# Pressure Measurement. Introduction. Engr325 Instrumentation. Dr Curtis Nelson 3/1/17

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1 3/1/17 Pressure Measurement Engr325 Instrumentation Dr Curtis Nelson Introduction A cluster of 72 helium-filled balloons over Temecula, California in April of The helium balloons displace approximately 230 m3 of air, providing the necessary buoyant force. Go ahead try it! 1

2 What Is Pressure? Pressure is defined as force per unit area that a fluid exerts on its surroundings. Pressure, P, is a function of force, F, and area, A: P = F/A The SI unit for pressure is the pascal (N/m 2 ), but other common units of pressure include pounds per square inch (psi), atmospheres (atm), bars, inches of mercury (in. Hg), millimeters of mercury (mm Hg), and torr. Pressure Measurement Absolute pressure is the pressure measured w.r.t. a vacuum (unit = psia). Gauge pressure is the pressure measured w.r.t. atmospheric pressure (unit = psig). Atmospheric pressure is the pressure on the earth s surface due to the weight of gases in the earth s atmosphere (14.7psi). Zero Pressure Pressure due to Atmosphere Absolute Pressure at point of interest Gauge Pressure at point of interest 2 2

3 Definitions Absolute Pressure The absolute measurement method is relative to 0 Pa, the static pressure in a vacuum. The pressure being measured is acted upon by atmospheric pressure in addition to the pressure of interest. Therefore, absolute pressure measurement includes the effects of atmospheric pressure. This type of measurement is well-suited for atmospheric pressures such as those used in altimeters or vacuum pressures. Gauge Pressure Gauge pressure is measured relative to ambient atmospheric pressure. This means that both the reference and the pressure of interest are acted upon by atmospheric pressures. Therefore, gauge pressure measurement excludes the effects of atmospheric pressure. These types of measurements include tire pressure and blood pressure measurements. Differential Pressure Differential pressure is similar to gauge pressure; however, the reference is another pressure point in the system rather than the ambient atmospheric pressure. You can use this method to maintain relative pressure between two vessels such as a compressor tank and an associated feed line. Pressure Measuring Instruments The techniques used for pressure measurement depend on the level of pressure (low, moderate, high). Low Pressure Measurement (below 133 Pa or 1 torr) McLeod gauge, Pirani gauge, or Ionization gauge. Moderate Pressure Measurement Manometer and elastic elements (diaphragm, bellows, capsules, bourdon tubes, spiral, helix). High Pressure Measurement (> 1000 atm) Electrical resistance pressure gauge. 3 3

4 Static Pressure of Atmosphere Gases differ from liquids in two respects: they are very compressible, and they completely fill any closed vessel in which they are placed. The nonlinear air pressure variation with altitude shown in the figure is an example of the effect of the compressibility of gases. Dynamic Effects Static pressure is measured under steady-state or equilibrium conditions, but most real-life applications deal with dynamic or changing pressure. For example, the measurement of blood pressure usually gives the two steady-state values of systolic and diastolic pressure. There is much additional information in the shape of the blood pressure signal which is the reason for the monitors used in critical-care situations. To measure changing pressures, the frequency response of the sensor must be considered. As a rough approximation, the sensor frequency response should be 5-10 the highest frequency component in the pressure signal. Another issue is the remote measurement of pressure where a liquid coupling medium is used. Care must be taken to purge all air because its compressibility will corrupt the waveform. 4 4

5 Pressure Sensing Pressure is sensed by mechanical elements such as plates, shells, and tubes that are designed and constructed to deflect when pressure is applied. This is the basic mechanism converting pressure to physical movement. Next, this movement must be transduced to obtain an electrical or other output. Finally, signal conditioning may be needed, depending on the type of sensor and the application. displacement electric Pressure Sensing Element Transduction element Signal Conditioner V or I output Pressure Measurement Methods A pressure measurement can further be described by the type of measurement being performed. The three methods for measuring pressure are absolute, gauge, and differential. Absolute pressure is referenced to the pressure in a vacuum, whereas gauge and differential pressures are referenced to another pressure such as the ambient atmospheric pressure or pressure in an adjacent vessel. 5 5

6 Sensing Elements The main types of sensing elements are Bourdon tubes, diaphragms, capsules, and bellows. All except diaphragms provide a fairly large displacement that is useful in mechanical gauges and for electrical sensors that require a significant movement. Bridge-Based Pressure Sensors Wheatstone bridge (strain-based) sensors are the most common because they offer solutions that meet varying accuracy, size, ruggedness, and cost constraints. Bridge-based sensors can measure absolute, gauge, or differential pressure in both high- and low- pressure applications. They use a strain gage to detect the deformity of a diaphragm subjected to the applied pressure. You can bond foil strain gages directly to a diaphragm or to an element that is connected mechanically to the diaphragm. Silicon strain gages are sometimes used as well. 6 6

7 Signal Conditioning for Bridge-Based Pressure Sensors Bridge-based pressure sensors are by far the most common pressure sensors. You need to consider several signal conditioning elements to make an effective bridge-based pressure measurement system: Excitation to power the Wheatstone bridge circuitry. Remote sensing to compensate for errors in excitation voltage from long lead wires. Amplification to increase measurement resolution and improve signal-tonoise ratio. Filtering to remove external, high-frequency noise. Offset nulling to balance the bridge to output 0 V when no strain is applied. Calibration to verify the output of the bridge to a known value. Capacitive Pressure Sensors A variable capacitance pressure transducer measures the change in capacitance between a metal diaphragm and a fixed metal plate. The capacitance between two metal plates changes if the distance between these two plates changes due to applied pressure. 7 7

8 Capacitive Pressure Sensors Capacitive pressure sensors typically use a thin diaphragm as one plate of a capacitor. Applied pressure causes the diaphragm to deflect and the capacitance to change. This change may or may not be linear and is typically on the order of several picofarads out of a total capacitance of pf. This change in capacitance may be used to control the frequency of an oscillator or to vary the coupling of an AC signal through a network. Piezoelectric Pressure Sensors Piezoelectric sensors rely on the electrical properties of quartz crystals rather than a resistive bridge transducer. These crystals generate an electrical charge when they are strained. Electrodes transfer the charge from the crystals to an amplifier built into the sensor. These sensors do not require an external excitation source, but they are susceptible to shock and vibration. 8 8

9 Piezoelectric Pressure Sensors Piezoelectric elements are bi-directional transducers capable of converting stress into an electric potential and vice versa. One important factor to remember is that this is a dynamic effect, providing an output only when the input is changing. This means that these sensors can be used only for varying pressures. The piezoelectric element has a high-impedance output and care must be taken to avoid loading the output by the interface electronics. Some piezoelectric pressure sensors include an internal amplifier to provide an easy electrical interface. Conditioned and Optical Pressure Sensors Sensors that include integrated circuitry, such as amplifiers, are referred to as amplified sensors. These types of sensors may be constructed using bridge-based, capacitive, or piezoelectric transducers. In the case of a bridge-based amplified sensor, the unit itself provides completion resistors and the amplification necessary to measure the pressure directly with a data acquisition system. Though excitation must still be provided, the accuracy of the excitation is less important. Optical Pressure Sensors Pressure measurement using optical sensing has many benefits including noise immunity and isolation. Read Fundamentals of FBG Optical Sensing for more information about this method of measurement. 9 9

10 Choosing the Right Pressure Sensor Bridge-based or piezoresistive sensors are the most common types of sensor because of their simple construction and durability. This translates to lower cost. In general, foil strain gages are used in high-pressure (up to 700M Pa) applications. They also have a higher operating temperature than silicon strain gages, but silicon strain gages offer the benefit of larger overload capability. Because they are more sensitive, silicon strain gages are often preferred in low-pressure applications (~2k Pa). Capacitive and piezoelectric pressure transducers are generally stable and linear, but they are sensitive to high temperatures and are more complicated to set up than most pressure sensors. Piezoelectric sensors respond quickly to pressure changes. For this reason, they are used to make rapid pressure measurements from events such as explosions. Because of their superior dynamic performance, piezoelectric sensors are the least cost-effective, and you must be careful to protect their sensitive crystal core. Conditioned sensors are typically more expensive because they contain components for filtering and signal amplification, excitation leads, and the regular circuitry for measurement. This is helpful for lower cost systems that do not warrant a dedicated signal conditioning system. Because the conditioning is built in, you can connect the sensor directly to a DAQ device as long as you provide power to the sensor in some way. Pressure Measuring Devices Barometer Atmospheric pressure is measured by a device called a barometer; thus, the atmospheric pressure is often referred to as the barometric pressure. A frequently used pressure unit is the standard atmosphere, which is defined as the pressure produced by a column of mercury 760 mm in height at 0 C (r Hg = 13,595 kg/m 3 ) under standard gravitational acceleration (g = m/s 2 ). The basic barometer. The length or the cross-sectional area of the tube has no effect on the height of the fluid column of a barometer, provided that the tube diameter is large enough to avoid surface tension (capillary) effects

11 Pressure Measuring Devices Bourdon Gage Principles: Change in curvature of the tube is proportional to difference of pressure inside from that outside the tube. Applications: Tire pressure, pressure at the top or along the walls of tanks or vessels Pressure Measuring Devices Strain Gage Principles: P à Resistance à Voltage Applications: Sensors for internal combustion engines, automotive, research etc

12 3/1/17 Pressure Measuring Devices Quartz Gage Principles: Pressure à Charge à Voltage Applications: Measurements with high accuracy, good repeatability, high resolution, e g. Quartz Clock. Piezoelectric transducers Pressure Measuring Devices Piezoresistive Gage Principles: Pressure = Charge = Resistance = Voltage Applications: Very accurate for small pressure differentials e.g. difference between indoor and outdoor pressure. Digital Manometer 12 12

13 Pressure Measuring Devices U-tube Manometer Principles: Hydrostatic Law P=ρ g h Pressure Measuring Devices U-tube Manometer Applications: Air pressure, pipe pressure, etc. Mercury Water Manometer Air Water Manometer 13 13

14 Elastic Elements Elastic elements, when subjected to pressure, get deformed. Measurement of the deformation gives an indication of pressure value. The deformation may be measured by mechanical or electrical means. Example of elastic elements are: diaphragms, capsules, bellows, Bourdon or helical tubes. Elastic Elements Flat diaphragm Corrugated diaphragm Capsule Bellows Straight tubes C-shape Bourdon tube Twisted Bourdon tube Helical Bourdon tube Spiral Bourdon tube 14 14

15 Electrical Resistance Pressure Gauge The concept of operation is based on electrical resistance change in a conductor when applied directly to a pressure. The sensing element consist of a loosely wound coil of relatively fine wire, and it will be compressed when high pressure is applied to it. The length and cross section of the wire affect its electrical resistance. McLeod Gauge It compresses the low pressure gas so that the increased pressure can be measured. The change in volume and pressure can then be used to calculate the original gas pressure, providing that the gas not condensed

16 Pirani Gauge It consist of platinum filament and thermocouple enclosed in a chamber. The pressure measurement is based on the relation of heat conduction and radiation from a heating element to the number of gas molecules per unit volume in the low pressure region. Ionization Gauge It can be used to measure pressure down to about 2 torr. The gas is ionized with a beam of electrons and the current is measured between two electrodes in the gas. The current is proportional to the number of ions per unit volume, which also proportional to the gas pressure

17 Piezoresistive Integrated Semiconductor Integrated Circuit processing is used to form the piezoresistors on the surface of a silicon wafer. There are four piezoresistors within the diaphragm area on the sensor. Two are subjected to tangential stress and two to radial stress when the diaphragm is deflected. They are connected in a fourelement bridge configuration and provide the following output: V OUT /V CC = ΔR / R Piezoresistive Integrated Semiconductor IC processing is used to form the piezoresistors on the surface of a silicon wafer to fabricate an integrated piezoresistive pressure sensor. Integrated silicon pressure sensor measures 0.52 in. long by 0.44 in. wide by 0.75 in. high, including the port

18 Calibration Dead-Weight Tester. A dead-weight tester uses calibrated weights that exert force on a piston which then acts on a fluid to produce a test pressure. Oil is the medium typically used for lower pressures. For high pressures (>500 psi), pneumatic bearing testers are available and are more convenient as well as less messy to use

19 The Manometer It is commonly used to measure small and moderate pressure differences. A manometer contains one or more fluids such as mercury, water, alcohol, or oil. Measuring the pressure drop across a flow section or a flow device by a differential manometer. The basic manometer. In stacked-up fluid layers, the pressure change across a fluid layer of density r and height h is rgh. 37 A simple U-tube manometer, with high pressure applied to the right side

20 In many structures of practical application, the submerged surfaces are not flat, but curved as here at Glen Canyon Dam in Utah and Arizona. 39 Exercise Find the absolute pressure, if a pressure gauge reads 8.3psi, while the atm pressure is 14.7psi. P abs = P at + P g = = 23 psi 20 20

21 Hydrostatic Pressure Hydrostatic pressure is the pressure in a liquid. The pressure increases as the depth in a liquid increases, due to its weight. In term of equation, P = ρgh ρ = density in kg/m 3 g = acceleration due to gravity (9.8m/s 2 ) h = depth in liquid in m P = pressure in Pa P = ρ w h ρ w = weight density in lb/ft 3 h = depth in liquid in ft P = pressure in lb/ft 2 Exercise If a pool has a water with a depth of 6 ft. Find the pressure at the bottom of the pool in Pa and psi. (assume density = 10 3 kg/m 3 ) 21 21

22 Manometer Manometer is the simplest device for measuring static pressure. It contains water/ mercury or any other suitable fluid in the manometer tube. When a pressure line is connected to one column of manometer, the fluid in the column will be forced down, and the fluid in the other will rise. By measuring the difference in height of the fluid in the two columns, the pressure of the inlet can be expressed in inches of fluid. Types of Manometer U-tube Manometer Well-type Manometer Incline-tube Manometer 22 22

23 Potentiometric Pressure Sensors Potentiometric pressure sensors use a Bourdon tube, capsule, or bellows to drive a wiper arm on a resistive element. For reliable operation the wiper must bear on the element with some force, which leads to repeatability and hysteresis errors. These devices are very low cost, however, and are used in lowperformance applications such as dashboard oil pressure gauges Several configurations based on varying inductance or inductive coupling are used in pressure sensors. They all require AC excitation of the coil(s) and, if a DC output is desired, subsequent demodulation and filtering. The LVDT types have a fairly low frequency response due to the necessity of driving the moving core of the differential transformer The LVDT uses the moving core to vary the inductive coupling between the transformer primary and secondary. Inductive Pressure Sensors 23 23

24 Capacitive Pressure Sensors Capacitive Pressure Sensors Piezoelectric Pressure Sensors. Piezoelectric sensors convert stress into an electric potential and vice versa. Sensors based on this technology are used to measure varying pressures

25 Strain Gauge Pressure Sensors Strain gauge sensors originally used a metal diaphragm with strain gauges bonded to it. the signal due to deformation of the material is small, on the order of 0.1% of the base resistance Semiconductor strain gauges are widely used, both bonded and integrated into a silicon diaphragm, because the response to applied stress is an order of magnitude larger than for a metallic strain gauge. Strain Gauge Pressure Sensors When the crystal lattice structure of silicon is deformed by applied stress, the resistance changes. This is called the piezoresistive effect. Following are some of the types of strain gauges used in pressure sensors. Deposited strain gauge. Metallic strain gauges can be formed on a diaphragm by means of thin film deposition. This construction minimizes the effects of repeatability and hysteresis that bonded strain gauges exhibit. These sensors exhibit the relatively low output of metallic strain gauges

26 Strain Gauge Pressure Sensors Bonded semiconductor strain gauge. A silicon bar may be bonded to a diaphragm to form a sensor with relatively high output. Making the diaphragm from a chemically inert material allows this sensor to interface with a wide variety of media Pressure Switches Pressure switches, combining a diaphragm or other pressure measuring means with a precision snap switch, can provide precise single-point pressure sensing. Alternatively, simple electronic switches may be combined with electrical sensors to construct a pressure switch with an adjustable set point and hysteresis

27 Electrical Interfacing Care must be taken to avoid corrupting the signal by noise of 60/50 Hz AC pickup. If the signal must be run some distance to the interface circuitry, twisted and/or shielded wire should be considered. A decoupling capacitor located at the sensor and connected from the supply to ground will also filter noise, as will a capacitor from output to ground. For long runs, a current output sensor should be considered. These devices have a 2-wire interface and modulate the supply current in response to applied pressure. Obviously, wire resistance has no effect and noise must change the loop current, not simply impress a voltage on the signal. The industry standard interface is: PL = 4 ma PH = 20 ma PL= low pressure range limit PH = high pressure range limit Manometer A mercury manometer is a simple pressure standard and may be used for gauge, differential, and absolute measurements with a suitable reference. It is useful mainly for lower pressure work because the height 27 27

28 Selection Considerations Selection of a pressure sensor involves consideration of the medium for compatibility with the materials used in the sensor, the type (gauge, absolute, differential) of measurement, the range, the type of electrical output, and the accuracy required. Manufacturer's specifications usually apply to a particular temperature range. If the range of operation in a given application is smaller, for example, the errors should ratio down. Total error can be computed by adding the individual errors (worstcase) or by computing the geometric sum or root sum of the squares (RSS). The latter is more realistic since it treats them as independent errors that typically vary randomly. Selection Considerations Following is a comparison of the two methods. Given the following error terms: Linearity = 1% F.S. Null calibration = 1% F.S. Sensitivity calibration = 1% F.S. Temperature errors are sometimes given as coefficients per ºC referenced to 25ºC. Simply multiply the coefficient by the temperature range of the application to obtain the total error. Temperature error = 0.5% F.S. Repeatability and hysteresis = 0.1% F.S

29 Selection Considerations Worst case error is equal to the sum of all the maximum errors: Worst case error = = 3.6% Industrial Applications Fluid level in a tank: A gauge pressure sensor located to measure the pressure at the bottom of a tank can be used for a remote indication of fluid level using the relation: h = P/ρg Fluid flow: An orifice plate placed in a pipe section creates a pressure drop. This approach is widely used to measure flow because the pressure drop may be kept small in comparison to some other types of flowmeters and because it is impervious to clogging, which may otherwise be a problem when measuring flow of a viscous medium or one containing particulate matter. The relation is: 29 29

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