depending on the application requirements, dynamic force can be measured as either compression, tensile, or torque force. Applications may include the measurement of spring or sliding friction forces, chain tensions, clutch release forces. train gauge. The electrical resistance of a length of wire varies in direct proportion to the change in any strain applied to it. That s the principle upon which the strain gauge works. The most accurate way to measure this change in resistance is by using the wheatstone bridge. The majority of strain gauges are foil types, available in a wide choice of shapes and sizes to suit a variety of applications. They consist of a pattern of resistive foil which is mounted on a backing material They operate on the principle that as the foil is subjected to stress, the resistance of the foil changes in a defined way. train gauge Configuration The strain gauge is connected into a wheatstone Bridge circuit with a combination of four active gauges(full bridge),two guages (half bridge) or,less commonly, a single gauge (quarter bridge)

23 Guage factor A fundamental parameter of the strain guage is its sensitivity to strain, expressed quantitatively as the guage factor (GF). Guage factor is defined as the ratio of fractional change in electrical resistance to the fractional change in length (strain). train 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 bridge which results in signal output with respect to stress value. As the signal value is small the signal conditioning electronics provides amplification to increase the signal hear Force Measurement The strain gauges are bonded on the flat upper and lower sections of the load cell at points of maximum strain. This load cell type is used for low capacities and performs with good linearity. Its disadvantage is that it must be loaded correctly to obtain consistent results V O V Where: A is the cross-sectional area E is the modulus of elasticity Therefore Force P is measured in terms of Voltage out put as V O v is Poissin s ratio of the material g is a gauge factor 9 9 V O = k PV

24 Torque ensors Torque is measured by either sensing the actual shaft deflection caused by a twisting force,orby detecting the effects of this deflection. The surface of a shaft under torque will experience compression and tension, as shown in Figure. To measure torque, strain gage elements usually are mounted in pairs on the shaft, one gauge measuring the increase in length (in the direction in which the surface is under tension), the other measuring the decrease in length in the other direction. Torque ensor 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 Technology Magnetoelastic : A magnetoelastic torque sensor detects changes in permeability by measuring changes in its own magnetic field. Piezoelectric : A piezoelectric material is compressed and generates a charge, which is measured by a charge amplifier. train guage : To measure torque,strain guage elements usually are mounted in pairs on the shaft,one guage measuring the increase in length the other measuring the decrease in the other direction. Figures showing Torque sensors 95 96

25 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. Flow Measurement 97 ince 989 there were at least 3 distinct type of technologies available the measurement of flow in closed conduit. Flow meters selection are part of the basic art of the instrument engineer, and while only handful of these technologies contribute to the majority of installations. And wide product knowledge is essential to find the most cost effective solution to any flow measurement application. Types of Flows Reynolds Number The performance of flow meters is also influenced by a dimensionless unit called the Reynolds Number. It is defined as the ratio of the liquid's inertial forces to its drag forces. The Reynolds number is used for determined whether a flow is laminar or turbulent. Laminar flow within pipes will occur when the Reynolds number is below the critical Reynolds number of 300 and turbulent flow when it is above 300. The value of 300 has been determined experimentally and a certain range around this value is considered the transition region between laminar and turbulent flow

26 Venturi Meter Differential Pressure (Obstruction-Type) Meters In the venturi meter velocity is increased and the pressure decreased in the upstream cone. The pressure drop from points FtoIcan be used to measure the rate of flow through the meter. Venturi meters are most commonly used for liquids, especially water

27 05 06 Venturi Meter ince friction cannot be eliminated in the venturi meter a permanent loss in pressure occurs. Because of the small angle of divergence in the recovery cone, the permanent pressure loss is relatively small (about 0% of the venturi differential p a p b )

28 Orifice Meter The orifice meter consists of an accurately machined and drilled plate concentrically mounted between two flanges. The position of the pressure taps is somewhat arbitrary. Orifice Meter The orifice meter has several practical advantages when compared to venturi meters. Lower cost maller physical size Flexibility to change throat to pipe diameter ratio to measure a larger range of flow rates Disadvantage: Large power consumption in the form of irrecoverable pressure loss 09 0

29 3 4 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. 5 6

30

31 Comparison Venturi High Capital Cost Low Operating Cost (good p recovery) Not Flexible (β fixed) Large Physical ize Orifice Low Capital Cost High Operating Cost (poor p recovery) More Flexibility (interchangeable) Compact Rotameters Rotameters fall into the category of flow measurement devices called variable area meters. These devices have nearly constant pressure and depend on changing cross sectional area to indicate flow rate. Rotameters are extremely simple, robust devices that can measure 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 float indicates the flow rate on a marked scale. Rotameters Three types of forces must be accounted for when analyzing rotameter performance: Flow Gravity Buoyancy For our analysis neglect drag effect Gravity Buoyancy Rotameter Mass Balance Assume Gradual Taper V V V V Q Flow Between Float and Tube V 3 Q V f 3 Flow 3 3 is annular flow area at plane 3 4

32 Rotameter Momentum Balance Note: p 3 = p Must account for force due to float f f V f gv z g p p V V Q 3 b f gv Q z g p 3 5 Rotameter Mechanical Energy Balance f h p z g V V W 3 ˆ 0 V 3 K h R f Assume: (Base velocity head on smallest flow area) 3 3 V K V V z g p R 6 Rotameter 3 3 K Q gv Q R b f Combining Momentum and Mechanical Energy Balance After ome Manipulation f f f f R f gv K Q 3 7 Rotameter f f f R gv C Q 3 Assuming f a discharge coefficient can be defined R C R K C R must be determined experimentally. As Q increases the float rides higher, the assumption that f = is poorer, and the previous expression is more nearly correct. 8

33 Turbine Meter Measure by determining RPM of turbine (3) via sensor (6). Turbine meters accurate but fragile Level Measurement Dipsticks Dipsticks offer a simple means of measuring the level of liquids approximately. The ordinary dipstick is the cheapest device available. This consists of a metal bar on which a scale is etched 3

34 ight-glass level indicator Pressure-Measuring Devices (Hydrostatic ystems) Pressure-measuring devices measure liquid level to a better accuracy and use the principle that the hydrostatic pressure due to a liquid is directly proportional to its depth and hence to the level of its surface Where liquid-containing vessels are totally sealed, the liquid level can be calculated by measuring the differential pressure between the top and bottom of the tank Capacitive Devices Capacitive devices are widely used for measuring the level of both liquids and solids in powdered or granular form

35 Ultrasonic Level Gauge Ultrasonic level measurement is one of a number of noncontact techniques available. It is primarily used to measure the level of materials that are either in a highly viscous liquid form or in a solid (powder or granular) form. The principle of the ultrasonic level gauge is that energy from an ultrasonic source above the material is reflected back from the material surface into an ultrasonic energy detector. Measurement of the time of flight allows the level of the material surface to be inferred Nucleonic (or Radiometric) ensors Nucleonic, sometimes called radiometric, sensors are relatively expensive. They use a radiation source and detector system located outside a tank in the manner shown in Figure Temperature Measurement 39

36 Temperature Measurement Temperature measurement is a crucial part of many industrial processes. Examples of industries where it is important are mineral processing, plastics, petrochemical, food etc. There are a large number of different methods to measure temperature. These use different physical properties. We will discuss some of these and look at some common temperature measurement sensors What is Temperature? Temperature is a measure of the average kinetic energy of particles in amedium The international unit for temperature is Kelvin (K) or degrees Celsius (ºC) where K = C The measurement of low to medium temperatures (-73 ºC - ~500 ºC) is defined as thermometry while the measurement of higher temperatures it is known as pyrometry. 4 4 Thermal Measurement Method: Linear Expansion of a olid Rod thermometers and bimetallic thermometers are based on this principle. These indicate temperature due to the different thermal expansion of two different metals. A solid bar will change in length when it experiences a change in temperature dl LdT Where is the linear temperature coefficient, L is the length of the bar and dt is the change in temperature If the original length of the bar is L 0 at T 0, the new length L at T can be calculated as follows: L L0 L0 T T0 L T 0 Thermal Measurement Method: Thermal Expansion of Liquids Used in liquid glass thermometers for a direct indication of temperature The principle is similar to that in solids except that we consider a volumetric temperature coefficient V V T 0 It is considered constant over a limited range 43 44

37 Thermal Measurement Method: Vapour Pressure of Liquids Vapor pressure is dependant on temperature The equation for an ideal gas is pv RT Where p is pressure, v is a specific volume, T is the temperature and R is the molar gas constant Therefore temperature can be measured in two ways: Measuring the volume change at a constant pressure Measuring the pressure difference at a constant volume Temperature Measurement with Electrical ensors Convert temperature to an electrical signal. They often require some form of power source. Great advantage is that the signals from these sensors are transmittable over long distances which makes remote measurement feasible 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 functions of temperature. As the temperature increases, the amplitude and frequency of vibration increases. The free electrons movement is now hindered through the medium and therefore the resistance of the material increases. If an increase in temperature causes an increase in resistance of a material it is said to have a Positive Temperature Coefficient (PTC). 47 The relationship between the temperature of metals and its electrical resistance is not liner but can be described by the following equation: T T T0 3 R ( t ) R a T b T c T... 0 Where R is the resistance at temperature T, R 0 is the resistance of the material at a reference temperature T 0. a, b and c are the temperature coefficients of resistivity and are dependant on the metal. They are only constant over a specific range However, for certain materials it is possible to neglect the higher terms for specific temperature ranges without introducing too large an error This reduces the equation to a linear relationship 48

38 Any metal used for temperature measurement should meet these requirements: Good long term stability in terms of resistance High temperature coefficient of resistivity 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 Electrical Temperature Measurement: Resistance Temperature Detectors (RTDs) Use the fact that certain materials resistance changes in a predictable way with a change in temperature. They are mainly made from metallic conductors and mostly of platinum. They are becoming the temperature sensor of choice in industry for temperature measurements below 600 ºC The most common types of RTD are: Wire-wound in a ceramic insulator Wires which are encapsulated in glass R( T ) R0 ( T ) Resistance often measured using a Wheatstone Bridge arrangement Advantages: High accuracy and can therefore be used in precision applications Has low drift with time Wide operating temperature range Disadvantages: Are not often used above 660ºC as it is difficult to keep the platinum pure AAiT 5 5

39 Thomas Johan eebeck A German-Estonian Physicist who discovered that a voltage was produced across a metal bar when a temperature difference existed in the bar in 8. From this he formulated the eebeck Principle which is used in some temperature measurement devices. The eebeck Effect If two different metals are joined together to form a continuous loop and their junctions are at different temperatures, ane.m.f.will be generated which cause a current to flow. If a millivoltmeter is inserted into the loop, its output reading will give us an indication of the temperature difference between the two junctions of the loop. This concept forms the basis of a thermocouple Electrical Temperature Measurement: Thermocouples Are the most commonly used electronic temperature measurement devices. Consists of two dissimilar metals which are joined together at both ends. One of the conductors is broken in the middle. A potential difference is generated across the break if the junctions are held at different temperatures Therefore if one end of a thermocouple is held at a known reference, the temperature of the other end can be calculated. 55 Thermocouples Types Various metal combinations can be used for different temperature and voltage ranges, the following are examples of common combinations: MAXMIUM ANI CODE ALLOY COMBINATION TEMPERATURE RANGE B E J K N R T AAiT Platinum/Rhodium Chromel/Constantan Iron/Constantan Chromel/Alumel Nicrosil/Nisil Platinum/Rhodium Platinum Platinum/Rhodium Platinum Copper/Constantan 0 C to +700 C 00 C to +900 C 0 C to +750 C 00 C to +50 C 70 C to +300 C 0 C to +450 C 0 C to +450 C 00 C to +350 C mv OUTPUT 0 to to to to to to to to

40 Thermocouples Advantages: Wide operating temperature range can be used at high temperatures Fairly cheap Interchangeable Have standard connectors Disadvantages: Lack of precision Electrical Temperature Measurement: emiconductor ensors ilicon Measuring Resistors (PTC) mall non-linearity -70ºC - 60ºC gives a resistance change of 4W to 4kW emiconductor Diodes If supplied with a constant current, the conducting voltage is a function of absolute temperature Almost linear between -50ºC - 50ºC Thermistors A semiconductor used as a temperature sensor. Mixture of metal oxides pressed into a bead, wafer or other shape. The resistance decreases as temperature increases, negative temperature coefficient (NTC) thermistor. Thermistors Most are seen in medical equipment markets. Thermistors are also used are for engine coolant, oil, and air temperature measurement in the transportation industry

41 Thermistors Advantages High sensitivity to small temperature changes Temperature measurements become more stable with use Copper or nickel extension wires can be used Disadvantages Limited temperature range Fragile ome initial accuracy drift Decalibration if used beyond the sensor s temperature ratings Lack of standards for replacement 6 Electrical Temperature Measurement: Radiation Thermometers Also known as pyrometers. They are non-contact sensors. Used in the measurement range -00 ºC ºC They are used to measure the temperature of a surface if it is visible. Often used for objects with rapid temperature changes, moving objects and small objects. 6 Infrared Thermometry Infrared thermometers measure the amount of radiation emitted by an object. Peak magnitude is often in the infrared region. urface emissivity must be known. This can add a lot of error. Reflection from other objects can introduce error as well. urface whose temp you re measuring must fill the field of view of your camera. Benefits of Infrared Thermometry Can be used for Moving objects Non-contact applications where sensors would affect results or be difficult to insert or conditions are hazardous Large distances Very high temperatures 63 64