Pressure Measurement PDF

# Instrument Consultant Program - Level 1 - Pressure Measurement ## Table of Contents - Introduction - What is Pressure? - The Pressure Equation - Pressure Variables - Hydrostatic Pressure - Level of a Liquid - Density of a Liquid - Pressure on t...

# Instrument Consultant Program - Level 1 - Pressure Measurement ## Table of Contents - Introduction - What is Pressure? - The Pressure Equation - Pressure Variables - Hydrostatic Pressure - Level of a Liquid - Density of a Liquid - Pressure on the Surface of a Liquid - Gas Pressure - Container Volume - Temperature of a Gas - Why Measure Pressure? - Safety - Process Efficiency - Cost Savings - Inferred Measurement of other Variables - Pressure Terminology - Pressure Units - Units of Force Over Area - Units Referenced to Columns of Fluid - Reference Pressures - Absolute Pressure - Gauge Pressure - Differential Pressure - Designating Reference Pressures - Converting Absolute Pressure Measurements - Measurable Pressures - Head Pressure - Static Pressure - Vapor Pressure - Inferring Nonpressure Variables - Flow - Level - Density Measurement - Interface Measurement - Pressure Measurement and Control - Pressure Gauges - Liquid Column Gauges - Barometer - Manometer - Mechanical Pressure Gauges - Bourdon Tube - Bellows and Capsules - Pneumatic Pressure Cells - Pneumatic Controllers - Electronic Pressure Transmitters - Variable Capacitance - Piezoresistive - Piezoelectric - Variable Inductance - Variable Reluctance - Vibrating Wire - Strain Gauge - Workbook Exercise - Workbook Exercise - Answers - Activity Answers ## Introduction Accurate measurement of liquid, gas, and steam pressure is a basic requirement for many industrial processes to operate safely, efficiently, and with optimum quality control. Many plants have more pressure-measurement and control devices in use than all other types of measurement and control instruments combined. Some pressure-measurement devices use complex technology, while others are quite simple. The accuracy and precision of the different pressure-measurement instruments also varies widely. This module introduces you to the basic principles of pressure measurement and explains the benefits of accurate pressure measurement and control in process industries. In addition, descriptions of the different pressure-measurement and control devices available will be presented. This module contains the following sections: - What is Pressure? - Why Measure Pressure? - Pressure Terminology - Inferring Nonpressure Variables - Pressure Measurement and Control ## PERFORMANCE OBJECTIVE After you have completed this module, you will understand and be able to explain the basis upon which pressure-measurement products are differentiated in the process control industry. ## What is Pressure? Before learning about pressure measurement, it is necessary to understand precisely what pressure is. This section describes the basic principles of pressure. ### LEARNING OBJECTIVES After you have completed this section, you will be able to: - Define pressure - Explain how changes in force and in the area over which force is applied affect pressure - Explain how level, density, and pressure on the surface of the liquid affect the pressure of a liquid - Explain how container volume and temperature affect the pressure of a gas ***Note:** To answer the activity questions the Hand Tool (H) should be activated. ### The Pressure Equation Pressure is the amount of force applied over a defined area. The relationship between pressure, force, and area is represented in the following formula: $P = \frac{F}{A}$ Where: - $P$= Pressure - $F$= Force - $A$= Area If a force (due to physical contact) is applied over an area, pressure is being applied. Pressure increases if the force increases or the size of the area over which the force is being applied decreases. ### Activities 1. What is the definition of pressure? - Density that acts on a defined area - Mass that acts on a defined area - Volume applied over a defined area - **Force applied over a defined area** 2. Increasing the surface area over which a force is applied results in an increase in pressure. Is this statement true or false? - **False** ### Pressure Variables The factors that influence the pressure of a liquid are different from the factors that influence the pressure of a gas. Therefore, when measuring pressure, it is important to understand the properties of liquids and gases. #### Hydrostatic Pressure (Head) The pressure exerted by a liquid is influenced by three factors: - Level of the liquid - Density of the liquid - Pressure on the surface of the liquid (vapor space) ##### Level of a Liquid The pressure at the bottom of the column of liquid increases as the depth of the liquid increases. Pressure is affected by the height, rather than the volume, of a liquid. If other factors (e.g., density of the liquid and pressure on the surface of the liquid) are constant, the pressure at the bottom of a 10 ft. water level in a larger tank will be equal to the pressure at the bottom of a 10 ft. water level in a smaller tank. ##### Density of a Liquid Density is the mass of a particular substance per unit of volume. A liquid with a greater density has more mass per unit of volume. Liquids with greater density will produce greater hydrostatic pressure (head) than liquids with lower density. $Density = Mass / Volume$ Variations in temperature cause liquids to expand and contract, which increases or decreases the volume of the liquid, and thus the density. That is why densities are typically shown at a reference temperature. Density is often represented in terms of specific gravity. Specific gravity is the ratio of the density of a particular liquid to the density of water at a reference temperature. Water has a density of 1,000 kg/m³ at 50 °F (10°C). Temperature is specified when giving a density value because temperature affects density. The density of gasoline is 660 kg/m³ at 50 °F (10°C). To calculate the specific gravity of gasoline, divide the density of gasoline by the density of water: $\frac{660 \ kg/m^{3}}{1000\ kg/m^{3}} = 0.66$ Because specific gravity is a ratio of densities, it does not change as units of measure change. Therefore, the specific gravity of gasoline at 60 °F (15.6 °C) is always 0.66, even if the density of gasoline and the density of water are expressed in a different unit of measure (e.g., lb/ft³): $\frac{41.2038 \ lb/ft^{3}}{62.43 \ lb/ft^{3}} = 0.66$ So now we can infer the level of liquid with a density and height measurement. ##### Pressure on the Surface of a Liquid Pressure on the surface of a liquid is pressure that is exerted above a column of liquid being measured. In an open tank, atmospheric pressure (the pressure exerted by the Earth's atmosphere) is the pressure on the surface. If a gas is added to the top of a column of liquid in a closed tank, pressure on the surface would result. If there is a vacuum above the liquid in a closed tank, a pressure less than atmospheric pressure will exist on the surface. In a closed-tank application, the pressure on the surface (vapor space) is often referred to as top pressure. The effects of pressure on the surface must be taken into account to produce an accurate pressure measurement. Pressure on the surface is often measured and subtracted from the pressure at the point of measurement to determine liquid pressure, particularly in level applications. #### Activities 3. Which are the factors that will influence the measurement of pressure exerted by a liquid? Select all options that apply. - **Depth** - **Pressure Pressure on the surface** - Conductivity - **Density** - Di-electric 4. The pressure at the bottom of a glass of water increases as the glass is filled. Is this statement true or false? - **True** #### Gas Pressure Unlike a liquid, a gas will exert equal pressure on all parts of the container in which it is held. Two factors affect the pressure exerted by a gas: - Volume of the container in which the gas is held - Temperature of the gas Common practice in process industries is to refer to both liquids and gases as fluids. ##### Container Volume The relationship between the pressure exerted by a gas and the volume of the container in which it is held is known as Boyle's law. Because a gas can be compressed, the pressure of a gas increases proportionately as the volume of the container in which the gas is held decreases. Conversely, if a set amount of gas is transferred to a larger container, the pressure will decrease in proportion to the increase in container volume. $V1*P1 = V2*P2$ ##### Temperature of a Gas The relationship between gas pressure and temperature is known as Charles 's law. Gas pressure is affected by changes in temperature. As the temperature of a gas increases, the energy of the individual gas molecules increases as well. As a result, the gas molecules collide with the vessel wall more frequently and with greater force, and the pressure exerted against the inside wall of the vessel increases. If the volume of the vessel holding a gas and the amount of gas are unchanged, the pressure exerted by the gas on the vessel walls will change in proportion to changes in the temperature of the gas. $V1T1 = V2T2$ ### Activities 8. In a tank filled with gas, the pressure at the bottom is ____ the pressure at the top. - **greater than** - smaller than - equal to 9. The contents of a tank holding 20m³ of gas are transferred to a tank with double the capacity, all other factors remain unchanged. What will happen to the gas pressure? - The pressure will be doubled. - The pressure will be reduced to half. - **The pressure will remain unchanged.** - The pressure will increase marginally. 10. A tank containing 20m³ of gas is heated, while all other factors remain unchanged. What will happen to the gas pressure? - **Pressure will increase as temperature increases.** - Pressure will decrease as temperature increases,. - Pressure will remain constant despite temperature increases. - Pressure will decrease marginally. ## COMPLETE WORKBOOK EXERCISE - WHAT IS PRESSURE? ## Why Measure Pressure? Process industries measure pressure for several reasons, the most common of which are discussed in this section. ### LEARNING OBJECTIVE After you have completed this section, you will be able to: - List and briefly explain the four most common reasons for measuring pressure: - Safety - Process efficiency - Cost savings - Inferred measurement of other variables ***Note:** To answer the activity questions the Hand Tool (H) should be activated. ### Activities 1. Why do process industries commonly measure pressure? Select all options that apply. - **Safety** - **Process efficiency** - **Inferred measurement of other variables** - **Cost saving** 2. Accurate pressure measurement helps process industries save money by keeping pumps, compressors, and other devices used to create pressure or vacuum from being run unnecessarily. Is this statement true or false? - **True** ### Safety Pipes, tanks, valves, flanges, and other equipment used with pressurized fluids in process industries are designed to withstand the stress of a specific range of pressures. Accurate pressure measurement and precise control help prevent pipes and vessels from bursting. In addition, pressure measurement and control help minimize equipment damage, reduce the risk of personal injury, and prevent leaks of potentially harmful process materials into the environment. Pressure measurement used to control the level and flow of process materials helps to prevent backups, spills, and overflows.By monitoring the pressure in the process, actions can be taken to prevent (or minimize) an environmental release or personell injury/ exposure. ### Process Efficiency In most cases, process efficiency is highest when pressures (and other process variables) are controlled at particular values or within a narrow range of values. Accurate pressure measurement can help sustain the conditions required for maximum efficiency. For example, the piece of paper on which these words are written was created from a pulp solution put through a paper machine at a specific pressure. If the pressure had gone above or below the setpoint (required range), the result would have been scrap instead of a usable sheet of paper. Efficiency of a process is directly related to the quality of the product being produced. ### Cost Savings The equipment used to create pressure or vacuum in process industries (e.g., pumps and compressors) uses considerable energy. Because energy costs money, precise pressure measurement can save money by preventing the unnecessary expense of creating more pressure or vacuum than is required to produce the desired results for a particular process. The scrap in the above example also adds to unnecessary costs since it now may need to be reworked (more energy is required) and the overall output is reduced (lost production). Therefore, quality is a sub-component of both process efficiency and cost savings. ### Inferred Measurement of other Variables Pressure measurements are frequently used to infer the measurement of other process variables, such as the rate of flow through a pipe, the level of a fluid in a tank, the density of a substance, or how two or more liquids in a tank interface. For example, if a constriction is placed in a pipe, pressure will drop in a predictable way. By measuring the pressure of fluid in a pipe before and after the constriction, the rate of flow through the pipe can be calculated. For a discussion on how pressure measurement can be used to infer the values of other process variables, see Inferring Nonpressure Variables on page 28. ## COMPLETE WORKBOOK EXERCISE - WHY MEASURE PRESSURE? ## Pressure Terminology Pressure measurements can be expressed in several different units. Some units are more popular in one part of the world than another. Some pressure-measurement units are more useful for one type of application than another. For a measurement to be useful, the reference point from which the measurement is being taken must be known. For example, a measurement of three miles is meaningless unless we know where three miles begin or start. Basic reference points of pressure measurement are introduced in this section, along with descriptions of measurable pressures you will encounter in the field. ### LEARNING OBJECTIVES After you have completed this section, you will be able to: - Recognize and explain the basis of the units used for pressure measurement - Differentiate between the following three reference points of pressure measurement: - Absolute - Gauge - Differential - Differentiate between the following three measurable pressures: - Head (hydrostatic) pressure - Static (line) pressure - Vapor pressure ***Note:** To answer the activity questions the Hand Tool (H) should be activated. ### Pressure Units Pressure units can be divided into two categories: units of force over area and units referenced to columns of fluid. #### Units of Force Over Area The following are units of force over a defined area: - Pounds per square inch (psi) - Kilograms per square centimeter (kg/cm²) - Grams per square centimeter (g/cm²)-1 g/cm² = 1/1,000 kg/cm² - Pascals (Pa or N/m²)-N stands for newton - Kilopascals (kPa)-1 kPa = 1,000 Pa - Bar-1 bar = 100,000 Pa - Millibar (mbar)-1 mbar = 1/1,000 bar #### Units Referenced to Columns of Fluid The following are units of pressure referenced to a column of fluid: - Inches of water (inH2O at 68 °F [20 °C] or at 39.2 °F [4°C]) - Feet of water (ftH2O) - Meters of water (mH2O) - Millimeters of water (mmH2O) - Inches of mercury (inHg) - Millimeters of mercury (mmHg) - Atmosphere (atm)-The pressure exerted by the earth's atmosphere at sea level - Torr-1 torr = 1 mmHg Pressure units referenced to a column of fluid serve as a useful measure of pressure, even though they do not represent a force over a defined area. Because of gravity, a column of fluid will exert a certain force (weight) downward and thus a certain predictable pressure. The higher a column of fluid, the greater the force exerted by that fluid. The more dense a fluid, the greater the force exerted by that fluid. Units of measure must have static values therefore, fluid column height and fluid density must be specified when representing pressure as a column of fluid. ### Activities 1. What is the abbreviation for kilopascals? - KpA - **kPa** - KPa - kpa 2. Why is temperature specified in inches of water pressure measurement units? - Every pressure measurement unit has the temperature specified as a standard. - With the temperature specified, the volume is a known constant and the the unit value will not fluctuate. - **With the temperature specified, the density is a known constant and the unit value will not fluctuate.** - Every liquid application requires the use of pressure measurement units with specified temperature. 3. Which of the following pressure measurement units are referenced to a column of fluid? Select all options that apply. - **in H₂O** - psi - torr - **in Hg** - KPa - atm ### Converting Units of Pressure Product literature (e.g., manuals, product data sheets, product price lists) for each pressure measurement instrument lists the pressure range within which that device can be effectively and safely operated. However, the pressure units used in the product literature may not be the same as the units specified by a customer for his or her application. Therefore, unit conversions are often required to determine if a particular pressure-measurement device will meet the requirements of a customer's application. For example, imagine that a customer identifies 40 bar as the maximum amount of pressure a particular process produces. The customer wants to know what range instrument to use. The product literature lists pressure ranges in psi, so a conversion from bar to psi is necessary before a recommendation can be made. Units of pressure can be converted using a conversion table, such as the table below, that shows the relationships between different units of pressure (e.g., how many bar equal 1 psi). To convert 40 bar to psi, look in the conversion table to find that one bar equals 14.5038 psi. Because you need the psi value of 40 bar, multiply 14.5038 by 40 to obtain a value of 580.151 psi. Now you can determine from the product literature that a Range Code 5 instrument is needed. | | psi | kPa | inH₂O | mmHg | inHg | mbar | bar | kg/cm² | gm/cm² | |:----------:|:-------:|:--------:|:--------:|:-------:|:-------:|:------:|:-------:|:-------:|:--------:| | **Convert From** | | | | | | | | | | | psi | 1 | 6.8948 | 27.7296 | 704.332 | 2.0360 | 68.9476| 0.0689 | 0.0703 | 70.3070 | | kPa | 0.1450 | 1 | 4.0218 | 102.155 | 0.2953 | 10.000 | 0.0100 | 0.0102 | 10.197 | | inH₂O | 0.0361 | 0.2486 | 1 | 25.4000 | 0.0734 | 2.4864 | 0.0025 | 0.0025 | 2.5355 | | mmHg | 0.0014 | 0.0098 | 0.0394 | 1 | 0.0295 | 0.0979 | 0.00001| 0.00001| 0.0998 | | inHg | 0.4912 | 3.3864 | 13.6195 | 345.936 | 1 | 33.8639| 0.0339 | 0.0345 | 34.532 | | mbar | 0.0145 | 0.1000 | 0.4022 | 10.2155 | 0.0295 | 1 | 0.001 | 0.001 | 1.0197 | | bar | 14.5038 | 100.000 | 402.184 | 10215.5 | 29.5300| 1000 | 1 | 1.0197 | 1019.72 | | kg/cm² | 14.2233 | 98.0665 | 394.408 | 10018.0 | 28.9590| 980.665| 0.9807 | 1 | 1000 | | gm/cm² | 0.0142 | 0.0981 | 0.3944 | 10.0180 | 0.0290 | 0.9807 | 0.001 | 0.001 | 1 | ### Activities 4. Refer to the table below and state the value of 115 inH₂O when converted into mbar. - 270.94 - 280.94 - 285.94 - **275.94** ### Reference Pressures Pressure-measurement devices can be categorised according to the reference pressure from which they measure. The three reference pressures are: - Absolute - Gauge - Differential Absolute and gauge devices measure the difference between the pressure of the process fluid and a reference pressure. Differential devices take two pressure measurements of the process fluid at different points and measure the difference between them. #### Absolute Pressure Absolute pressure measurements compare measured pressure to a perfect vacuum (or 0 psia). Because no pressure reading can be less than a perfect vacuum, an absolute pressure-measurement device will never have a negative reading. The reference pressure of an absolute pressure-measurement device (i.e., a perfect vacuum) never changes. One example of an absolute pressure application is the monitoring of certain chemical reactions. #### Activities 5. An absolute pressure transmitter uses ____ as the reference. - a perfect vacuum - atmosphere - 1 bar #### Gauge Pressure A gauge pressure-measurement instrument uses the pressure of the surrounding atmosphere (approximately 14.7 psi) as a reference pressure. Changes in atmospheric pressure (such as those due to changes in the weather) cause the output of a gauge sensor to change. Depending on the application, the output change may or may not be desirable. In process systems not open to atmosphere (e.g., a process in an unvented tank), pressures of the process material being measured could be less than the surrounding atmospheric pressure, which would result in a negative pressure reading. Gauge devices are often used on holding tanks that are open to atmosphere. #### Activities 6. A gauge pressure transmitter uses ____ as the reference. - a perfect vacuum - **atmosphere** - 0 psia #### Differential Pressure A differential pressure measurement uses a second process pressure as a reference pressure. Differential pressure measurements are often used to infer the rate of flow through a pipe by determining the pressure drop that occurs from one point in a system to another, such as the pressure drop that occurs across an orifice plate in a pipe. For example, if a differential pressure (DP) instrument is installed so that the high side of the instrument measures the pressure on the upstream side of the flow element in a pipe and the low side of the instrument measures the pressure on the downstream side of the flow element, with the high side pressure at 12 psi and the low side pressure at 10 psi, the differential pressure is 2 psi. Changes in atmospheric pressure do not affect the output of a differential pressure-measurement instrument because both measured pressure and reference pressure are equally influenced by exposure to the atmosphere. Differential devices are often used in flow or level applications. #### Activities 7. How many process connections do differential pressure-measurement instruments have? - One - **Two** - Four #### Designating Reference Pressures The designator a for absolute and g for gauge are often attached to the end of pressure units to indicate the reference pressure or type of instrument being used. Thus, the pressure unit "psi" is sometime represented as psig or psia and the unit "bar" as bar g or bar a. #### Converting Absolute Pressure Measurements An absolute pressure measurement registers the pressure of the surrounding atmosphere as part of the pressure reading, whereas a gage pressure measurement uses atmospheric pressure as its reference. Therefore, absolute values can be converted to gage values by subtracting atmospheric pressure from the absolute pressure reading (Figure 1.2). $Ptotal = Pgauge + Patm$ #### Activities 8. What does the designation psig represent? - Pounds per square inch gauge - Pounds per square in gas - Pressure per square inch of gas - **Pressure per square inch gauge** 9. A gauge pressure transmitter is measuring atmospheric pressure. What is the pressure reading? - 20 psig - Approx -14.7 psig - **0 psig** - Approx 14.7 psig 10. An absolute pressure transmitter is measuring atmospheric pressure. What is the approximate pressure reading in psia? - Approx -14.7 psia - 0 psia - **Approx 14.7 psia** - 20 psia ### Measurable Pressures The three types of measurable pressures in the process control industry follow: - Head pressure - Static pressure - Vapor pressure #### Head Pressure Head pressure, also known as hydrostatic pressure, is the pressure exerted by a column of fluid (Figure 1.3). Head pressure is directly proportional to the specific gravity of the fluid and the height of the fluid column. $Head Pressure = Height x S.G.$ #### Activities 11. Head pressure is the pressure exerted by a column of fluid. Is this statement true or false? - **True** 12. Head pressure is proportional to the specific gravity of a fluid. Is this statement true or false? - **True** #### Static Pressure Static pressure, or line pressure, is the pressure exerted in a closed system. A closed system is a system that is sealed from atmosphere. An example of static pressure can be found in a common boiler system. As the water in the boiler is heated, pressure increases. The term static or line pressure is more commonly used in flow applications and refers to the pressure exerted by the fluid in the pipe. #### Vapor Pressure Vaporization is the transformation of a substance from a liquid state to a gas state (e.g., water to steam). The transformation occurs at a specific temperature for each liquid. For example, water turns to steam (boils) at 212 °F (100 °C). Increased pressure causes the boiling point of a liquid to rise. Conversely, a decrease in pressure causes the boiling point of a liquid to fall. For example, water boils at 212 °F at or near sea level, butat high altitudes where the atmospheric pressure is lower, water boils at less than 212 °F. #### Activities 13. Pressure exerted by the fluid in the pipe can be referred to as static pressure. Is this statement true or false? - **True** 14. ____ is the transformation of a liquid into a gas. - **Vaporization** - Emulsification - Condensation 15. As pressure increases, the boiling point of a liquid ____ - decreases - remains constant - **increases** #### The relationship between pressure, temperature, and the boiling point of a substance can be plotted on a simple, two-axis graph. Figure 1.4 shows the vapor pressure curve. Each substance has its own respective vapor pressure curve. The vapor pressure curve of oil, for instance, differs from the vapor pressure curve of glycerin. #### Activities 16. Vapor pressure curves are identical for all substances. Is this statement true or false? - **False** ## COMPLETE WORKBOOK EXERCISE - PRESSURE TERMINOLOGY ## Inferring Nonpressure Variables Pressure-measurement readings can be used to calculate such nonpressure variables as the density of a process fluid, the level of a process liquid in a tank or vessel, and the rate of flow of a substance through a pipe. ### LEARNING OBJECTIVES After completing this section, you will be able to describe how pressure measurement can be used to infer (calculate): - The rate of flow of a fluid through a pipe - The level of a liquid in a tank - The density of a fluid in a tank - The way different fluids interface in a vessel ***Note:** To answer the activity questions the Hand Tool (H) should be activated. ### Flow A common use of pressure measurement is to infer a fluid's flow rate through a pipe. As a fluid flows through a pipe with a decreasing diameter, fluid velocity increases at a rate proportional to the decrease in pipe diameter. Bernoulli's principle states that as a fluid speeds up to bypass an obstruction, pressure drops. The pressure of the fluid flowing through a pipe will be greater on the upstream side of an obstruction in the pipe than on the downstream side. If pressure is measured before and after an orifice plate in the pipe (e.g., a flow element such as a venturi tube, flow nozzle, wedge, or annubar) the difference between the two measurements, or differential pressure, is proportionate to the flow rate of the fluid through the pipe. The flow equation used for DP flowmeters is based on Bernoulli's equation, which shows that flow rate (Q) is proportional (a) to the square root of differential pressure (ΔΡ): $Q \propto \sqrt{\Delta P}$ Approximately half of all flow measurements are made by inferring the flow rate from a differential pressure measurement. ***Note:** For more information on inferring flow rates from pressure measurements, see the Flow Measurement module. ### Activities 1. The velocity of the fluid flowing through a pipe ____ at a rate proportional to the reduction in pipe diameter. - increases - remains constant - **decreases** 2. The pressure of a fluid flowing through a pipe will be greater on the downstream side of an obstruction in a pipe, than on the upstream side. Is this statement true or false? - **True** ### Level If specific gravity is known, then the level of a liquid in a tank or vessel can be determined from the pressure measurement by rearranging the equation used for density calculation: $Height of Liquid = \frac{Pressure}{Specific Gravity}$ The units used to express height and pressure must be comparable. Remember that pressure on the surface of a liquid can affect a pressure measurement. For example, if you are using a pressure measurement to infer the level of a tank open to the surrounding atmosphere, then the atmospheric pressure must first be subtracted from the pressure reading in order to obtain an accurate level calculation. Over half of all level measurements in process industries are made with a pressure-measurement device. ***Note:** For more information on inferring level from pressure measurements, see the Level Measurement module. ### Activities 3. What factors are required to calculate the level of liquid in an open tank? Select all options that apply. - **Pressure** - **Specific gravity of the liquid** - **Diameter of the tank** - Atmospheric pressure ### Density Measurement Pressure is equal to the height of the column of liquid being measured multiplied by the specific gravity of the liquid. Therefore, if the height of the column is a known constant (as in the case of the distance between two pressure measurement points on a vessel), the density can be inferred from the pressure reading using the following equation: $Specific Gravity = \frac{Pressure}{Height of Liquid}$ Units of pressure are usually different than units of height. The equation requires comparable units. Most pressure measurements used for density calculations are therefore made in units based on referenced columns of fluid (e.g., inches of water). The height in the equation can also be expressed in inches, and the units will cancel each other out of the equation: $Specific Gravity = \frac{Pressure \ inH_{2}O}{Height \ of \ Liquid \ in}$ The specific gravity value can be converted into mass per unit of volume units, such as grams per cubic centimeter (gm/cm³). Density measurements are often used in the brewing industry to determine stages of fermentation. ### Activities 4. To infer density from a pressure measurement, divide pressure by the ____ of the column of liquid. - specific gravity - **height** - diameter ### Interface Measurement An interface is the boundary between two immiscible (incapable of being mixed) fluids with different densities (e.g., oil and water). An interface measurement finds the boundary between two liquids stored in the same tank, each with a different density. For example, when oil and water occupy the same vessel, the oil floats on top of the water. The interface between the two fluids is the upper level of the water and the lower level of the oil. If the density of both fluids is known, interface can be inferred from a pressure measurement. ### Activities 5. Interface is often used when a manufacturer has two fluids in a tank and wants to pour off only the top fluid-the interface measurement indicates when to stop. ## COMPLETE WORKBOOK EXERCISE - INFERRING NONPRESSURE VARIABLES ## Pressure Measurement and Control Pressure-measurement instruments vary widely in accuracy, complexity, the amount of maintenance they require, and their suitability to different applications. ### LEARNING OBJECTIVES After you have completed this section, you will be able to: - Identify two types of pressure gauges - Explain the operations of the two types of liquid column gauges: - Barometers - Manometers - Name the parts of a mechanical pressure gauge - Describe the operation and use of pneumatic pressure cells - Describe the operation of the following electronic pressure transmitters: - Variable capacitance - Piezoresistive - Piezoelectric - Variable inductance - Variable reluctance - Vibrating wire - Strain gauge ***Note:** To answer the activity questions the Hand Tool (H) should be activated. ### Pressure Gauges All pressure measurements depend upon some portion of the instrument being physically moved by the pressure source being measured. Two types of pressure-measurement gauges are liquid column gauges and mechanical gauges. In a liquid column gauge, the height of a column of liquid varies in response to applied pressure. Mechanical gauges have mechanical parts that move in response to applied pressure. #### Liquid Column Gauges Below are two types of liquid column pressure gauges: - Barometer - Manometer ##### Barometer A barometer is a device that measures atmospheric pressure. A barometer consists of a clear, hollow tube with one end blocked off. The tube is filled with liquid and set, with the blocked end pointing up, into a reservoir of fill liquid (typically mercury) (Figure 1.5). ##### Activities 1. Which of these are examples of liquid column gauges? - Pyrometer - **Manometer** - Tachometer - Barometer ##### Manometer A derivation of the barometer is the manometer. A manometer is a clear, U-shaped tube partially filled with fluid. One leg of the manometer is the reference side; the other leg is the measured side. A pressure measurement is made by comparing the fluid levels of the column in each leg of the manometer U (Figure 1.6). ##### Activities 2. A U-tube manometer measures pressure by comparing the fluid level in one leg to the fluid level in the other leg of the manometer. Is this statement true or false? - **True** #### Mechanical Pressure Gauges Mechanical pressure gauges have two basic parts: - Sensing device - Mechanical dial or indicator (connected to the sensing device; gives a pressure reading) The most commonly used types of pressure-sensing devices are: - Bourdon tube - Bellows and capsules Mechanical pressure gauges are still widely used in the process control industry. ##### Bourdon Tube Bourdon tubes are curled, flexible tubes