Chapter 6 Pressure and Sound Measurement by Yixin Ma 10/04/2013 2/44 Contents 1.Standards and Calibration 2.Basic Methods of Pressure Measurement 3.Deadweight Gages and Manometers 4.Elastic Transducers 5.Vibrating-Cylinder and Other Resonant Transducer 6.High-Pressure Measurement 7.Low-Pressure(Vacuum)Measurement 8.Sound Measurement
Chapter 6 Pressure and Sound Measurement by Yixin Ma 10/04/2013 Contents 1. Standards and Calibration 2. Basic Methods of Pressure Measurement 3. Deadweight Gages and Manometers 4. Elastic Transducers 5. Vibrating-Cylinder and Other Resonant Transducer 6. High-Pressure Measurement 7. Low-Pressure (Vacuum) Measurement 8. Sound Measurement 2/44
3/44 6.1 standards and calibration Definition:P=F/A (N/m2=Pa), Pressure developed at the base of the liquid column is P=pg h Units:1 bar 105 Pa;1 lbf/in2=1 psi 6.895 kPa;1 mmHg 133.32 Pa; 1 atm(Standard atmosphere)=760.00 mmHg (0C)=10332mm Ag(4C) Hg=Mercury;Ag=water ◆Standards: Medium vacuum (about 0.1mmHg)-several 100k Ibflin2:precision mercury columns (manometers)and deadweight piston gages. 0.001mmHg-0.1mmHg:the McLeod vacuum gage. Less than 0 001mmHg:a pressure-dividing technique allows flow through a succession of accurate orifices to relate the low downstream pressure to higher upstream pressure. Measurement Uncertainties: Gage and Pressure Measurement Uncertainties Type of Instrument Range Uncertainty Gas-operated PG 1.4 kPa to 17 MPa ±57ppm Oil-operated PG 700 kPa to 100 MPa ±63ppm 100 MPa to 280 MPa ±60to±150ppm Cil-operated PG 40 to 400 MPa ±186ppm 4/44 6.2 Basic Methods of Pressure Measurement High vacuum region-a variety of special methods not directly related to force measurement are necessary: General pressure measurement-pressure transduced into force: Comparison with known deadweights acting on known areas; Deflection of elastic element subjected to the unknown pressure
6.1 standards and calibration Definition: ܲൌܨ ܣ) ⁄N/m2=Pa), Pressure developed at the base of the liquid column is ࡼ ൌ ࣋ ࢍ ࢎ Units: 1 bar = 105 Pa; 1 lbf/in2 = 1 psi = 6.895 kPa; 1 mmHg = 133.32 Pa; 1 atm (Standard atmosphere) = 760.00 mmHg (0℃) = 10332mm Ag (4℃) Hg=Mercury; Ag=water Standards: Medium vacuum (about 0.1mmHg) - several 100k lbf/in2: precision mercury columns (manometers) and deadweight piston gages. 0.001mmHg - 0.1mmHg: the McLeod vacuum gage. Less than 0.001mmHg: a pressure-dividing technique allows flow through a succession of accurate orifices to relate the low downstream pressure to higher upstream pressure. Measurement Uncertainties: 3/44 6.2 Basic Methods of Pressure Measurement High vacuum region - a variety of special methods not directly related to force measurement are necessary: General pressure measurement - pressure transduced into force: ¾ Comparison with known deadweights acting on known areas; ¾ Deflection of elastic element subjected to the unknown pressure. 4/44
5/44 6.3.1 Deadweight Gages ◆Principles: Air buoyoncy on weights and piston >Mainly employed as standards for the calibration of less accurate gages or transducers. Gage to be >The gage to be calibrated is Oil film colibrated connected to a chamber filled with fluid whose pressure can be Goge reference point adjusted by some type of pump and bleed valye(泄流阀). 5 s >The chamber also connects with a vertical piston-cylinder to which various standard weights may be applied. Bleed When the piston and weights valve are seen to "float",the fluid "gage" pressure equal the deadweight Figure 6.2 Deadweight Gage Calibrator supported by piston,divided by the piston area. 6/44 6.3.1 Deadweight Gages Refinements and Corrections: >Piston and cylinder deform under pressure; >To reduce/correct the friction force between the cylinder and piston. >A small clearance between the piston and the cylinder is necessary to allow fluid to flow from high pressure end to low pressure end.The flow produces a viscous shear force tending to support part of the deadweight. >The effective area generally is taken as the average of the piston and cylinder areas. >Height differences between the lower and of the piston and the reference point for the gage being calibrated. >Temperature effects on areas of piston and cylinder. >Air and pressure-medium buoyancy effects. >Local gravity conditions
6.3.1 Deadweight Gages Principles: ¾ Mainly employed as standards for the calibration of less accurate gages or transducers. ¾ The gage to be calibrated is connected to a chamber filled with fluid whose pressure can be adjusted by some type of pump and bleed valve (泄流阀). ¾ The chamber also connects with a vertical piston-cylinder to which various standard weights may be applied. ¾ When the piston and weights are seen to “float”, the fluid “gage” pressure equal the deadweight supported by piston, divided by the piston area. Figure 6.2 Deadweight Gage Calibrator 5/44 6.3.1 Deadweight Gages Refinements and Corrections: ¾ Piston and cylinder deform under pressure; ¾ To reduce/correct the friction force between the cylinder and piston. ¾ A small clearance between the piston and the cylinder is necessary to allow fluid to flow from high pressure end to low pressure end. The flow produces a viscous shear force tending to support part of the deadweight. ¾ The effective area generally is taken as the average of the piston and cylinder areas. ¾ Height differences between the lower and of the piston and the reference point for the gage being calibrated. ¾ Temperature effects on areas of piston and cylinder. ¾ Air and pressure-medium buoyancy effects. ¾ Local gravity conditions. 6/44
Z44 6.3.1 Deadweight Gages Gauge pressure calculation: Mg1(1 Pair)+DT GaugePressure A20ol1+(ap+)(0-20)](1+7P -Pfhrid-Pair)gh (Eq6.1) Where: M=the total mass load; g1=the local acceleration of gravity; p=density; D=piston diameter(computed fromA(2.),the piston/cylinder effective area at 20C and 0 gage pressure); T=gage-fluid surface tension; ap,ac=thermal expansion coefficients of piston and cylinder respectively; 0=the piston/cylinder temperature; piston/cylinder elastic deformation coefficient; h the height difference between piston gage reference level and reference level of the unit under calibration 8/44 6.3.1 Deadweight Gages The Tilting-Piston Gage: >Conventional deadweight gages are not capable of measuring pressures lower than the piston weight/area ratio ("tare"pressure). >The tilting-piston gage can overcome this difficulty.The cylinder and piston can be tilted from vertical through an accurately measured angle. >Use nitrogen or other inert gas as the pressure medium,covers the range 0 to 600 Ib/in2,have two interchangeable piston-cylinders and 14 weights. Highly Instrumented and Automated Gage: >For more convenient and rapid use. >The device includes sensors for relative humidity,barometric pressure(),ambient temperature,piston/cylinder temperature,piston rotation speed and acceleration, and piston drop rate. >The reading is manipulated in software according to proper formula to provide a readout of the calibration pressure
6.3.1 Deadweight Gages Gauge pressure calculation: ൌ ࢋ࢛࢙࢙࢘ࢋ࢘ࡼ ࢋࢍ࢛ࢇࡳ ࢘ࢇ࣋ ି ࢍࡹ ࢀࡰ࣊ା ࢙࢙ࢇ࣋ ሺ,ሻ∙ ା ࡼࢻାࢉࢻ ࣂ ∙ ିାࡼࣅ െ ࢊ࢛ࢌ࣋ െ࢘ࢇ࣋∙ ࢍࢎ) ... Eq.6.1) Where: M = the total mass load; ࢍ = the local acceleration of gravity; ρ = density; D = piston diameter (computed fromሺ,ሻ, the piston/cylinder effective area at 20℃ and 0 gage pressure); T = gage-fluid surface tension; ࡼࢻ ,ࢉࢻ = thermal expansion coefficients of piston and cylinder respectively; θ = the piston/cylinder temperature; λ = piston/cylinder elastic deformation coefficient; h = the height difference between piston gage reference level and reference level of the unit under calibration 7/44 6.3.1 Deadweight Gages The Tilting-Piston Gage: ¾ Conventional deadweight gages are not capable of measuring pressures lower than the piston weight/area ratio (“tare” pressure). ¾ The tilting-piston gage can overcome this difficulty. The cylinder and piston can be tilted from vertical through an accurately measured angle. ¾ Use nitrogen or other inert gas as the pressure medium, covers the range 0 to 600 lb/in2, have two interchangeable piston-cylinders and 14 weights. Highly Instrumented and Automated Gage: ¾ For more convenient and rapid use. ¾ The device includes sensors for relative humidity, barometric pressure(气压), ambient temperature, piston/cylinder temperature, piston rotation speed and acceleration, and piston drop rate. ¾ The reading is manipulated in software according to proper formula to provide a readout of the calibration pressure. 8/44
9/44 6.3.1 Deadweight Gages A Convenient Standard: 2① ③ >As shown in Fig 6.3,very convenient ① pressure standard combines a precision gage with a magnetic null-balance ① laboratory scale. 0 ③ ⑩ >Since deadweights are not utilized to ⑩ ⑩ ⑤ 6 measure the pressure force,periodic recalibration against a set of four ⑦@ 号⑧四 ④ precision masses is required. 16 ⑨ 33 15 2 2 B 西① 3四32 Y 200×300 Fig.6.3 Pressure standard using electromagnetic balance 10/44 6.3.2 Manometers ◆Principles: >The U-tube manometer of Fig.6.4 is the basic form and has the following relation between input and output for static conditions. h=P1-P2 (6.2) pg where g local gravity p mass density of manometer fluid. >Water and mercury are the most commonly used fluids. The cross-sectional area of the tubing (even if not uniform)has no effect. Fig.6.4 U-tube manometer >The manometer become unwieldy(不便利的at high pressures because of the long liquid columns involved
6.3.1 Deadweight Gages A Convenient Standard: ¾ As shown in Fig 6.3, very convenient pressure standard combines a precision gage with a magnetic null-balance laboratory scale. ¾ Since deadweights are not utilized to measure the pressure force, periodic recalibration against a set of four precision masses is required. Fig. 6.3 Pressure standard using electromagnetic balance 9/44 6.3.2 Manometers Principles: ¾ The U-tube manometer of Fig.6.4 is the basic form and has the following relation between input and output for static conditions. ࡼିࡼ ൌ ࢎ ࢍ࣋ (6.2) where ࢍ≜ local gravity ; ࣋≜ mass density of manometer fluid. ¾ Water and mercury are the most commonly used fluids. ¾ The cross-sectional area of the tubing (even if not uniform) has no effect. ¾ The manometer become unwieldy (不便利的) at high pressures because of the long liquid columns involved. Fig. 6.4 U-tube manometer 10/44
11/44 6.3.2 Manometers Comparison with deadweight gages: >The manometer is self-balancing,is a deflection rather than a null instrument,and has continuous rather than stepwise output. The accuracies of deadweight gages and manometers of similar ranges are quite comparable. Accuracy improvements: >Temperature expansion of the engraved(雕刻的)scale when visual reading of the height h is employed; >The variation of p with temperature for the manometer fluid; Local value of g; >Non-verticality(不垂直度)of the tubes;; Fig.6.4 U-tube manometer >The difficulty in reading h because of the meniscus 液面)formed by capillarity(毛细管作用). 12/44 6.3.3 Practically Variations of Manometers l.The cistern(蓄水池)or well-type manometer: Widely utilized because of the convenience in requiring reading of only a single leg. 41,42 Areas The well area is made much larger than the tube;thus the zero level moves very little when pressure is applied. And even this small error is compensated by suitable distorting the length scale. >Different from U tube,this arrangement is sensitive to Fig.6.5a nonuniformity of the tube cross-sectional area,and thus is Well-type (single-leg) considered somewhat less accurate. manometer 一Evacuated 2.Barometer(气压计)： >A"single-leg"instrument; >Set the zero level of the well at the zero level of the scale before each reading is taken to achieve high accuracy; The pressure in the evacuated portion of the barometer is not really absolute zero but rather the vapor pressure of the filling fluid,mercury,at ambient temperature.And it is usually negligible as a correction. Fig.6.5b Barometer
6.3.2 Manometers Comparison with deadweight gages: ¾ The manometer is self-balancing, is a deflection rather than a null instrument, and has continuous rather than stepwise output. ¾ The accuracies of deadweight gages and manometers of similar ranges are quite comparable. Accuracy improvements: ¾ Temperature expansion of the engraved(雕刻的) scale when visual reading of the height h is employed; ¾ The variation of࣋with temperature for the manometer fluid; ¾ Local value ofࢍ; ¾ Non-verticality (不垂直度) of the tubes; ¾ The difficulty in reading h because of the meniscus (凹凸 液面) formed by capillarity(毛细管作用). Fig. 6.4 U-tube manometer 11/44 6.3.3 Practically Variations of Manometers 1. The cistern(蓄水池) or well-type manometer: ¾ Widely utilized because of the convenience in requiring reading of only a single leg. ¾ The well area is made much larger than the tube; thus the zero level moves very little when pressure is applied. And even this small error is compensated by suitable distorting the length scale. ¾ Different from U tube, this arrangement is sensitive to nonuniformity of the tube cross-sectional area, and thus is considered somewhat less accurate. 2. Barometer (气压计): ¾ A “single-leg” instrument; ¾ Set the zero level of the well at the zero level of the scale before each reading is taken to achieve high accuracy; ¾ The pressure in the evacuated portion of the barometer is not really absolute zero but rather the vapor pressure of the filling fluid, mercury, at ambient temperature. And it is usually negligible as a correction. Fig. 6.5b Fig. 6.5a 12/44
13/44 6.3.3 Practically Variations of Manometers 3.The inclined manometer: Fig.6.5C >To increase the sensitivity,the manometer maybe tilted with respect to gravity,thus giving a greater motion of liquid along the tube for a given vertical- Inclined Micrometer height change. >A single-leg device; >The calibrated scale is corrected for the slight changes in well level so that rezeroing of the scale for each reading is not required. 4.Micromanometer: Magnifier >A variation on the inclined-manometer principle for accurate measurement of extremely small pressure difference; Flexible tube >Optional Fluid:water,alcohol. Micromanometer Fig.6.5D 14/44 6.3.3 Practically Variations of Manometers 4.Micromanometer:(continued-how it works) >The instrument is initially adjusted so that when P,=P2,the meniscus in the inclined tube is located at a reference point given by a fixed hair line viewed through a magnifier. >Application of the unknown pressure difference cause the meniscus to move off the hairline, but it can be restored to its initial position by raising or lowering the well with the micrometer. The difference in initial and final micrometer readings gives the Micrometer height change h and thus the pressure. >In a different version,the inclined tube is moved,not the well. 5.Monometers with Automatic Readout: >Sonar Monometer using an ultrasonic transducer at each column a digital counter to measure the height difference. Magnifier 6.Two large mercury cisterns(水箱connected by flexible tubing to create a U-tube manometer. Flexible tube >One cistern fixed and one vertically moveable by an electromechanical servo-system; >The mercury surface,a metal plate and the air in 727 Fig.6.5D between them form a capacitance Micromonometer
6.3.3 Practically Variations of Manometers 3. The inclined manometer: ¾ To increase the sensitivity, the manometer maybe tilted with respect to gravity, thus giving a greater motion of liquid along the tube for a given verticalheight change. ¾ A single-leg device; Fig. 6.5C Fig. 6.5D ¾ The calibrated scale is corrected for the slight changes in well level so that rezeroing of the scale for each reading is not required. 4. Micromanometer: ¾ A variation on the inclined-manometer principle for accurate measurement of extremely small pressure difference; ¾ Optional Fluid: water, alcohol. 13/44 6.3.3 Practically Variations of Manometers Fig. 6.5D ¾ The difference in initial and final micrometer readings gives the height change h and thus the pressure. ¾ In a different version, the inclined tube is moved, not the well. 4. Micromanometer: (continued – how it works) ¾ The instrument is initially adjusted so that when P1=P2, the meniscus in the inclined tube is located at a reference point given by a fixed hair line viewed through a magnifier. ¾ Application of the unknown pressure difference cause the meniscus to move off the hairline, but it can be restored to its initial position by raising or lowering the well with the micrometer. 5. Monometers with Automatic Readout: ¾ Sonar Monometer using an ultrasonic transducer at each column + a digital counter to measure the height difference. 6. Two large mercury cisterns (水箱) connected by flexible tubing to create a U-tube manometer. ¾ One cistern fixed and one vertically moveable by an electromechanical servo-system; ¾ The mercury surface, a metal plate and the air in between them form a capacitance 14/44
15/44 6.4 Elastic Transducers ◆Introduction: >The majority of practical pressure transducers utilize Bourdon tube( 管)，diaphragm(波纹管)，or bellows(膜片)as their sensitive element. >The gross deflection of these elements may directly actuate a pointer/scale readout through suitable linkages or gears,or the motion may be transduced to an electrical signal by one means or another. >Strain gages bonded directly to diaphragms or to diaphragm-actuated beams are widely used to measure local strains that are directly related to pressure. 16/44 6.4 Elastic Transducers-Bourdon Tubes Bourdon tube is the basis of many mechanical pressure gages. Tube cross section The basic element is a tube of noncircular cross section( 圆横截面).A pressure difference between the inside and outside of the tube causes the tube to attempt to attain a circular cross section. C-type Resulted distortion lead to >A curvilinear(曲线的translation of the free end,in the: ●C type; Spiral ·Spiral types; .Helical type. >An angular rotation (the output)in the in the: ●Twisted type. The construction of a higher accuracy C-type Bourdon test Twisted tube gage with an optional bimetal temperature compensator.It corrects for both thermal zero shift and span shift. The C-type Bourdon tube has been utilized up to about 1000lb/in2.The spiral and helical configurations have been 77m元 Helicol used mainly blow 1000 lb/in2. Fig.6.8a Bourdon Tubes
6.4 Elastic Transducers Introduction: ¾ The majority of practical pressure transducers utilize Bourdon tube(布尔登 管), diaphragm(波纹管), or bellows(膜片) as their sensitive element. ¾ The gross deflection of these elements may directly actuate a pointer/scale readout through suitable linkages or gears, or the motion may be transduced to an electrical signal by one means or another. ¾ Strain gages bonded directly to diaphragms or to diaphragm-actuated beams are widely used to measure local strains that are directly related to pressure. 15/44 6.4 Elastic Transducers - Bourdon Tubes Bourdon tube is the basis of many mechanical pressure gages. The basic element is a tube of noncircular cross section (非 圆横截面). A pressure difference between the inside and outside of the tube causes the tube to attempt to attain a circular cross section. Resulted distortion lead to ¾ A curvilinear(曲线的)translation of the free end, in the : z C type; z Spiral types; z Helical type. ¾ An angular rotation (the output) in the in the : z Twisted type. The construction of a higher accuracy C-type Bourdon test gage with an optional bimetal temperature compensator. It corrects for both thermal zero shift and span shift. The C-type Bourdon tube has been utilized up to about 1000lb/in2. The spiral and helical configurations have been used mainly blow 1000 lb/in2. Fig. 6.8a Bourdon Tubes 16/44
17/44 6.4 Elastic Transducers-Diaphragms Bellows Chamber with Differentiol reference pressure sealed inside Flat Evocuated Sealed Capsule Absolute Corrugated (波纹的：有瓦楞的) Fig.6.8 b Diaphragms(膜片) A diaphragm usually is designed so that the deflection-versus-pressure characteristics are as linear as possible over a specified pressure range,and with a minimum of hysteresis and minimum shift in the zero point. 18/44 6.4 Elastic Transducers-Diaphragms Bellows m Ann門 AL肜 n 你 mn Differential or absolute Fig.6.8 c Bellows(波纹管) ◆The movement is proportional to number of convolutions(卷曲；卷积)； Sensitivity is proportional to size; In general a bellows can detect a slightly lower pressure than a diaphragm; The range is from 0-5 mmHg to 0-2000 psi; Accuracy is in the range of 1%span
6.4 Elastic Transducers – Diaphragms & Bellows Fig. 6.8b Diaphragms (膜片) A diaphragm usually is designed so that the deflection-versus-pressure characteristics are as linear as possible over a specified pressure range, and with a minimum of hysteresis and minimum shift in the zero point. (波纹的；有瓦楞的) 17/44 6.4 Elastic Transducers – Diaphragms & Bellows Fig. 6.8c Bellows (波纹管) The movement is proportional to number of convolutions(卷曲; 卷积); Sensitivity is proportional to size; In general a bellows can detect a slightly lower pressure than a diaphragm; The range is from 0-5 mmHg to 0-2000 psi; Accuracy is in the range of 1% span. 18/44
19/44 6.4 Elastic Transducers-Electrical Readout Electrical output pressure transducers are available in forms combining various elastic elements with most of the displacement transducers,i.e.,potentiometers, strain gages,LVDTs,capacitance pickups,eddy-current probes,reluctance and inductance pickups,piezoelectric elements,etc. Piezoelectric pressure transducers share many common characteristics with piezoelectric accelerometers and force transducers.Generally they have high natural frequencies and little response to spurious acceleration inputs. Pressure transducers based on foil-type metal strain gages may either apply the strain gages directly to a flat metal diaphragm or use a convoluted(旋转的；盘绕的 diaphragm to apply force to a strain-gage beam. >A line of piezoresistive pressure transducers available in the ranges from 2 to 50k lb/in2 applies the fluid pressure directly to a silicon diaphragm with a complete Wheatstone bridge of strain elements diffused into the diaphragm. >Diffused (strain-gage pressure transducers intended for high-volume,low- cost applications such as appliances ([e'plaiens],),automotive parts,etc.,are available also. 20/44 6.4 Elastic Transducers-Electrical Readout (continued) Differential-pressure transmitters are utilized widely in process instrumentation and control systems for flow,liquid level,density,viscosity,etc. LEADWIRES CAPACITOR PLATES SENSING DIAPHRAGM GLASS INSULATION SILICONE FILL THE 8-CELL ISOLATING DIAPHRAGM ·VELDED SEALS Fig.6.16 Capacitive Differential-Pressure Transmitter
6.4 Elastic Transducers – Electrical Readout Electrical output pressure transducers are available in forms combining various elastic elements with most of the displacement transducers, i.e., potentiometers, strain gages, LVDTs, capacitance pickups, eddy-current probes, reluctance and inductance pickups, piezoelectric elements, etc. ¾ Piezoelectric pressure transducers share many common characteristics with piezoelectric accelerometers and force transducers. Generally they have high natural frequencies and little response to spurious acceleration inputs. ¾ Pressure transducers based on foil-type metal strain gages may either apply the strain gages directly to a flat metal diaphragm or use a convoluted (旋转的；盘绕的) diaphragm to apply force to a strain-gage beam. ¾ A line of piezoresistive pressure transducers available in the ranges from 2 to 50k lb/in2 applies the fluid pressure directly to a silicon diaphragm with a complete Wheatstone bridge of strain elements diffused into the diaphragm. ¾ Diffused (扩散) strain-gage pressure transducers intended for high-volume, lowcost applications such as appliances ([ə'plaɪəns], 家电), automotive parts, etc., are available also. 19/44 6.4 Elastic Transducers – Electrical Readout (continued) ¾ Differential-pressure transmitters are utilized widely in process instrumentation and control systems for flow, liquid level, density, viscosity, etc. Fig. 6.16 Capacitive Differential-Pressure Transmitter 20/44