V=N(d - Section :S32



Measurement of PressurePressure?is the amount of force applied perpendicular to the surface of an object per unit area. The symbol for it is?p?or?P.Mathematically: p= FA{\displaystyle p={\frac {F}{A}},}where: p {\displaystyle p}?is the pressure,{\displaystyle F}?F is the?normal force,{\displaystyle A}?A is the area of the surface on contact.Pressure is a?scalar?quantity. UnitsThe?SI?unit for pressure is the?HYPERLINK "(unit)" \o "Pascal (unit)"pascal?(Pa), equal to one?HYPERLINK "(unit)" \o "Newton (unit)"newton?per?square metre?(N/m2, or kg·m?1·s?2). Other units of pressure, such as?pounds per square inch?and?bar, are also in common use. The?CGS?unit of pressure is the?HYPERLINK "" \o "Barye"barye?(Ba), equal to 1?dyn·cm?2, or 0.1?Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre (g/cm2?or kg/cm2). The?technical atmosphere?(symbol: atm) is 1?kgf/cm2?(98.0665?kPa, or 14.223?psi).{\displaystyle p={\frac {F\times {\text{distance}}}{A\times {\text{distance}}}}={\frac {\text{work}}{\text{volume}}}={\frac {\text{energy (J)}}{{\text{volume }}({\text{m}}^{3})}}.}Pressure unitsunitPascalBarTechnical atmosphereStandard atmosphereTorrPounds per square inch(Pa)(bar)(at)(atm)(Torr)(psi)1?Pa≡ 1?N/m210?51.0197×10?59.8692×10?67.5006×10?31.450377×10?41?bar105≡ 100?HYPERLINK "" \o "Kilopascal"kPa≡ 106?HYPERLINK "" \o "Dyne"dyn/cm21.01970.98692750.0614.503771?at9.80665×1040.980665≡ 1?HYPERLINK "" \o "Kilogram-force"kp/cm20.9678411735.559214.223341?atm1.01325×1051.013251.03321≡?76014.695951?Torr133.32241.333224×10?31.359551×10?3≡ 1/760 ≈?1.315789×10?3≡ 1 Torr≈ 1?mmHg1.933678×10?21?psi6.8948×1036.8948×10?27.03069×10?26.8046×10?251.71493≡ 1?HYPERLINK "" \o "Pound-force"lbf?/in2Pressure(Absolute) = Pressure(Atmospheric) + Pressure(Vacuum/Gauge)Pressure measurement?is the analysis of an applied?force?by a?fluid?(liquid?or?gas) on a surface.?Pressure?is typically measured in units of force per unit of surface area. Many techniques have been developed for the measurement of pressure and?vacuum. Instruments used to measure and display pressure in an integral unit are called?pressure gauges?or?vacuum gauges. A?manometer?is a good example as it uses a column of liquid to both measure and indicate pressure. Likewise the widely used?Bourdon gauge?is a mechanical device which both measures and indicates, and is probably the best known type of gauge.A vacuum gauge is a pressure gauge used to measure pressures lower than the ambient atmospheric pressure, which is set as the zero point, in negative values (e.g.: -15 psi or -760 mmHg equals total vacuum). Most gauges measure pressure relative to atmospheric pressure as the zero point, so this form of reading is simply referred to as "gauge pressure". However, anything greater than total vacuum is technically a form of pressure..Pressure may be measured with Reference to arbitrary Datum. i) Absolute zero Pressure ii) Local atmospheric pressure iii) Gauge pressure or Vacuum pressure i) Absolute Pressure: When the pressure is measured above the absolute zero as a datum is called as absolute pressure. Absolute pressure has always positive value. ii) Atmospheric Pressure: Air, other gases possesses weight and hence it must exert some intensity of pressure. Atmospheric pressure is, the pressure exerted by the atmospheric air on the surfaces in contact. It varies with the height (i.e. elevation). Atmospheric pressure is measured by a barometer and it is also termed as barometric pressure. The values of atmospheric pressure are: In MKS units: 1.033 kgf/cm2 In SI units: 101300 N/m2 = 10.33 m of water = 760 mm of mercury iii) Gauge Pressure: When the pressure is measured above or below the atmospheric pressure, it is known as gauge pressure. It is measured with the help of pressure measuring instrument in which atmospheric pressure is taken as datum. Vacuum Pressure: The pressure of the fluid below the atmospheric pressure is known as vacuum pressure.The dynamic response of pressure-measuring instruments is depends on two factors: (1) The response of the transducer element that senses the pressure (2) The response of the pressure-transmitting fluid and the connecting tubing etc. Mechanical pressure measurement devicesThese devices are responds to the pressure inputs and gives corresponding converted output in the form of a deflection or the compression of a member.Mercury manometer-U-shape, well-typeUses the manometric fluid compression to indicate applied pressureii. Diaphragms-Flat, corrugated, SG basedUses the deflection of member to indicated applied pressure. iii. Bellows-Corrugated, LVDT coupledUses the compressive length change of convolution as in terms of applied pressure.iv. Dead weight pressure tester-Balance typeBalanced pressure due to applied weight and buoyancy force are set equal to indicated pressure. v. Bourdon pressure gauge-Pressure to displacementUnknown pressure is converted into displacement and is indicated by a indicator.vi. Mc Leod gauge-Low pressure compressionUses the compression of low valued known pressure to indicate applied pressure. Pressure gage types and ranges1. Dead Weight Tester :The dead weight tester apparatus consists of a chamber which is filled with oil free impurities and a piston – cylinder combination is fitted above the chamber as shown in diagram. The top portion of the piston is attached with a platform to carry weights. A plunger with a handle has been provided to vary the pressure of oil in the chamber. The pressure gauge to be tested is fitted at an appropriate plate.the dead weight tester is basically a pressure producing and pressure measuring device. It is used to calibrate pressure gauges. The following procedure is adopted for calibrating pressure gauges. Calibration of pressure gauge means introducing an accurately known sample of pressure to the gauge under test and then observing the response of the gauge. In order to create this accurately known pressure, the following steps are followed.The valve of the apparatus is closed, A known weight is placed on the platform. Now by operating the plunger, fluid pressure is applied to the other side of the piston until enough force is developed to lift the piston-weight combination. When this happens, the piston weight combination floats freely within the cylinder between limit stops. In this condition of equilibrium, the pressure force of fluid is balanced against the gravitational force of the weights puls the friction drag. Therefore, PA = Mg + F.Hence : P = (Mg + F) / A where, P = pressure M = Mass; Kg g = Acceleratoion due to gravity ; m/s? F = Friction drag; N A = Eqivalent area of piston – cylinder combination; m? Thus the pressure P which is caused due to the weights placed on the platform is calculated.Now the pressure gauge to be calibrated is fitted at an appropriate place on the dead weight tester. The same known weight which was used to calucated P is placed on the platform. Due to the weight, the piston moves downwards and exerts a pressure P on the fluid. Now the valve in the apparatus is opened so that the fluid pressure P is transmitted to the gauge, which makes the gauge indicate a pressure value. This pressure value shown by the gauge should be equal to the known input pressure P. If the gauge indicates some other value other than p the gauge is adjusted so that it reads a value equal to p. Thus the gauge is calibrated.2. Manometers are one of the oldest type of pressure measurement.Manometers can be used to measure gauge pressure,differential pressure and absolute pressure.Various?types of Manometers1.U tube Manometer2.Well type or reservoir manometer3.Inclined manometer4.Float type manometerU – tube manometer:The difference in pressure between the unknown pressure p and the atmospheric pressure p0 is determined as a function of the differential height h. The difference between the densities of the manometer fluid and fluid transmitting the pressure p is = ρm – ρf.Then the unknown pressure can be found out by the equation below:P – P0 = g . h (ρm – ρf )U tube Manometer.U tube is made of glass. The tube is filled with a fluid known as Manometer fluid.Manometer fluid may be ?mercury , water etc...If the manometer is connected to same pressure source (P1 = P2) the level of the manometer will be same.If the manometer is connected to two different pressure source there will be a difference in level of the manometer fluid in both the limps.If P1>P2 the differential pressure?P2-P1=@gh@=density of the fluidh=height differenceWhile choosing the manometer fluid for a particular application we need to remember following things.Manometer fluid should not wet the wallManometer fluid should not absorb gasManometer fluid should not react chemicallyManometer fluid should have low vapor pressureMove freelyMercury is one of the most commonly used manometer fluid.Well type ManometerIn a well type manometer, one leg is replaced by a large diameter well. Since the cross sectional area of the well is much larger than the other leg, when pressure is applied to the well, the manometer liquid in the well lowers only slightly compared to the liquid rise in the other leg. As a result of this, the pressure difference can be indicated only by the height of the liquid column in single leg.For static balance,P2-P1= @*g*(1+A1/A2)hwhereA1= area of smaller-diameter legA2= area of wellIf A1/A2 << 1 then P2-P1 = @ghIf the area of well is 500 or more times larger than the area of vertical leg, the error involved in neglecting the area is negligible.?Inclined-Tube ManometersThe inclined ?leg expands the scale so that lower pressure differentials may be read easily.Sensitivity of the manometer increases.The scale of the manometer can be extended greatly by decreasing the angle of inclined leg to a small value.Float-Type ManometersThis is a variation of well-type manometerRecording type manometerSpan of the measurement can be changed by changing the diameter of the legA large float can be placed to generate enough force?Velocity and acceleration Measurements:Velocity TransducersVelocity transducers are contact transducers, used to measure velocity. They are usually mounted on bearing housing. Velocity transducers are still used in industry to some extent, mostly in condition monitoring such as industrial?fans, pumps, etc. The use of velocity transducers has shifted to accelerometers that are internally “integrated” to velocity. Velocity transducers are suitable for mid-range frequency measurement.A velocity transducer/sensor consists of a moving coil suspended in the magnetic field of a permanent magnet. The velocity is given as the input, which causes the movement of the coil in the magnetic field. This causes an emf to be generated in the coil. This induced emf will be proportional to the input velocity and thus, is a measure of the velocity. The instantaneous voltage produced is given by the equationv=N(d?/dt)N – Number of turns of the coild?/dt – Rate of change of flux in the coilThe voltage produced will be proportional to any type of velocities like linear, sinusoidal or random.Basic principle of Moving magnet type velocity TransducerWhen a permanent magnet moves inside a coil, the change in the length of the air gap varies the reluctance. Hence the output voltage is directly proportional to the rate of change of the length of the air gap (change in length produced by velocity). Thus the output voltage becomes a measure of the velocity when calibrated.The sensing element which is a rod is a permanent magnet.The rod is rigidly coupled to the device whose velocity is being measured.There is a coil surrounding the permanent magnet.The permanent magnet is movable, that is, it can move in and out of the coil.Operation of Moving magnet type velocity TransducerThe instrument is fixed to the device whose velocity is to measured.Due to the application of the velocity, the permanent magnet moves in or out of the coil. Due to its motion, the length of the air gap varies.The output voltage also varies due to the motion of the magnet and the amplitude of the voltage is directly proportional to velocity.The polarity of the output voltages determines the direction of the velocity.Acceleration Transducers:Acceleration transducers or accelerometers are contact transducers and are mounted on the bearing housing. Accelerometers are the most common types of transducers used in industry for machinery vibration analysis such as?angle grinder, electric motor, etc. There are a number of different types of accelerometers. The most common accelerometer is the internally amplified piezoelectric. Accelerometers are suitable for high frequency measurement.An accelerometer contains piezoelectric material-crystal, which is placed under a load. As the transducer vibrates, the crystal is compressed or decompressed, and a charged is produced. The charge output is proportional to the force, and therefore acceleration (Newton’s second law). An amplifier is required to convert that charge output to a voltage output. Accelerometers are mainly used for two specific types of acceleration measurements- impact (shock) and vibration. Impact is effectively a large acceleration over a short period of time, while vibration is a small. repeatable acceleration. Accelerometers are also used to measure the position, velocity or acceleration of bodies, such as aircraft and ships. Accelerometers are normally mechanically bonded to the object whose acceleration is to be measured. The accelerometer detects acceleration along one axis and is insensitive in orthogonal directions.the operating principle of an accelerometer is based on the inertial effects associated with a mass connected to a moving object through a spring and damper. When the moving object accelerates, there is a relative displacement between the object and the mass. the relative displacement is directly measures using position sensor, such as a linear potentiometer or in directly sensed by the output voltage of a piezoelectric crystal.Seismic accelerometers are intended maily for low frequency accelerations, piezo electric accelerometers dynamic measurements i.e. high frequency vibrations and impacts.When the object accelerates, the mass displaces relative to the object. causing a deformation in the crystal. this deformation in the piezoelectric crystal causes in turn a electric charge between its conductive coatings as a result of the piezoelectric effect. this electric charge is proportional to the mechanical deformationq= Kq * Xowhere q is the electric charge in coulombs(C), Xo is the relative displacement between the mass and the housing, Kq is the proportionality constant .Measurement of Mass and WeightMass?is a measure of the amount of material in an object, being directly related to the number and type of atoms present in the object. Mass does not change with a body's position, movement or alteration of its shape, unless material is added or removed.an object with mass?1 kg?on earth would have the same mass of?1 kg?on the moonThe unit of mass, the kilogram, remains the only base unit in the International System of Units (SI), which is still defined in terms of a physical artifact. Its definition is:Weight?is the?gravitational force?acting on a body mass. The generic expression of?Newton's Second Law?(1)?can be transformed to express?weight as a force?by replacing the acceleration -?a?- with the acceleration of gravity -?g?- asFg?= m ag?????? ? ? ? ? ? ? ? ? ? ? ?? (2)whereFg?= gravitational force - or?weight?(N, lbf)m?= mass?(kg,?slugs)ag?=?acceleration of gravity?on earth?(9.81 m/s2,?32.17405 ft/s2)However, for trading purposes weight is often taken to mean the same as mass.The international prototype of the kilogram is kept at BIPM, the International Bureauof Weights and Measures in Sèvres, Paris. It consists of an alloy of 90% platinum and 10% iridium in the form of a cylinder, 39 mm high and 39 mm in diameter. It is stored at atmospheric pressure in a specially designed triple bell-jar.Weighing techniques:There are many weighing techniques currently employed in mass metrology. This isindicative of the wide range of processes that rely on weighing and the uncertaintydemands that are required by different industrial sectors and end-users.Direct reading measurements:The most simple method of weighing is to simply place a test piece on a mass balanceand take the displayed reading as its weight. This type of measurement is only suitablefor low accuracy applications but even in this most straight-forward application it isessential to follow good practice.Weighing by differences:This technique is particularly common in analytical chemistry. In general it involvesplacing a container on the balance pan, noting the reading, and then adding a substance to it. The final balance reading is noted and the difference between the two readings is taken to be the amount of material in the container. This approach is fine for relatively low accuracy requirements but is not ideal for more demandingmeasurements. ................
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