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5. Fluid flow
For a fluid flowing through a pipe of cross-sectional area A1 with a velocity v1 (FIG. 26), in 1 s the fluid advances a distance v1 and so amount of fluid passing a particular point per second is A1v1 and the volume rate of flow A1v1. If the fluid then flows through a constriction of cross-sectional area A2 in the pipe then we must have: and so there must be an increase in velocity. An increase in velocity means an acceleration and therefore a force is required to move the fluid through the constriction. This force is provided by the pressure in the fluid dropping at the constriction. The traditional methods used for the measurement of fluid flow involve devices based on the measurement of the pressure difference occurring at a constriction and using it as a measure of the flow rate. The relationship between the pressure drop and the volume rate of flow is non-linear, i.e. the flow rate is not directly proportional to the pressure difference but to the square root of the pressure difference. The venturi tube and the orifice plate described below are common examples.
Other methods have, however, been developed which more rapidly and efficiently record the flow rate and often with less interference to the flow.
FIG. 26 Pressure drop at a constriction
FIG. 27 Venturi tube
5.1 Differential pressure methods
There are a number of forms of differential pressure devices based on the above equation and involving constant size constrictions, e.g. the venturi tube, nozzles, Dall tube and orifice plate. In addition there are other devices involving variable size constrictions, e.g. the rotameter. The following are discussions of the characteristics of the above devices.
The venturi tube (FIG. 27) has a gradual tapering of the pipe from the full diameter to the constricted diameter. The presence of the venturi tube results in a pressure loss occurring in the system of about 10 to 15%, a comparatively low value. The pressure difference between the flow prior to the constriction and the constriction can be measured with a simple U-tube manometer or a differential diaphragm pressure cell. The instrument can be used with liquids containing particles, is simple in operation, capable of accuracy of about ±0.5%, has a long-term reliability, but is comparatively expensive and has a non-linear relationship between pressure and the volume rate of flow.
A cheaper form of venturi is provided by the nozzle flow meter (FIG. 28). Two types of nozzle are used, the venturi nozzle and the flow nozzle. The venturi nozzle (FIG. 28(a)) is effectively a venturi tube with an inlet which is considerably shortened. The flow nozzle (FIG. 28(b)) is even shorter. Nozzles produce pressure losses of the order of 40 to 60%. Nozzles are cheaper than venturi tubes, give similar pressure differences, and have an accuracy of about ±0.5%. They have the same non-linear relationship between the pressure and the volume rate of flow.
The Dall tube (FIG. 29) is another variation of the venturi tube. It gives a higher differential pressure and a lower pressure drop. The Dall tube is only about two pipe diameters long and is often used where space does not permit the use of a venturi tube.
The orifice plate (FIG. 30) is simply a disc with a hole. The effect of introducing it is to constrict the flow to the orifice opening and the flow channel to an even narrower region downstream of the orifice. The narrowest section of the flow is not through the orifice but downstream of it and is referred to as the vena contracta. The pressure difference is measured between a point equal to the diameter of the tube upstream of the orifice and a point equal to half the diameter downstream. The orifice plate has the usual non-linear relationship between the pressure difference and the volume rate of flow. It is simple, reliable, produces a greater pressure difference than the venturi tube and is cheaper but less accurate, about ±1.5%. It also produces a greater pressure drop.
Problems of silting and clogging can occur if particles are present in liquids.
FIG. 28 Nozzles: (a) venturi, (b)flow
FIG. 29 Dall tube
FIG. 30 Orifice plate
FIG. 31 Rotameter
The rotameter (FIG. 31) is an example of a variable area flow meter; a constant pressure difference is maintained between the main flow and that at the constriction by changing the area of the constriction.
The rotameter has a float in a tapered vertical tube with the fluid flow pushing the float upwards. The fluid has to flow through the constriction which is the gap between the float and the walls of the tube and so there is a pressure drop at that point. Since the gap between the float and the tube walls increases as the float moves upwards, the pressure drop decreases. The float moves up the tube until the fluid pressure is just sufficient to balance the weight of the float. The greater the flow rate the greater the pressure difference for a particular gap and so the higher up the tube the float moves. A scale alongside the tube can thus be calibrated to read directly the flow rate corresponding to a particular height of the float. The rotameter is cheap, reliable, has an accuracy of about ±1% and can be used to measure flow rates from about 30 x 10^-6 m^3 to 1 m^3/s.
The Pitot tube can be used to directly measure the velocity of flow of a fluid, rather than the volume rate of flow and consists essentially of just a small tube inserted into the fluid with an opening pointing directly upstream (FIG. 32). The fluid impinging on the open end of the tube is brought to rest and the pressure difference measured between this point and the pressure in the fluid at full flow. The difference in pressure between where the fluid is in full flow and the point where it is stopped is due to the kinetic energy of the fluid being transformed to potential energy, this showing up as an increase in pressure. Because kinetic energy is 1/2 mv^2, the velocity is proportional to the square root of the pressure difference.
5.2 Turbine meter
The turbine flowmeter (FIG. 33) consists of a multi-bladed rotor that is supported centrally in the pipe along which the flow occurs. The rotor rotates as a result of the fluid flow, the angular velocity being approximately proportional to the flow rate. The rate of revolution of the rotor can be determined by attaching a small permanent magnet to one of the blades and using a pick-up coil. An induced e.m.f pulse is produced in the coil every time the magnet passes it. The pulses are counted and so the number of revolutions of the rotor can be determined. The meter is expensive, with an accuracy of typically about ±0.1%. Another form uses helical screws which rotate as a result of the fluid flow.
5.3 Ultrasonic time of flight flow meter
FIG. 34 shows one way ultrasonic waves can be used to determine the flow rate of a fluid. There are a pair of ultrasonic receiver transmitters, one on each side of the pipe through which the fluid flows.
If c is the velocity of the sound in still fluid, for the beam of sound going from left-to-right in the direction of the fluid flow the speed is (c + V cos 9) while for the sound going from right-to-left in the opposite direction to the fluid flow the speed is (c - v cos 0). If L is the distance between the two transmitter-receivers, then the times taken to go in the two directions are L/(c + v cos ^ and L/(c - v cos 9). The differences in these times is:
delta_t = 2Lvcos^ 2Lvcos^ C2
Thus measurement of the time can be used to determine the flow velocity. This method can be used for pipes from 75 mm to 1500 mm diameter, with fluid velocities from about 0.2 m/s to 12 m/s with an accuracy of about ±1% or better.
FIG. 32 Pitot tube
FIG. 33 Basic principle of the turbine flowmeter
FIG. 34 Ultrasonic flow meter
Application---A commercially available time of flight ultrasonic flow meter includes the following in its specification:
Accuracy ±1 % of flow value
Non-linearity en-or ±1 % of flow value
Repeatability ±0.5% of flow value
5.4 Vortex flow rate method
When a fluid flow encounters a body, the layers of fluid close to the surfaces of the body are slowed down. With a streamlined body, these boundary layers follow the contours of the body until virtually meeting at the rear of the object. This results in very little wake being produced.
With a non-streamlined body, a so-called bluff body, the boundary layers detach from the body much earlier and a large wake is produced. When the boundary layer leaves the body surface it rolls up into vortices. These are produced alternately from the top and bottom surfaces of the body (FIG. 35). The result is two parallel rows of vortices moving downstream with the distance between successive vortices in each row being the same, a vortex in one row occurring halfway between those in the other row.
For a particular bluff body, the number of vortices produced per second/ i.e. the frequency, is proportional to the flow rate. A number of methods are used for the measurement of the frequency. For example, a thermistor might be located behind the face of the bluff body (FIG. 37(a)). The thermistor, heated as a result of a current passing through it, senses vortices due to the cooling effect caused by their breaking away. Another method uses a piezoelectric crystal mounted in the bluff body (FIG. 36(b)). Flexible diaphragms react to the pressure disturbances produced by the vortices and are detected by the crystal.
Vortex flow meters are used for both liquids and gases, having an output which is independent of density, temperature or pressure, and having an accuracy of about ±1%. They are used at pressures up to about 10 MPa and temperatures of 200°C.
FIG. 35 Vortex shedding
FIG. 36 Detection systems: (a) thermistor, (b) piezoelectric crystal
FIG. 37 Coriolis flow meter
5.5 Coriolis flow meter
If a skater is spinning with arms outstretched and then pulls in his or her arms, they spin faster. As a consequence we can think of there being a torque acting on the skater's body to result in the increased angular velocity. This torque is considered to arise from a tangential force called the Coriolis force. When we move an object in a rotating system, it seems to be pushed sideways. For a body of mass M moving with constant linear radial velocity v and subject to an angular velocity o) the Coriolis force is 2Mwv.
The Coriolis flow meter consists basically of a C-shaped pipe (FIG. 37) through which the fluid flows. The pipe, and fluid in the pipe, is given an angular acceleration by being set into vibration, this being done by means of a magnet mounted in a coil on the end of a tuning fork-like leaf spring. Oscillations of the spring then set the C-tube into oscillation.
The result is an angular velocity that alternates in direction. At some instant the Coriolis force acting on the fluid in the upper limb is in one direction and in the lower limb in the opposite direction, this being because the velocity of the fluid is in opposite directions in the upper and lower limbs. The resulting Coriolis forces on the fluid in the two limbs are thus in opposite directions and cause the limbs of the C to become displaced. When the direction of the angular velocity is reversed then the forces reverse in direction and the limbs become displaced in the opposite direction. These displacements are proportional to the mass flow rate of fluid through the tube. The displacements are monitored by means of optical sensors, their outputs being a pulse with a width proportional to the mass flow rate. The flow meter can be used for liquids or gases and has an accuracy of ±0.5%. It is unaffected by changes in temperature or pressure.
6. Liquid level
Methods used to measure the level of liquid in a vessel include those based on:
1. Floats whose position is directly related to the liquid level.
2. Archimedes' principle and a measurement of the upthrust acting on an object partially immersed in the liquid; the term displacer is used.
3. A measurement of the pressure at some point in the liquid, the pressure due to a column of liquid of height h being hpg, where p is the liquid density and g the acceleration due to gravity.
4. A measurement of the weight of the vessel containing the liquid plus liquid. The weight of the liquid is Ahpg, where A is the cross sectional area of the vessel, h the height of liquid, p its density and g the acceleration due to gravity and thus changes in the height of liquid give weight changes.
5. A change in electrical conductivity when the liquid rises between two probes.
6. A change in capacitance as the liquid rises up between the plates of a capacitor.
7. Ultrasonic and nuclear radiation methods.
The following give examples of the above methods used for liquid level measurements.
Application---A problem with floats and displacers is that such instruments tend to incorporate seals which require frequent maintenance in corrosive liquid applications, also there is the problem of fluids coating the floats and apparently changing the buoyancy.
6.1 Floats
FIG. 38 shows a simple float system. The float is at one end of a pivoted rod with the other end connected to the slider of a potentiometer.
Changes in level cause the float to move and hence move the slider over the potentiometer resistance track and so give a potential difference output related to the liquid level.
FIG. 38 Potentiometer float gauge
FIG. 39 Displacer gauge
6.2 Displacer gauge
When an object is partially or wholly immersed in a fluid it experiences an upthrust force equal to the weight of fluid displaced by the object.
This is known as Archimedes' principle. Thus a change in the amount of an object below the surface of a liquid will result in a change in the upthrust. The resultant force acting on such an object is then its weight minus the upthrust and thus depends on the depth to which the object is immersed. For a vertical cylinder of cross-sectional area A in a liquid of density p, if a height h of the cylinder is below the surface then the upthrust is hApg, where g is the acceleration due to gravity, and so the apparent weight of the cylinder is (mg – hA pi g), where m is the mass of the cylinder. Such displacer gauges need calibrating for liquid level determinations for particular liquids since the upthrust depends on the liquid density. FIG. 39 shows a simple version of a displacer gauge.
6.3 Differential pressure
The pressure due to a height h of liquid above some level is hpg, where p is the liquid density and g the acceleration due to gravity. With a tank of liquid open to the atmosphere, the pressure difference can be measured between a point near the base of the tank and the atmosphere. The result is then proportional to the height of liquid above the pressure measurement point (FIG. 40(a)). With a closed tank, the pressure difference has to be measured between a point near the bottom of the tank and in the gases above the liquid surface (FIG. 40(b)). The pressure gauges used for such measurements tend to be diaphragm instruments.
6.4 Load cell
The weight of a tank of liquid can be used as a measure of the height of liquid in the tank. Load cells are commonly used for such weight measurements. Typically, a load cell consists of a strain gauged cylinder (FIG. 41) which is included in the supports for the tank of liquid.
When the level of the liquid changes, the weight changes and so the load on the load cell changes and the resistances of the strain gauges change.
The resistance changes of the strain gauges are thus a measure of the level of the liquid. Since the load cells are completely isolated from the liquid, the method is useful for corrosive liquids.
FIG. 40 Pressure level gauges
FIG. 41 Load cell
FIG. 42 Conductivity level indicator
Application An integrated circuit LM1830N can be used for signal processing with conductivity probes so that an output is given which can be used to activate a loudspeaker or a LED. The circuit compares the resistance of the liquid with the IC's internal reference resistance.
6.5 Electrical conductivity level indicator
Conductivity methods can be used to indicate when the level of a high electrical conductivity liquid reaches a critical level. One form has two probes, one probe mounted in the liquid and the other either horizontally at the required level or vertically with its lower end at the critical level (FIG. 42). When the liquid is short of the required level, the resistance between the two probes is high since part of the electrical path between the two probes is air. However, when the liquid level reaches the critical level, there is a path entirely through the liquid and so the conductivity drops. Foaming, splashing and turbulence can affect the results.
6.6 Capacitive level indicator
A common form of capacitive level gauge consists of two concentric conducting cylinders, or a circular rod inside a cylinder, acting as capacitor plates with the liquid between them acting as the dielectric of a capacitor (FIG. 43). If the liquid is an electrical insulator then the capacitor plates can be bare metal, if the liquid is conducting then they are metal coated with an insulator, e.g. Teflon. The arrangement consists essentially of two capacitors in parallel, one formed between the plates inside the liquid and the other from that part of the plates in the air above the liquid. A change in the liquid level changes the total capacitance of the arrangement. Errors can arise as a result of temperature changes since they will produce a change in capacitance without any change in level. Errors can also arise if , when the liquid level drops, the electrodes remain coated with liquid. The system can be used, with suitable choice of electrode material, for corrosive liquids and is capable of reasonable accuracy.
FIG. 43 Capacitive gauge
FIG. 45 Radionic gauges
6.7 Ultrasonic level gauge
In one version of an ultrasonic level indicator, an ultrasonic transmitter/ receiver is placed above the surface of the liquid (FIG. 44). Ultrasonic pulses are produced, travel down to the liquid surface and are then reflected back to the receiver. The time taken from emission to reception of the pulses can be used as a measure of the position of the liquid surface. Because the receiver/transmitter can be mounted outside the liquid, it is particularly useful for corrosive liquids. Errors are produced by temperature changes since they affect the speed of the sound wave. Such errors are typically about 0.18% per °C.
6.8 Nucleonic level indicators
One form of level indicator uses gamma radiation from a radioactive source, generally cobalt-60, caesium-137 or radium-226. A detector is placed on one side of the container and the source on the other. The intensity of the radiation depends on the amount of liquid between the source and detector and can be used to determine the level of the liquid.
FIG. 45 shows two possible arrangements. With a compact source and extended detector, level changes over the length of the detector can be determined. A compact source and a compact detector can be used where small changes in a small range of level are to be detected. Such methods can be used for liquids, slurries and solids, and, since no elements of the system are in the liquid, for corrosive and high temperature liquids.
7. Temperature sensors
FIG. 46 Bimetallic strip
The expansion or contraction of solids, liquids or gases, the change in electrical resistance of conductors and semiconductors, thermoelectric e.m.fs and the change in the current across the junction of semiconductor diodes and transistors are all examples of properties that change when the temperature changes and can be used as basis of temperature sensors. The following are some of the more commonly used temperature sensors.
7.1 Bimetallic strips
A bimetallic strip consists of two different metal strips of the same length bonded together (FIG. 46). Because the metals have different coefficients of expansion, when the temperature increases the composite strip bends into a curved strip, with the higher coefficient metal on the outside of the curve. The amount by which the strip curves depends on the two metals used, the length of the composite strip and the change in temperature. If one end of a bimetallic strip is fixed, the amount by which the free end moves is a measure of the temperature. This movement may be used to open or close electric circuits, as in the simple thermostat commonly used with domestic heating systems. Bimetallic strip devices are robust, relatively cheap, have an accuracy of the order of ±\% and are fairly slow reacting to changes in temperature.
7.2 Liquid in glass thermometers
The liquid in glass thermometer involves a liquid expanding up a capillary tube. The height to which the liquid expands is a measure of the temperature. With mercury as the liquid, the range possible is -35 C to +600 C, with alcohol -80°C to +70°C, with pentane -200 C to +30 C. Such thermometers are direct reading, fragile, capable of reasonable accuracy under standardized conditions, fairly slow reacting to temperature changes, and cheap.
7.3 Resistance temperature detectors (RTDs)
The resistance of most metals increases in a reasonably linear way with temperature (FIG. 47) and can be represented by the equation:
R1 = R0(1+at)
where R, is the resistance at a temperature t degree C, Ro the resistance at 0°C and a a constant for the metal, termed the temperature coefficient of resistance. Resistance temperature detectors (RTDs) are simple resistive elements in the form of coils of metal wire, e.g. platinum, nickel or copper alloys. Platinum detectors have high linearity, good repeatability, high long term stability, can give an accuracy of ±0.5% or better, a range of about -200 to +850 C, can be used in a wide range of environments without deterioration, but are more expensive than the other metals.
They are, however, very widely used. Nickel and copper alloys are cheaper but have less stability, are more prone to interaction with the environment and cannot be used over such large temperature ranges.
FIG. 47 Resistance variation with temperature for metals
Application---A commercially available platinum resistance thermometer
Includes the following
In its specification:
Range -200 C to +800 C
Accuracy ±0.01 C
Sensitivity 0.4 n/ C for 100 n
FIG. 48 Variation of resistance with temperature for thermistors
FIG. 49 Thermistors: (a) rod, (b) disc, (c) bead
7.4 Thermistors
Thermistors are semiconductor temperature sensors made from mixtures of metal oxides, such as those of chromium, cobalt, iron, manganese and nickel. The resistance of thermistors decreases in a very non-linear manner with an increase in temperature, FIG. 48 illustrating this.
The change in resistance per degree change in temperature is considerably larger than that which occurs with metals. For example, a thermistor might have a resistance of 29 k-Ohm at -20 C, 9.8 k-Ohm at 0 C, 3.75 k-Ohm at 20 C, 1.6 k-Ohm at 40 C, 0.75 k-Ohm at 60 C. The material is formed into various forms of element, such as beads, discs and rods (FIG. 49). Thermistors are rugged and can be very small, so enabling temperatures to be monitored at virtually a point. Because of their small size they have small thermal capacity and so respond very rapidly to changes in temperature. The temperature range over which they can be used will depend on the thermistor concerned, ranges within about -100 C to +300 C being possible. They give very large changes in resistance per degree change in temperature and so are capable, over a small range, of being calibrated to give an accuracy of the order of 0.1 C or better. However, their characteristics tend to drift with time. Their main disadvantage is their non-linearity.
Application---The following is part of the specification for a bead thermistor temperature sensor: Accuracy ±5% Maximum power 250 mW
Dissipation factor 7 mW/ C
Response time 1.2 s
Thermal time constant 11 s
Temperature range -40 to 125 C
FIG. 50 Thermocouple
FIG. 51 Thermocouples: chromel-constantan (E), chromel alumel (K), copper-constantan
(T)
Table 1 Thermocouples
7.5 Thermocouples
When two different metals are joined together, a potential difference occurs across the junction. The potential difference depends on the two metals used and the temperature of the junction. A thermocouple involves two such junctions, as illustrated in FIG. 50. If both junctions are at the same temperature, the potential differences across the two junctions cancel each other out and there is no net e.m.f If, however, there is a difference in temperature between the two junctions, there is an e.m.f The value of this e.m.f E depends on the two metals concerned and the temperatures / of both junctions. Usually one junction is held at 0** C and then, to a reasonable extent, the following relationship holds:
E = at + bt^2
where a and b are constants for the metals concerned. FIG. 51 shows how the e.m.f varies with temperature for a number of commonly used pairs of metals. Standard tables giving the e.m.fs at different temperatures are available for the metals usually used for thermocouples.
Commonly used thermocouples are listed in Table 1, with the temperature ranges over which they are generally used and typical sensitivities. These commonly used thermocouples are given reference letters. The base-metal thermocouples, E, J, K and T, are relatively cheap but deteriorate with age. They have accuracies which are typically about dbl to 3%. Noble-metal thermocouples, e.g. R, are more expensive but are more stable with longer life. They have accuracies of the order of ±1% or better. Thermocouples are generally mounted in a sheath to give them mechanical and chemical protection. The response time of an unsheathed thermocouple is very fast. With a sheath this may be increased to as much as a few seconds if a large sheath is used.
A thermocouple can be used with the reference junction at a temperature other than 0°C. However, the standard tables assume that the junction is at 0°C junction and hence a correction has to be applied before the tables can be used. The correction is applied using what is known as the law of intermediate temperatures, namely:
Et0 = Etj + E 1,0
The e.m.f E t0 at temperature t when the cold junction is at 0 C equals the e.m.f E1,0 at the intermediate temperature / plus the e.m.f EJA at temperature / when the cold junction is at 0 C. Consider a type E thermocouple. The following is data from standard tables.
Temp. (°C): 0 20 200
e.m.f. (mV) 0 1.192 13.419
Thus, using the law of intermediate temperatures, the thermoelectric e.m.f. at 200° C with the cold junction at 20°C is:
Note that this is not the e.m.f. given by the tables for a temperature of 180 C with a cold junction at 0 C, namely 11.949 mV.
To maintain one junction of a thermocouple at 0 C, it needs to be immersed in a mixture of ice and water. This, however, is often not convenient and a compensation circuit (FIG. 52) is used to provide an e.m.f. which varies with the temperature of the 'cold' junction in such a way that when it is added to the thermocouple e.m.f. it generates a combined e.m.f which is the same as would have been generated if the cold junction had been at 0°C.
When a thermocouple is connected to a measuring circuit, other metals are involved (FIG. 54). Thus we can have as the 'hot' junction that between metals A and B and the 'cold' junction effectively extended by the introduction of copper leads and the measurement instrument.
Provided
The junctions with
The intermediate materials are at the same temperature, there is no extra e.m.f involved and we still have the e.m.f. as due to the junction between metals A and B.
FIG. 52 Cold junction compensation
Application---Integrated circuits are available which combine amplification with cold junction compensation for thermocouples, e.g. the Analog Devices AD594 (FIG. 53). This, when used with a -J- S V supply and a constantan-iron thermo couple, gives an output of 10 mV/°C.
FIG. 53 AD594
FIG. 54 The junctions with a measurement instrument
Application---The specification for an integrated LM35 temperature sensor includes:
Accuracy at 25 C ±0.4%
Non-linearity 0.2 C
Sensitivity 10 mV/C
7.6 Thermo-diodes and transistors
When the temperature of doped semiconductors changes, the mobility of their charge carriers change. As a consequence, when a p-n junction has a potential difference across it, the current through the junction is a function of the temperature. Such junctions for use as temperature sensors are supplied, together with the necessary signal processing circuitry as integrated circuits, e.g. LM3911 which gives an output voltage proportional to temperature. In a similar manner, transistors can be used as temperature sensors. An integrated circuit temperature sensor using transistors is LM35. This gives an output, which is a linear function of temperature, of 10 mV/°C when the supply voltage is 5 V.
7.7 Pyrometers
Methods used for the measurement of temperature which involve the radiation emitted by the body include:
1. Optical pyrometer
This is based on comparing the brightness of the light emitted by the hot body with that from a known standard.
2. Total radiation pyrometer
This involves the measurement of the total amount of radiation emitted by the hot body by a resistance element or a thermopile.
The optical pyrometer, known generally as the disappearing filament pyrometer, involves just the visible part of the radiation emitted by a hot object. The radiation is focused onto a filament so that the radiation and the filament can both be viewed in focus through an eyepiece (FIG. 55). The filament is heated by an electrical current until the filament and the hot object seem to be the same colour, the filament image then disappearing into the background of the hot object. The filament current is then a measure of the temperature. A red filter between the eyepiece and the filament is generally used to make the matching of the colors of the filament and the hot object easier. Another red filter may be introduced between the hot object and the filament with the effect of making the object seem less hot and so extending the range of the instrument.
FIG. 55 Disappearing filament pyrometer
FIG. 56 Total radiation pyrometer
The disappearing filament pyrometer has a range of about 600°C to 3000°C , an accuracy of about ±0.5% of the reading and involves no physical contact with the hot object. It can thus be used for moving or distant objects.
The total radiation pyrometer involves the radiation from the hot object being focused onto a radiation detector. FIG. 56 shows the basic form of an instrument which uses a mirror to focus the radiation onto the detector. Some forms use a lens to focus the radiation. The detector is typically a thermopile with often up to 20 or 30 thermocouple junctions, a resistance element or a thermistor. The detector is said to be broad band since it detects radiation over a wide band of frequencies and so the output is the summation of the power emitted at every wavelength.
It is proportional to the fourth power of the temperature (the Stefan-Boltzmann law). The accuracy of broad band total radiation pyrometers is typically about ±0.5% and ranges are available within the region 0 C to 3000°C. The time constant (a measure of how fast the system responds to a change in temperature and is the time taken to reach about 63% of the final value) for the instrument varies from about 0.1s when the detector is just one thermocouple or small bead thermistor to a few seconds with a thermopile involving many thermocouples. Some instruments use a rotating mechanical chopper to chop the radiation before it impinges on the detector. The aim is to obtain an alternating output from the detector, since amplification is easier with an alternating voltage. It is thus of particular benefit when the level of radiation is low.
However, choppers can only be used with detectors which have a very small time constant and thus tend to be mainly used with small bead thermistor detectors.
8. Sensor selection
The selection of a sensor for a particular application requires a consideration of:
1. The nature of the measurement required, i.e. the sensor input. This means considering the variable to be measured, its nominal value, the range of values, the accuracy required, the required speed of measurement, the reliability required and the environmental conditions under which the measurement is to be made.
2. The nature of the output required from the sensor, this determining the signal processing required. The selection of sensors cannot be taken in isolation from a consideration of the form of output that is required from the system after signal processing, and thus there has to be a suitable marriage between sensor and signal processing.
Then possible sensors can be identified, taking into account such factors as their range, accuracy, linearity, speed of response, reliability, life, power supply requirements, ruggedness, availability and cost.
Example:
Select a sensor which can be used to monitor the temperature of a liquid in the range 10 C to 80 C to an accuracy of about 1 C and which will give an output which can be used to change the current in an electrical circuit.
There are a number of forms of sensor that can be used to monitor such a temperature in the range, and to the accuracy, indicated. The choice is, however, limited by the requirement for an output which can change the current in an electrical circuit. This would suggest a resistance thermometer. In view of the limited accuracy and range required, a thermistor might thus be considered.
Example:
Select a sensor which can be used for the measurement of the level of a corrosive acid in a circular vessel of diameter 1 m and will give an electrical output. The acid level can vary from 0 to 3 m and the minimum change in level to be detected is 0.1 m. The empty vessel has a weight of 50 kg. The acid has a density of 1050 kg/ml Because of the corrosive nature of the acid there could be problems in using a sensor which is inserted in the liquid. Thus a possibility is to use a load cell, or load cells, to monitor the weight of the vessel.
Such cells would give an electrical output. The weight of the liquid changes from 0 when empty to, when full, 1050 x 3 x 7r(lV4) x 9.8 = 24.3 kN. Adding this to the weight of the empty vessel gives a weight that varies from about 0.5 kN to 4.9 kN. A change of level of 0.1 m gives a change in weight of 0.10 x 1050 x 7r(lV4) x 9.8 = 0.8 kN. If the load of the vessel is spread between three load cells, each will require a range of about 0 to 5 kN with a resolution of about 0.3 kN.
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