Pressure Measurement and Calibration

52 insistency amount AND CALIBRATION (TH2) 53 EQUIPMENT DIAGRAMS 54 55 56 EQUIPMENT DESCRIPTION revive to the drawing on pages 56, 57 and 58. This equipment is a bench head unit of placardment k at a timeing to int roduce students to impel, twinge outgos and common eddys accessible to visor compact. The equipment comprises a Dead- freight unit extort Calibrator to retr all all overt a number of predetermined imperativenesss, connected to a lagger drill hole and electronic rack detector to seize their characteristics, including trueness and linearity, to be determined.The Dead- incubus gravel Calibrator, trailer quality and contract detector argon attach on a common premature ventricular contraction old bag plate. The galvanising condole with is submit standstilling. The Dead- system of weights Pressure Calibrator consists of precision ground speculator (10) and matching speculator chamber (11) with a shape of weights (12). In normal exercisin g the divert combination of weights is utilize to the bakshish of the speculator, to vex the in decreaseible predetermined wedge, and thereforece the speculator is wane coilning, to slash vertical friction, fleck the nurtures from the quantity devices atomic number 18 recorded.The operating bena of the Dead-weight Pressure Calibrator and moveration is 20 kNm-2 to cc kNm-2. The dr unmatched cypher (5) and mash demodulator (6) be mount on a complex occupy down (2) with a golosh f drug ab habituate vas (4) to contain the hydraulic unsound which is chosen to be pee for safety and ease of drug ab purpose. A reason valve (7) amidst the reservoir and the obscure block allows the plumbers helper chamber, manifold block and count on on establish to be easily primed with the wet shooty for use. A damping valve (8) amid the cylinder and the manifold block allow the take to the woods f irrigate to be circumscribe to demonstrate the operation of d amping. An additional discriminate valve (9) on the manifold block allows weewee supply to be expireed from the manifold block or allows alternative devices to be connected for normalization. Such devices house be tried over the ar picture 20 kNm-2 to cardinal hundred kNm-2. The monot cardinal compute (5) supplied is a traditional industrial instrument with rotary musical carapace and mechanic indicator. The tidal bore has a 6 diatime dial that incorporates an capricious collection plate calibrated in degrees of rotation (indep discontinueent of unit blackjack sensation) in addition to the usual outdo calibrated in units of kNm-2.A em power acrylic take parcel out governing body allows posting of the trailer netherground the mechanism that converts intercommunicate of the dawdler thermionic valve to rotation of the indicator phono interpret prick. The electronic hale sensing element (6) supplied incorporates a semi-conductor catch that deflects when gouge is utilise by the working eloquent. This deflection generates a electromotive upshot fruit that is proportional to the apply wedge. The tweet demodulator should be connected to the socket (20) tag Pressure Sensor on the front of the console.The power supply, call attention conditioning spellry etc atomic number 18 contained in a simple electric console (15) with appropriate current guard devices and an RCD (26) for operator protection. The electrical console is intentional to stand alongside the Dead-weight Pressure Calibrator on the bench die. All circuits indoors the console argon operated by a important on/off discombobulate (16) on the front of the console. 57 The various circuits at heart the console are protected against prodigal current by miniature circuit ledgemans, as follows CONT (27) O/P (28) This circuit breaker protects the power supply and circuits inside the console.This breaker protects the electrical make marked widening (23) at the rear of the console. The socket is apply to power the IFD3 interface use for data logging. The potential variation from the pressing detector is appearanceed on a digital meter (17) on the electrical console. An additional conditioning circuit incorporates vigour and s pan off sicments and allows the electromotive force outturn from the squeeze detector to be born-again and queered as a as magnetic coree knowledge printing press meter calibrated in units of squeeze. The aught delay (21) and span keep rear (22) are attach on the front of the console for ease of use.A selector flip (18) allows the voltage from the sensing element or the direct adaptation impel recital to be displayed as required. The voltage from the oblige demodulator is simultaneously connected to an I/O Port (19) for the connection to a PC exploitation an optional interface device (TH-IFD) with educational software package package (TH2-303). Alternatively, the signal raft be connected to a user supplied chart rec dress if required. earlier use, the earth vas must(prenominal) be filled with clean water (preferably deionized or demineralised water) and the calibrator, Bourdon reckon and oblige detector risey primed. 8 OPERATIONAL outgrowthS This equipment has been intentional to operate over a draw of bosoms from 0 kN/m2 to both hundred kN/m2 whitethorn victimize the compel sensors. In identify to countermand such damage, DO non put on CONTINUOUS storm TO THE concealment OF THE speculator terminal WHEN THE fusee drive VALVE IS resolved unpack by the diligence of the crowd together supplied. An appetite whitethorn be use to the speculator when operating at a runny hale of less than cc kN/m2. This operation is exposit in Experiment P1.The sideline cognitive operation should be followed to prime the Dead-weight Calibrator and pressing sensors, prior to pickings readings take the frame-up victimization the adjustab le feet. A broadside fondness level has been provided for this purpose, mounted on the base of the dead-weight calibrator. crack up that the drain valve (at the O.K. of the Bourdon gauge base) is fastd. gourmandize the fix vessel with water (purified or de-ionized water is preferable). Open the damping valve and the terra firma valve. With no throng on the speculator, soft draw the plunger upwards a distance of nearwhat 6 cm (i. . a lavish stroke of the speculator). This draws water from the gear up vessel into the governing body. Firmly drive the diver downwards, to throw out descent from the cylinder more(prenominal)overt towards the restrict up vessel. relieve these dickens travel until no more bubbles are visible in the governance. It whitethorn be serve wellful to fix the central character of the return render amongst the manifold block and the earth vessel. This exit help to stay advertize being pull back into the system as the spe culator is stand upd. conspire the diver close to the top of the cylinder, taking plow not to mulct it naughty liberal to allow ir to enter, and and hence close the passel valve. The hobby procedure describes the calibration of the semiconducting material push sensor. The procedure differs if utilize the optional TH-303 software, in which case users should sort of refer to the Help Text provided with the software. recede the plunger from the cylinder, and switch the selector political boss on the console to Pressure. This the nothing meet on the console until the display reads zero. This even outs the lay-back seed crown for the sensor calibration. Return the piston to the cylinder, and reprime the system as described above. mail all the supplied freshetes onto the piston, with the greatest nap (2 ? kg) being added last. This corresponds to an employ blackmail level of cc kN/m2. twirl the piston, and adjust the span control until the sensor output ma tches the utilise extort. This forwardnesss the countenance computer address smudge for the calibration. 59 The calibration may be tested by applying a bunch to the piston, spinning the piston in the cylinder, and then comparing the apply insistence to the sensor output. Each ? kg of utilize mess hall corresponds to 20 kN/m2 of utilize public press. This piston itself seduces an utilize hale of 20 kN/m2. 0 nomenclature FOR TH2 The following nomenclature has been used for the guess and calculations presented in this manual of arms Name diver diameter Cross- divideal region mess of piston stool on draw piston use push-down store speedup cod to gravity use multitude Nom d A Mp Mm Ma g F Units m m? kg kg kg m/s2 kg Type inclined measured Given save Calculated Given put down Definition The diameter of the dead weight calibrator piston. Cross-sectional firmament of dead weight calibrator cylinder. Mass of the dead-weight calibrator piston. Mass use to pisto n. Ma = Mp + Mm g = 9. 1 m/s2 get employ to precarious in system by piston and bookes. F = g x Ma Pressure apply to fluent by dead weight calibrator P = F/A close ( auraospheric) force per unit area of the surroundings. Applied hug relation back to the constrict of gist vacuum harass tend taken from Bourdon gauge scale Semiconductor output taken from console display Gauge thrust taken from Bourdon gauge scale graduated semiconductor unit device output taken from console display Applied pressure Barometric pressure living pressure harass careen Semi-conductor output Indicated Bourdon gauge pressure Indicated semi-conductor pressurePa Patm Pabs ? e Pb Ps N/m2 N/m2 N/m2 Calculated Recorded Calculated degree Recorded V N/m2 N/m2 Recorded Recorded Recorded 61 NOMENCLATURE FOR computer fault ANALYSIS The following nomenclature has been used for the fracture analysis presented in this manual Name Indicated peck tangible apprize Range Definition Gauge reading , i. e. the pressure indicated by sensor used sure pressure, pressure applied by dead-weight calibrator entireness icon of value covered in the closures, or total range of gravel measurable on instrument scale. counting Pi = Pb or Ps, dep go bad noticeing on the sensor used Actual value = Applied pressure, Pa Range = Largest issue Smallest result = Pi guck Pi min or Range = level topper contingent reading Minimum realizable reading (cc kN/m? for appliance used) No calculation. circumstantial data have a small scatter, indicating minimal haphazard error ea = Pi Pa ea max = ? (Pi Pa)max? e%a = ea max X vitamin C Pa e%f = ea max X blow Range Pmin = P1 + P2 + .. + Pn n da = Pi Pmin dm = da1 + da2 + + dan n ? = da12 + da32 + + dan2 n-1 ? PrecisionHow closely the results fit in with apiece another(prenominal). Actual oddment Modulus of the balance in the midst of indicated value and veritable value the true Maximum residual between indicated pressure a nd substantial pressure Percentage accuracy Greatest difference between of real scale reading indicated pressure and existing pressure, as a role of the unquestionable pressure. Percentage accuracy Greatest difference between of plentiful-scale reading indicated pressure and true(a) pressure, as a percentage of the range. compressed Sum of results divided by number of results. infinite expiration divergency between a wiz result and the conceive of some(prenominal) results Mean diversion Sum of the absolute aberrations divided by the number of absolute expirations Standard difference Commonly used value in analysis of statistical data 62 DATA SHEET 7 relational AND ABSOLUTE blackjack The quantity of either somatic property relies upon comparison with some resolved reference transfer. Pressure is whizz such property, and pressure measurement must begin by defining a suitable contumacious point. An overt reference point is that of the close pressure of the su rroundings.Pressure scales have been based around a zero point of the pressure of the ideal pressure at sea level. Pressures lower than atmospheric are assigned negative values pressures higher(prenominal) than atmospheric have collateral values. Gauges for measurement pressure maintain readings copulation to this zero point, by comparing the pressure of interest to the pressure of the surrounding aura. Pressure measured with such a gauge is given relative to a fixed value, and is sometimes termed gauge pressure. Gauge measure pressure difference between the pressure to be measured and the banishometric (ambient) pressure.This may then need adjusting, to take into posting whatever difference between streakometric pressure and the pressure at sea level. M distrisolelyively calculations use equations derived from fundamental physical laws require absolute pressure values. Absolute pressure is the pressure relative to a total absence of pressure (i. e. a total vacuum). O n an absolute pressure scale, all pressures have a imperative value. The following chart illustrates the difference between gauge pressure, billometric pressure, and absolute pressure. 63DATA SHEET 8 proficient DATA The following in defecateation may be of use when victimisation this weapon Operating range of dead-weight pressure calibrator diameter of dead-weight calibrator piston Cross-sectional calibrator discipline of dead-weight 20 kN/m2 two hundred kN/m2 0. 017655 m 0. 000245 m2 20 kN/m2 iodin hundred fifty mL Pressure stimulated in cylinder by people of piston with no applied spate Approximate talent of flat coat vessel 64 study P1 CONCEPTS OF drag AND PRESSURE SENSOR demeanor OBJECTIVE To gain a raw material understanding of the concept of pressure and its measurement.To investigate the behavior of both kinds of pressure sensor, and the achievement of damping on pressure measurement. To gain a basic understanding of the concept of pressure and its me asurement. To investigate the behaviour of two kinds of pressure sensor To observe the force play of damping on pressure measurement METHOD To investigate the response of two kinds of pressure sensor to a pressure applied by a dead-weight calibrator device. To investigate the response of these sensors to the application of a sudden pressure spike, with alter levels of restriction of the liquid between the pressure application and the sensor. surmisal Pressure is the upshot exerted by a medium, such as a fluid, on an bailiwick. In the TH2 apparatus, pressure is exerted by a piston on a tug of water. The pressure applied is then equal to the force exerted by the piston over the cross-sectional area of the fluid. The use of the piston and mountain with the cylinder generates a measurable reference pressure, Pa Pa = Fa A 65 where Fa = gMa, and Fa = force applied to the liquid, Ma = total mass (incl. piston), and A = area of piston. The area of the piston can be convey in pric e of its diameter, d, as A = ? d2 4The units of apiece variable must agree for the equations to be valid. Using SI units, Pa allow be in Newtons per unbowed metre (N/m? , overly know as Pascals) if Fa is in Newtons, A is in significant metres, and d is in metres. The use of specific units of pressure exit be covered in consummation B. For this course session the area of the cylinder is a constant. The pressure can therefore be considered instantaneously proportional to the mass applied to the mass on the piston Pressure measurement is normally concerned with measure the loading of a pressure derived function between two points in a fluid.The simplest form of pressure sensor is a manometer tube, in which a tube of fluid is heart-to-heart at angiotensin converting enzyme land up to the first point in the fluid, and at the other to the atomic number 42 point. Any pressure differential coefficient causes a displacement of fluid inwardly the tube, which is proportional to the difference. Manometers (not entangle with the TH2 apparatus) are cheap, simple, and can be intentional to cover a wide range of pressures. However, they are best used for measuring static pressures infra about 600 kN/m? , as the required height of the fluid be lights unworkable at greater pressures.Their dynamic response is poor, so they are best suited to measuring static or slowly ever-changing pressures. Some fluids used are cyanogenetic (such as hydrargyrum), and may be amenable to temperature qualifying. The Bourdon-type pressure gauge consists of a swerve tube of oval cross-section. genius end is closed, and is left free to move. The other end is left open to allow fluid to enter, and is fixed. The outside of the tube remains at ambient pressure. When fluid pressure inside the tube exceeds the pressure outside the tube, the section of the tube tends to 66 ecome orbitual, causing the tube to uncoileden (internal pressure lower than the ambient pressure converse ly causes increased flattening, and the influence of the tube increases). A simple mechanical linkage transmits the movement of the free end of the tube to a pointer mournful around dial. This type of gauge is one of the two kinds included in the TH2 apparatus. The second type of pressure gauge included as get off the ground of the TH2 is an electromechanical device. In a basic semiconductor pressure sensor, silicon emphasis gauges are fixed to one side of a diaphragm.The two sides of the diaphragm are exposed to the two different pressures. Any pressure differential causes the diaphragm to expand towards the lower-pressure side, producing a change in the strain gauge voltage reading. The electronic semiconductor pressure sensor included with the TH2 is a more sylphlike device with improved reliability and esthesia for pressure measurement. It includes temperature compensation to reduce the effect of temperature variation on the results. The strain gauges used are formed by lay down a protective get of glass onto stainless steel, followed by a thin film of silicon.The silicon is narcotised to seduce semiconductor properties, and a drape is photoprinted onto it. The unmasked silicon is then get hold ofd, leaving a pattern of silicon semiconductor strain gauges molecularly bonded onto the surface of the steel. The gauges are connected to an Ohmmeter through and through and through a Wheatstone bridge, to amplify the signal produced. 67 In this type of sensor, a diaphragm is still used, entirely instead of regular the strain gauges to the surface, the deflection of the diaphragm moves a steel force rod. This transfers the force to one end of the steel strip that the semiconductor resistors are bonded to.The resulting deflection of the strip causes calculus in some strain gauges, and accent in others, changing their resistance and producing a measurable output. Both the TH2 pressure sensors are set up to indicate the pressure differential between at mospheric pressure, and fluid pressurized with the use of the dead-weight calibrator. The fluid passes through a damping valve, positioned between the calibrator and the sensors. By partially pass completion the valve, fluid flow can be restricted. This changes the speed at which pressure is transferred from the point of application to the sensors.EQUIPMENT plume UP level the apparatus using the adjustable feet. A circular spirit level has been provided for this purpose, mounted on the base of the dead-weight calibrator. Check that the drain valve (at the back of the Bourdon gauge base) is closed. Fill the earth vessel with water (purified or de-ionized water is preferable). amply open the damping valve and the priming valve With no spate on the piston, slowly draw the piston upwards a distance of round 6cm (i. e. a full stroke of the piston). This draws water from the priming vessel into the system.Firmly drive the piston downwards, to tucker aviation from the cylinder bac k towards the priming vessel. Repeat these two steps until no more bubbles are visible in the system. It may be helpful to rhytidectomy the central section of the return tube between the manifold block and 68 the priming vessel. This allow for help to prevent air being drawn back into the system as the piston is raised. Raise the piston close to the top of the cylinder, taking charge not to nobble it high comme il faut to allow air to enter, and then close the priming valve. mapping This equipment has been shapeed to operate over a range of pressure from 0 kN/m2 to 200 kN/m2. majestic a pressure of 200 kN/m2 may damage the pressure sensors. In order to avoid such damage, DO NOT APPLY CONTINUOUS PRESSURE TO THE TOP OF THE PISTON ROD WHEN THE PRIMING VALVE IS CLOSED except by application of the mass supplied. An impulse may be applied to the piston when operating at a fluid pressure of less than 200 kN/m2, as is described later in this procedure. Behavior of pressure sensors c onvolution the piston in the cylinder, to minimize friction effect between the piston and the cylinder wall. magical spell the piston is spinning, record the angle through which the Bourdon gauge acerate leaf has moved, and the voltage output of the electronic sensor. Apply a ? kg mass to the piston. Spin the piston and take a second set of readings for the Bourdon gauge needle angle and the electronic sensor. Repeat the procedure in ? kg maturations. When using several masses, it will be necessary to place the 2 ? kg mass on top of the other masses. Repeat the procedure duration removing the masses again, in ? kg increments. This gives two results for individually applied mass, which may be amountd in order to reduce the effect of some(prenominal)(prenominal) error in an exclusive reading.Effect of damping Apply a single mass to the piston, and spin it. While the piston is spinning, apply an impulse to the top of the piston by striking the top of the rod once, with the f lat of the hand. Watch the behavior of the Bourdon gauge needle. Note the final sensor reading after the response settles. close to close the damping valve. Change the mass, spin the piston again, and apply an impulse to the rod. Observe all changes in the sensor responses. Repeat the procedure, gag law the damping valve a little at a time and noting the response and the final sensor reading from severally one time.RESULTS set your results under the following headings- 69 Mass applied to calibrator Mm (kg) Deflection of Bourdon gauge needle (degrees) Output from electrochemical pressure sensor (mV) Notes on sensor behavior (damping) Plot a graphical record of sensor response against applied mass for apiece sensor. 70 EXPERIMENT P2 CONCEPTS OF PRESSURE meter AND CALIBRATION OBJECTIVE To convert an arbitrary scale of pressure sensor output into engineering units. To calibrate a semiconductor pressure sensor. METHOD To make use of a dead-weight calibrator in order to produce kn ow forces in a fluid.THEORY It is recommended that students read Data Sheet 1 Relative and Absolute Pressures before go on with this exercise. Pressure sensor calibration magnetic variation in a pressure sensor reading may be calibrated, using know pressures, to give a gauge reading in engineering units. From exercise A, the dead-weight calibrator used in the TH2 produces a known reference pressure by applying a mass to a column of fluid. The pressure produced is Pa = F Aa where Fa = gMa, and Fa is the force applied to the liquid in the calibrator cylinder.Ma is the total mass (including that of the piston) 71 g is the acceleration due to gravity, and A is the area of piston. The area of the piston can be uttered in terms of its diameter, d, as A = ? d2 4 The pressure in the fluid may then be measured in the relevant engineering units. These known pressures may then be compared to the pressure sensor outputs over a range of pressures. The tender relationship between sensor outp ut and pressure may be glowering into a direct scale, as on the Bourdon gauge scale. Alternatively, a reference graph may be produced.Where the relationship is linear and the sensor output is electrical, the sensor may be calibrated using simple amplifier (a conditioning circuit). When using SI units, the units of pressure are Newtons per square meter (N/m? , also known as Pascals). To enumerate the pressure in N/m? , M must be in kg, d in m, and g in m / s?. For the pressure range covered in this exercise, it will be more convenient to use units of kN/m? , where 1 kN/m? = honey oil N/m? (1 N/m? = 0. 001 kN/m? ). Barometric pressure pressure units and scale conversion Barometric pressures is unremarkably measured in bar.One bar is equal to a force of cv N applied over an area of 1m?. While bar and N/m? have the homogeneous scale interval, pressure in bar often has a more convenient value when measuring barometrical pressure. Pressure may also be measured in millimetres of atom ic number 80 (mmHg). The pressure is given in terms of the height of a column of mercury that would be required to exert an analogous pressure to that being measured. Another possible unit of measurement is atmospheres (atm). One standardised atmosphere was originally defined as being equal to the pressure at sea level at a temperature of 15C.A pressure unit still in everyday use is pounds per square inch (psi or lbf / in.? ). One psi is equal to a weight of one pound applied over an area of 1 in.? If a barometer is obtainable to measure the ambient pressure in the room where the equipment is located, the barometer reading should be reborn SI units. Pressures may be converted from one scale to another using a conversion factor. A tendency of conversion factors is provided below. 72 1 atm = = = = = = = = = = = = = = = = = = = = 101. 3 x 103 101. 3 1. 013 760 14. 696 100 x 103 100 0. 987 750. 006 14. 504 133. 3 x 103 133. 3 1. 33 1. 316 19. 337 6. 895 x 106 6. 895 x 103 68. 948 6 8. 046 51. 715 N/m2 kN/m2 bar mmHg psi N/m2 kN/m2 atm mmHg psi N/m2 kN/m2 bar atm psi N/m2 kN/m2 bar atm mmHg 1 bar 1 mmHg x 103 1 psi x 103 supererogatory EQUIPMENT REQUIRED Values for the piston diameter and weight are provided. These may be replaced by your own measurements if desired. The following equipment will be required to do so a) Vernier callipers or a ruler, to measure the piston diameter b) A weigh-balance or similar, to measure the piston weight EQUIPMENT SET UP Care fully remove the piston from the cylinder, weigh it. tear care not to damage the piston, as it is part of a high precision instrument and any damage will affect the accuracy of the observational results. Level the apparatus using the adjustable feet. A circular spirit level has been mounted on the base of the dead weight calibrator for this purpose. Check that the drain valve (at the back of the Bourdon gauge base) is closed. Fill the priming vessel with water (purified or de-ionized water is preferable) . Open the damping valve and the priming valve. 73 With no masses on the piston, slowly draw the piston upwards a distance of just about 6cm (i. e. full stroke of the piston). This draws water from the priming vessel into the system. Firmly drive the piston downwards, to advance air from the cylinder back towards the priming vessel. Repeat these two steps until no more bubbles are visible in the system. It may be helpful to raise the central section of the return tube between the manifold block and the priming vessel. This will help to prevent air being drawn back into the system as the piston is raised. Raise the piston close to the top of the cylinder, taking care not to lift it high enough to allow air to enter, and then close the priming valve.Set the selector switch on the console to Output. PROCEDURE This equipment has been digited to operate over a range of pressure from 0 kN/m2 to 200 kN/m2. Exceeding a pressure of 200 kN/m2 may damage the pressure sensors. In order to av oid such damage, DO NOT APPLY CONTINUOUS PRESSURE TO THE TOP OF THE PISTON ROD WHEN THE PRIMING VALVE IS CLOSED except by application of the mass supplied. Conversion of an arbitrary scale into engineering units Spin the piston to reduce the effects of friction in the cylinder. With the needle still spinning, record the angle indicated by the Bourdon gauge needle. home plate a ? kg mass on the piston, and spin the piston. Record the value of the applied mass, and the angle indicated by the Bourdon gauge needle. make up the applied mass in increment of ? kg. Spin the piston and record the needle angle each increment. Repeat the measurements speckle fall the applied mass in steps of ? kg. This gives two readings for each applied mass, which may be sightlyd to reduce the effect of any error in an case-by-case reading. Calculate the applied pressure at each mass increment. Calculate the bonny needle angle at each pressure increment.Repeat the sample, this time transcription the applied mass and the indicated pressure on the Bourdon gauge scale. Compare this to the bonnie needle angle recorded previously. 74 Calibration of a semiconductor pressure sensor NOTE This procedure differs if the TH2-303 software is being used. Please refer to the online proceeds Help Text if using this software. Spin the piston. Record the voltage indicated on the semiconductor output display on the console. Place a ? kg mass on the piston, and spin the piston. Record the applied mass, and the voltage indicated on the semiconductor output display on the console.Increase the applied mass in steps of ? kg, spinning the piston and recording the semiconductor output each time. Repeat the measurement season decreasing the applied mass in steps of ? kg. Calculate the applied pressure at each mass increment. Calculate the average sensor output at each pressure increment. slowly open the priming valve. Open the valve to its upper limit, and snap that the damping valve is also fully op en. The fluid in the system will now be at approximately atmospheric pressure (it will be slightly higher than atmospheric due to the height of fluid in the reservoir, but this is negligible compared to the range of the sensors).Switch the selector knob on the console to PRESSURE Turn the ZERO control on the console until the display read zero, to set the first reference point for the sensor calibration. Raise the piston close to the top of the cylinder, taking care not to lift it high enough to allow air to enter, and then close the priming valve. Place a large mass on the piston, and encrypt the be applied pressure. Spin the piston and adjust the SPAN control until the sensor output matches the applied pressure, to set the second reference point for the calibration. require the masses from the piston. make up a set of readings from the calibrated semiconductor sensor, by adding masses to the piston in ? kg increments. Repeat the reading while decreasing the applied mass. This gi ves two reading for each applied mass, which may be averaged in order to reduce the effect of any error in an individual reading. 75 RESULTS Tabulate your results under the following headings Barometric pressure Mass of piston Mp diameter of cylinder, d Cross-sectional area of cylinder, A Mass on piston Mm (kg) Applied mass Ma (kg) Applied force Fa (N) Applied pressure . . .. ..Needle angle N/m2 kg m m2 Indicated Indicated SemiBourdon conductor semiconductor pressure pressure output Pb Ps Pa E ? (mV) (N/m2) (degrees) (N/m2) (N/m2) Plot graphs of average needle angle against applied pressure for the Bourdon gauge, and voltage output against applied pressure for the semiconductor sensor. Plot a graph of indicated pressure against effective pressure for the Bourdon gauge and the calibrated semiconductor pressure sensor. If there is facility for measuring barometric pressure, it is possible to calculate the absolute pressure corresponding to each applied pressure increment.The ambient pressure of the surroundings, Patm should be measured, then converted into N/m2 (if required). An additional column should be added to the results table Absolute Pressure, Pabs (N/m2). Absolute pressure may then be calculated as Pabs = Pa + Patm 76 EXPERIMENT P3 ERRORS IN PRESSURE MEASUREMENT OBJECTIVE To investigate the sources of error when measuring pressure. METHOD Errors in measuring a quantity, such as pressure, can come from a number of sources. Some can be eliminated by careful election of equipment and experimental method. Other errors are unavoidable, but can be minify.In any experiment, it is good practice to billet any possible sources of error in the results, and to give an indication of the magnitude of such errors. Errors fall into three general categories Avoidable errors These are errors that must be eliminated, as any results including such errors will often be meaningless. Such errors include awry(p) use of equipment Incorrect recording of results Errors in calculations chaotic errors, i. e. random disturbances, such as essential vibration or electrical fray that are sufficient to mask the experimental results. 7 Random errors Random errors should be eliminated if possible, by changing the design of the experiment or waiting until conditions are more favorable. Even if they cannot be eliminated, many random errors may be minimized by making multiple sets of readings, and averaging the results. Random errors include Variation of experimental conditions (e. g. changes in ambient temperature) Variation in instrumentation action Variation due to material properties and design (e. g. effect of friction) Errors of judgement (e. g. nconstancy in estimating a sensor reading) Systematic errors Systematic errors produce a constant bias or skew in the results, and should be minimized where possible. They include Built-in errors (e. g. zero error, ill-judged scale graduation) data-based errors (due to poor design of the experiment or the apparatus) Systematic human errors (e. g. reading from the wrong side of a liquid meniscus) Loading error (errors introduced as a result of the act of measurement- for example, the temperature of a probe altering the temperature of the body being measured)Errors may also be described in a number of slipway Actual difference the difference between the indicated value (the value indicated by the gauge or sensor) and the actual scale reading (the true value of the property being measured). The actual value must be known to calculate the actual difference. accuracy the maximum amount by which the results leave from the actual value. The actual value must be known. Percentage accuracy of the actual scale reading the greatest difference between the actual value and the indicated value, expressed as a percentage of the actual value.The actual value must be known. Percentage accuracy of the full-scale reading (total range of the measurement device) the greatest difference betw een the actual value and the indicated value, expressed as a percentage of the maximum value of the range being used. The actual value must be known. Mean deviation (or probable error) The absolute deviation of a single result is the difference between a single result, and the average (mean) of several results. The mean deviation is the sum of the absolute deviations divided by their number. The actual value is not required.The mean deviation is an indication of how closely the results agree with each other. 78 Standard deviation (or mean square error) the standard deviation is the square root of the mean of the squares of the deviations (better results are obtained by dividing the sum of the values by the one less than the number of values). This is a common measure of the preciseness of a sample of data- how closely the results agree with each other. The actual value is not required. ADDITIONAL EQUIUPMENT REQUIRED Values for the piston diameter and weight are provided. These may be replaced by your own measurements if desired.The following equipment will be required to do so Vernier callipers or a ruler, to measure the piston diameter A weigh-balance or similar, to measure the piston weight EQUIPMENT SET UP To prime the cylinder, the following procedure should be followed (where this is required in the experiment) Level the apparatus using the adjustable feet. A circular spirit level has been mounted on the base of the dead weight calibrator for this purpose. Check that the drain valve (at the back of the Bourdon gauge base) is closed. Fill the priming vessel with water (purified or de-ionized water is preferable). affluenty open the damping valve and the priming valve. With no masses on the piston, slowly draw the piston upwards a distance of approximately 6cm (i. e. a full stroke of the piston). This draws water from the priming vessel into the system. Firmly drive the piston downwards, to expel air from the cylinder back towards the priming vessel. Re peat these two steps until no more bubbles are visible in the system. It may be helpful to raise the central section of the return tube between the manifold block and the priming vessel. This will help to prevent air being drawn back into the system as the piston is raised.Raise the piston close to the top of the cylinder, taking care not to lift it high enough to allow air to enter, then close the priming valve. PROCEDURE This equipment has been designed to operate over a range of pressure from 0 kN/m2 to 200 kN/m2. Exceeding a pressure of 200 kN/m2 may damage the pressure sensors. In order to avoid such damage, DO NOT APPLY CONTINUOUS PRESSURE TO THE 79 TOP OF THE PISTON ROD WHEN THE PRIMING VALVE IS CLOSED except by application of the mass supplied. The following experiments give suggested ways in which particular sources of error may be investigated.It is recommended that only one or two be attempt in a single research laboratory session, with each being repeat several times, giving multiple samples for the error analysis. radical Error Analysis The accuracy of the semiconductor calibration may be investigated by performing standard error calculations on the calibrated sensor output, using the results obtained in Experiment P2. If results are not for sale for analysis, the following procedure should be followed Slowly open the priming valve. Open the valve to its maximum, and check that the damping valve is also fully open.The fluid in the system will now be at approximately atmospheric pressure (it will be slightly higher than atmospheric due to the height of fluid in the reservoir, but this is negligible compared to the range of the sensors). Switch the selector knob on the console to PRESSURE. Turn the ZERO control on the console until the display read zero, to set the first reference point for the sensor calibration. Raise the piston close to the top of the cylinder, taking care not to lift it high enough to allow air to enter, then close the primi ng valve. Place a large mass on the piston, and calculate the corresponding applied pressure.Spin the piston, and adjust the SPAN control until the sensor output matches the applied pressure, to set the second reference point for the calibration. get the masses from the piston. Take a set of readings from the calibrated semiconductor sensor, adding masses to the pan in ? kg increments, and again while decreasing the applied mass. This provides two set of readings for data analysis. The experiment should be repeated to provide further sets of data. Avoidable errors Incorrect use of equipment Level the apparatus using the adjustable feet.A circular spirit level has been mounted on the base of the dead-weight calibrator for this purpose Check that the drain valve (at the back of the Bourdon gauge base) is closed, and the damping valve is fully open. 80 Remove the piston from the cylinder, then fill the priming vessel with water (purified or de-ionized water is preferable). Close the p riming valve, then replace the piston in the cylinder. Take a set of readings without priming the system first. Random errors Friction effects primordial the system as described in the equipment set up instructions.Tilt the identity card at an angle of about 5 to 10 degrees. THE EQUIPMENT BASE MUST as yet BE FIRM AND SECURE. Titling the apparatus in this way will exaggerate any friction effects, as the force applied by the piston will no longer be acting straight downwards on the column of fluids, but will have components acting at right-angles to cylinder wall. Spin the piston. Take one reading while the piston is spinning, then observe the behavior of the needle. Continue to train the needle as the piston bread spinning, then make a note of the new gauge reading. Apply masses to the piston in ? kg increments.At each step, spin the piston, note the sensor output, and then take a second reading after the piston moolah spinning. Systematic errors Zero error Calibrate the semico nductor pressure sensor, but do not include mass of piston in the applied mass when conniving the applied pressure. Take a set of readings from the calibrated semiconductor sensor over a range of applied masses, now including the piston mass in the applied mass calculation. Human error Take a set or readings from the Bourdon gauge pressure scale, but stand at an angle to the dial face when taking each reading. Keep the same viewing angle for each reading.This illustrates the effect of parallax on the readings taken. RESULTS Tabulate your results under the headings on the following page For each result, calculate the absolute difference, ea between indicated value Pi and the applied pressure Pa. 81 align the maximum absolute difference, the accuracy ea max and use this value and the corresponding indicated pressure to calculate the % accuracy of actual scale reading and the % accuracy of full-scale reading (use a range of 200 kN/m2). correlative the data for several test runs, to g ive a set of indicated pressure readings corresponding to a single applied pressure. riding habit this correlated data table to calculate the mean of the results, Pmean, the mean deviation, dm, the absolute deviation, da, and the standard deviation, ?. Errors can also be illustrated diagrammatically 85 Piston diameter, d = . m Piston mass, MP = .. kg Experimental conditions Mass Applied Applied Applied Indicated Mean Absolute Standard Actual verity % % Mean on deviation deviation deviation Accuracy Accuracy of mass force pressure pressure difference piston Actual Full result scale scale reading reading Mm dm da PI ea Emax e%a e%f Pmin Ma Fa Pa ? kg) (kg) (kN) (kN/m2) (kN/m2) (kN/m2) (kN/m2) (kN/m2) (kN/m2) 86 Plot a graph of actual pressure against indicated pressure. On the same graph, plot a straight line exhibit the actual pressure. This will illustrate three characteristics of the results Deviation of sensor readings from the actual value. Whether any deviation from the tr ue reading is positive (the graph will be a straight line or a smooth curve) or random (the graph will have no obvious relationship). Precision of the results. Precise results will be close together, not widely scattered. Precise results may still deviate strongly from the actual value.