Introduction to Instrumentation, Sensors, and Process Control PDF

This E-Book and More From http://ali-almukhtar.blogspot.com Introduction to Instrumentation, Sensors, and Process Control For a listing of related titles from Artech House, turn to the back of this book Introduction to Instrumentation, Sensors, and Process Control...

This E-Book and More From http://ali-almukhtar.blogspot.com Introduction to Instrumentation, Sensors, and Process Control For a listing of related titles from Artech House, turn to the back of this book Introduction to Instrumentation, Sensors, and Process Control William C. Dunn artechhouse.com Library of Congress Cataloging-in-Publication Data Dunn, William C. Introduction to instrumentation, sensors, and process control/William C. Dunn. p. cm. —(Artech House Sensors library) ISBN 1-58053-011-7 (alk. paper) 1. Process control. 2. Detectors. I. Title. II. Series. TS156.8.D86 2005 670.42'7—dc22 2005050832 British Library Cataloguing in Publication Data Dunn, William C. Introduction to instrumentation, sensors, and process control. —(Artech House sensors library) 1. Engineering instruments 2. Electronic instruments 3. Process control I. Title 681.2 ISBN-10: 1-58053-011-7 Cover design by Cameron Inc. © 2006 ARTECH HOUSE, INC. 685 Canton Street Norwood, MA 02062 All rights reserved. Printed and bound in the United States of America. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, includ- ing photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. All terms mentioned in this book that are known to be trademarks or service marks have been appropriately capitalized. Artech House cannot attest to the accuracy of this informa- tion. Use of a term in this book should not be regarded as affecting the validity of any trade- mark or service mark. International Standard Book Number: 1-58053-011-7 10 9 8 7 6 5 4 3 2 1 Contents Preface xv Acknowledgment xvi CHAPTER 1 Introduction to Process Control 1 1.1 Introduction 1 1.2 Process Control 1 1.2.1 Sequential Process Control 2 1.2.2 Continuous Process Control 2 1.3 Definition of the Elements in a Control Loop 4 1.4 Instrumentation and Sensors 5 1.4.1 Instrument Parameters 5 1.5 Control System Evaluation 9 1.5.1 Stability 9 1.5.2 Regulation 9 1.5.3 Transient Response 9 1.6 Analog and Digital Data 10 1.6.1 Analog Data 10 1.6.2 Digital Data 10 1.6.3 Pneumatic Data 10 1.6.4 Smart Sensors 11 1.7 Process Facility Considerations 11 1.8 Summary 12 Definitions 12 References 14 CHAPTER 2 Units and Standards 15 2.1 Introduction 15 2.1.1 Units and Standards 15 2.2 Basic Units 16 2.3 Units Derived from Base Units 16 2.3.1 Units Common to Both the English and SI Systems 16 2.3.2 English Units Derived from Base Units 16 2.3.3 SI Units Derived from Base Units 18 2.3.4 Conversion Between English and SI Units 18 v vi Contents 2.3.5 Metric Units not Normally Used in the SI System 20 2.4 Standard Prefixes 21 2.5 Standards 22 2.5.1 Physical Constants 22 2.5.2 Standards Institutions 22 2.6 Summary 23 References 23 CHAPTER 3 Basic Electrical Components 25 3.1 Introduction 25 3.2 Circuits with R, L, and C 25 3.2.1 Voltage Step Input 25 3.2.2 Time Constants 27 3.2.3 Sine Wave Inputs 28 3.3 RC Filters 32 3.4 Bridge Circuits 34 3.4.1 Voltage Dividers 34 3.4.2 dc Bridge Circuits 34 3.4.3 ac Bridge Circuits 38 3.5 Summary 39 References 40 CHAPTER 4 Analog Electronics 41 4.1 Introduction 41 4.2 Analog Circuits 41 4.2.1 Operational Amplifier Introduction 41 4.2.2 Basic Op-Amp 42 4.2.3 Op-Amp Characteristics 42 4.3 Types of Amplifiers 45 4.3.1 Voltage Amplifiers 45 4.3.2 Converters 50 4.3.3 Current Amplifiers 52 4.3.4 Integrating and Differentiating Amplifiers 53 4.3.5 Nonlinear Amplifiers 54 4.3.6 Instrument Amplifiers 55 4.3.7 Input Protection 57 4.4 Amplifier Applications 57 4.5 Summary 58 References 58 CHAPTER 5 Digital Electronics 59 5.1 Introduction 59 5.2 Digital Building Blocks 59 5.3 Converters 61 Contents vii 5.3.1 Comparators 62 5.3.2 Digital to Analog Converters 64 5.3.3 Analog to Digital Converters 68 5.3.4 Sample and Hold 72 5.3.5 Voltage to Frequency Converters 72 5.4 Data Acquisition Devices 74 5.4.1 Analog Multiplexers 74 5.4.2 Digital Multiplexers 74 5.4.3 Programmable Logic Arrays 75 5.4.4 Other Interface Devices 75 5.5 Basic Processor 75 5.6 Summary 76 References 77 CHAPTER 6 Microelectromechanical Devices and Smart Sensors 79 6.1 Introduction 79 6.2 Basic Sensors 80 6.2.1 Temperature Sensing 80 6.2.2 Light Intensity 80 6.2.3 Strain Gauges 81 6.2.4 Magnetic Field Sensors 82 6.3 Piezoelectric Devices 84 6.3.1 Time Measurements 86 6.3.2 Piezoelectric Sensors 87 6.3.3 PZT Actuators 88 6.4 Microelectromechanical Devices 88 6.4.1 Bulk Micromachining 89 6.4.2 Surface Micromachining 91 6.5 Smart Sensors Introduction 94 6.5.1 Distributed System 95 6.5.2 Smart Sensors 96 6.6 Summary 96 References 97 CHAPTER 7 Pressure 99 7.1 Introduction 99 7.2 Pressure Measurement 99 7.2.1 Hydrostatic Pressure 99 7.2.2 Specific Gravity 100 7.2.3 Units of Measurement 101 7.2.4 Buoyancy 103 7.3 Measuring Instruments 105 7.3.1 Manometers 105 7.3.2 Diaphragms, Capsules, and Bellows 106 7.3.3 Bourdon Tubes 108 viii Contents 7.3.4 Other Pressure Sensors 109 7.3.5 Vacuum Instruments 110 7.4 Application Considerations 111 7.4.1 Selection 111 7.4.2 Installation 112 7.4.3 Calibration 112 7.5 Summary 113 Definitions 113 References 114 CHAPTER 8 Level 115 8.1 Introduction 115 8.2 Level Measurement 115 8.2.1 Direct Level Sensing 115 8.2.2 Indirect Level Sensing 118 8.2.3 Single Point Sensing 124 8.2.4 Level Sensing of Free-Flowing Solids 125 8.3 Application Considerations 126 8.4 Summary 128 References 128 CHAPTER 9 Flow 129 9.1 Introduction 129 9.2 Fluid Flow 129 9.2.1 Flow Patterns 129 9.2.2 Continuity Equation 131 9.2.3 Bernoulli Equation 132 9.2.4 Flow Losses 134 9.3 Flow Measuring Instruments 136 9.3.1 Flow Rate 136 9.3.2 Total Flow 142 9.3.3 Mass Flow 144 9.3.4 Dry Particulate Flow Rate 144 9.3.5 Open Channel Flow 145 9.4 Application Considerations 145 9.4.1 Selection 145 9.4.2 Installation 147 9.4.3 Calibration 147 9.5 Summary 147 Definitions 148 References 148 Contents ix CHAPTER 10 Temperature and Heat 149 10.1 Introduction 149 10.2 Temperature and Heat 149 10.2.1 Temperature Units 149 10.2.2 Heat Energy 151 10.2.3 Heat Transfer 153 10.2.4 Thermal Expansion 155 10.3 Temperature Measuring Devices 157 10.3.1 Expansion Thermometers 157 10.3.2 Resistance Temperature Devices 160 10.3.3 Thermistors 161 10.3.4 Thermocouples 162 10.3.5 Pyrometers 164 10.3.6 Semiconductor Devices 165 10.4 Application Considerations 166 10.4.1 Selection 166 10.4.2 Range and Accuracy 166 10.4.3 Thermal Time Constant 167 10.4.4 Installation 168 10.4.5 Calibration 168 10.4.6 Protection 168 10.5 Summary 169 Definitions 169 References 170 CHAPTER 11 Position, Force, and Light 171 11.1 Introduction 171 11.2 Position and Motion Sensing 171 11.2.1 Position and Motion Measuring Devices 171 11.2.2 Position Application Considerations 176 11.3 Force, Torque, and Load Cells 177 11.3.1 Force and Torque Introduction 178 11.3.2 Stress and Strain 178 11.3.3 Force and Torque Measuring Devices 181 11.3.4 Strain Gauge Sensors 183 11.3.5 Force and Torque Application Considerations 186 11.4 Light 186 11.4.1 Light Introduction 186 11.4.2 EM Radiation 186 11.4.3 Light Measuring Devices 188 11.4.4 Light Sources 188 11.4.5 Light Application Considerations 189 11.5 Summary 190 Definitions 190 References 191 x Contents CHAPTER 12 Humidity and Other Sensors 193 12.1 Humidity 193 12.1.1 Humidity Introduction 193 12.1.2 Humidity Measuring Devices 194 12.1.3 Humidity Application Considerations 197 12.2 Density and Specific Gravity 198 12.2.1 Density and Specific Gravity Introduction 198 12.2.2 Density Measuring Devices 199 12.2.3 Density Application Considerations 202 12.3 Viscosity 202 12.3.1 Viscosity Introduction 202 12.3.2 Viscosity Measuring Instruments 203 12.4 Sound 204 12.4.1 Sound Measurements 204 12.4.2 Sound Measuring Devices 205 12.4.3 Sound Application Considerations 206 12.5 pH Measurements 206 12.5.1 pH Introduction 206 12.5.2 pH Measuring Devices 207 12.5.3 pH Application Considerations 207 12.6 Smoke and Chemical Sensors 208 12.6.1 Smoke and Chemical Measuring Devices 208 12.6.2 Smoke and Chemical Application Consideration 208 12.7 Summary 209 Definitions 209 References 210 CHAPTER 13 Regulators, Valves, and Motors 211 13.1 Introduction 211 13.2 Pressure Controllers 211 13.2.1 Pressure Regulators 211 13.2.2 Safety Valves 213 13.2.3 Level Regulators 214 13.3 Flow Control Valves 215 13.3.1 Globe Valve 215 13.3.2 Butterfly Valve 217 13.3.3 Other Valve Types 218 13.3.4 Valve Characteristics 219 13.3.5 Valve Fail Safe 219 13.3.6 Actuators 220 13.4 Power Control 221 13.4.1 Electronic Devices 222 13.4.2 Magnetic Control Devices 227 13.5 Motors 227 13.5.1 Servo Motors 228 Contents xi 13.5.2 Stepper Motors 228 13.5.3 Synchronous Motors 229 13.6 Application Considerations 230 13.6.1 Valves 230 13.6.2 Power Devices 231 13.7 Summary 231 References 232 CHAPTER 14 Programmable Logic Controllers 233 14.1 Introduction 233 14.2 Programmable Controller System 233 14.3 Controller Operation 235 14.4 Input/Output Modules 236 14.4.1 Discrete Input Modules 236 14.4.2 Analog Input Modules 238 14.4.3 Special Function Input Modules 238 14.4.4 Discrete Output Modules 239 14.4.5 Analog Output Modules 240 14.4.6 Smart Input/Output Modules 240 14.5 Ladder Diagrams 243 14.5.1 Switch Symbols 243 14.5.2 Relay and Timing Symbols 244 14.5.3 Output Device Symbols 244 14.5.4 Ladder Logic 245 14.5.5 Ladder Gate Equivalent 245 14.5.6 Ladder Diagram Example 246 14.6 Summary 249 References 249 CHAPTER 15 Signal Conditioning and Transmission 251 15.1 Introduction 251 15.2 General Sensor Conditioning 251 15.2.1 Conditioning for Offset and Span 252 15.2.2 Linearization in Analog Circuits 253 15.2.3 Temperature Correction 253 15.2.4 Noise and Correction Time 255 15.3 Conditioning Considerations for Specific Types of Devices 255 15.3.1 Direct Reading Sensors 255 15.3.2 Capacitive Sensors 255 15.3.3 Magnetic Sensors 256 15.3.4 Resistance Temperature Devices 257 15.3.5 Thermocouple Sensors 259 15.3.6 LVDTs 259 15.3.7 Semiconductor Devices 260 15.4 Digital Conditioning 260 xii Contents 15.4.1 Conditioning in Digital Circuits 260 15.5 Pneumatic Transmission 261 15.5.1 Signal Conversion 261 15.6 Analog Transmission 262 15.6.1 Noise Considerations 262 15.6.2 Voltage Signals 262 15.6.3 Current Signals 264 15.7 Digital Transmission 264 15.7.1 Transmission Standards 264 15.7.2 Foundation Fieldbus and Profibus 265 15.8 Wireless Transmission 267 15.8.1 Short Range Protocols 267 15.8.2 Telemetry Introduction 267 15.8.3 Width Modulation 268 15.8.4 Frequency Modulation 268 15.9 Summary 269 Definitions 269 References 270 CHAPTER 16 Process Control 271 16.1 Introduction 271 16.2 Sequential Control 271 16.3 Discontinuous Control 273 16.3.1 Discontinuous On/Off Action 273 16.3.2 Differential Closed Loop Action 273 16.3.3 On/Off Action Controller 274 16.3.4 Electronic On/Off Controller 275 16.4 Continuous Control 275 16.4.1 Proportional Action 276 16.4.2 Derivative Action 278 16.4.3 Integral Action 280 16.4.4 PID Action 281 16.4.5 Stability 284 16.5 Process Control Tuning 285 16.5.1 Automatic Tuning 286 16.5.2 Manual Tuning 286 16.6 Implementation of Control Loops 287 16.6.1 On/Off Action Pneumatic Controller 287 16.6.2 Pneumatic Linear Controller 288 16.6.3 Pneumatic Proportional Mode Controller 289 16.6.4 PID Action Pneumatic Controller 289 16.6.5 PID Action Control Circuits 290 16.6.6 PID Electronic Controller 293 16.7 Summary 294 Definitions 295 References 296 Contents xiii CHAPTER 17 Documentation and P&ID 297 17.1 Introduction 297 17.2 Alarm and Trip Systems 297 17.2.1 Safety Instrumented Systems 297 17.2.2 Safe Failure of Alarm and Trip 298 17.2.3 Alarm and Trip Documentation 299 17.3 PLC Documentation 300 17.4 Pipe and Instrumentation Symbols 300 17.4.1 Interconnect Symbols 301 17.4.2 Instrument Symbols 302 17.4.3 Functional Identification 302 17.4.4 Functional Symbols 304 17.5 P&ID Drawings 308 17.6 Summary 309 References 311 Glossary 313 About the Author 321 Index 323 Preface Industrial process control was originally performed manually by operators using their senses of sight and feel, making the control totally operator-dependent. Indus- trial process control has gone through several revolutions and has evolved into the complex modern-day microprocessor-controlled system. Today’s technology revo- lution has made it possible to measure parameters deemed impossible to measure only a few years ago, and has made improvements in accuracy, control, and waste reduction. This reference manual was written to provide the reader with a clear, concise, and up-to-date text for understanding today’s sensor technology, instrumentation, and process control. It gives the details in a logical order for everyday use, making every effort to provide only the essential facts. The book is directed towards indus- trial control engineers, specialists in physical parameter measurement and control, and technical personnel, such as project managers, process engineers, electronic engineers, and mechanical engineers. If more specific and detailed information is required, it can be obtained from vendor specifications, application notes, and ref- erences given at the end of each chapter. A wide range of technologies and sciences are used in instrumentation and process control, and all manufacturing sequences use industrial control and instru- mentation. This reference manual is designed to cover the aspects of industrial instrumentation, sensors, and process control for the manufacturing of a cost-effec- tive, high quality, and uniform end product. Chapter 1 provides an introduction to industrial instrumentation, and Chapter 2 introduces units and standards covering both English and SI units. Electronics and microelectromechanical systems (MEMS) are extensively used in sensors and process control, and are covered in Chapters 3 through 6. The various types of sen- sors used in the measurement of a wide variety of physical variables, such as level, pressure, flow, temperature, humidity, and mechanical measurements, are dis- cussed in Chapters 7 through 12. Regulators and actuators, which are used for con- trolling pressure, flow, and other input variables to a process, are discussed in Chapter 13. Industrial processing is computer controlled, and Chapter 14 intro- duces the programmable logic controller. Sensors are temperature-sensitive and nonlinear, and have to be conditioned. These sensors, along with signal transmis- sion, are discussed in Chapter 15. Chapter 16 discusses different types of process control action, and the use of pneumatic and electronic controllers for sensor signal amplification and control. Finally, Chapter 17 introduces documentation as applied to instrumentation and control, together with standard symbols recommended by the Instrument Society of America for use in instrumentation control diagrams. xv xvi Preface Every effort has been made to ensure that the text is accurate, easily readable, and understandable. Both engineering and scientific units are discussed in the text. Each chapter con- tains examples for clarification, definitions, and references. A glossary is given at the end of the text. Acknowledgment I would like to thank my wife Nadine for her patience, understanding, and many helpful suggestions during the writing of this text.  CHAPTER 1 Introduction to Process Control 1.1 Introduction The technology of controlling a series of events to transform a material into a desired end product is called process control. For instance, the making of fire could be considered a primitive form of process control. Industrial process control was originally performed manually by operators. Their sensors were their sense of sight, feel, and sound, making the process totally operator-dependent. To maintain a pro- cess within broadly set limits, the operator would adjust a simple control device. Instrumentation and control slowly evolved over the years, as industry found a need for better, more accurate, and more consistent measurements for tighter process control. The first real push to develop new instruments and control systems came with the Industrial Revolution, and World Wars I and II added further to the impetus of process control. Feedback control first appeared in 1774 with the devel- opment of the fly-ball governor for steam engine control, and the concept of propor- tional, derivative, and integral control during World War I. World War II saw the start of the revolution in the electronics industry, which has just about revolution- ized everything else. Industrial process control is now highly refined with computer- ized controls, automation, and accurate semiconductor sensors. 1.2 Process Control Process control can take two forms: (1) sequential control, which is an event-based process in which one event follows another until a process sequence is complete; or (2) continuous control, which requires continuous monitoring and adjustment of the process variables. However, continuous process control comes in many forms, such as domestic water heaters and heating, ventilation, and air conditioning (HVAC), where the variable temperature is not required to be measured with great precision, and complex industrial process control applications, such as in the petro- leum or chemical industry, where many variables have to be measured simulta- neously with great precision. These variables can vary from temperature, flow, level, and pressure, to time and distance, all of which can be interdependent vari- ables in a single process requiring complex microprocessor systems for total con- trol. Due to the rapid advances in technology, instruments in use today may be obsolete tomorrow. New and more efficient measurement techniques are constantly being introduced. These changes are being driven by the need for higher accuracy, 1 2 Introduction to Process Control quality, precision, and performance. Techniques that were thought to be impossible a few years ago have been developed to measure parameters. 1.2.1 Sequential Process Control Control systems can be sequential in nature, or can use continuous measurement; both systems normally use a form of feedback for control. Sequential control is an event-based process, in which the completion of one event follows the completion of another, until a process is complete, as by the sensing devices. Figure 1.1 shows an example of a process using a sequencer for mixing liquids in a set ratio. The sequence of events is as follows: 1. Open valve A to fill tank A. 2. When tank A is full, a feedback signal from the level sensor tells the sequencer to turn valve A Off. 3. Open valve B to fill tank B. 4. When tank B is full, a feedback signal from the level sensor tells the sequencer to turn valve B Off. 5. When valves A and B are closed, valves C and D are opened to let measured quantities of liquids A and B into mixing tank C. 6. When tanks A and B are empty, valves C and D are turned Off. 7. After C and D are closed, start mixing motor, run for set period. 8. Turn Off mixing motor. 9. Open valve F to use mixture. 10. The sequence can then be repeated after tank C is empty and Valve F is turned Off. 1.2.2 Continuous Process Control Continuous process control falls into two categories: (1) elementary On/Off action, and (2) continuous control action. On/Off action is used in applications where the system has high inertia, which prevents the system from rapid cycling. This type of control only has only two states, On and Off; hence, its name. This type of control has been in use for many decades, Liquid A Liquid B Valve A Valve B Liquid Liquid level B Tank Tank sensor level A A B Mixer sensor Valve C Valve D Tank Mixture out Sequencer C Valve F Figure 1.1 Sequencer used for liquid mixing. 1.2 Process Control 3 long before the introduction of the computer. HVAC is a prime example of this type of application. Such applications do not require accurate instrumentation. In HVAC, the temperature (measured variable) is continuously monitored, typically using a bimetallic strip in older systems and semiconductor elements in newer sys- tems, as the sensor turns the power (manipulated variable) On and Off at preset temperature levels to the heating/cooling section. Continuous process action is used to continuously control a physical output parameter of a material. The parameter is measured with the instrumentation or sensor, and compared to a set value. Any deviation between the two causes an error signal to be generated, which is used to adjust an input parameter to the process to correct for the output change. An example of an unsophisticated automated control process is shown in Figure 1.2. A float in a swimming pool is used to continuously monitor the level of the water, and to bring the water level up to a set reference point when the water level is low. The float senses the level, and feedback to the control valve is via the float arm and pivot. The valve then controls the flow of water (manipulated variable) into the swimming pool, as the float moves up and down. A more complex continuous process control system is shown in Figure 1.3, where a mixture of two liquids is required. The flow rate of liquid A is measured with a differential pressure (DP) sensor, and the amplitude of the signal from the DP measuring the flow rate of the liquid is used by the controller as a reference signal (set point) to control the flow rate of liquid B. The controller uses a DP to measure the flow rate of liquid B, and compares its amplitude to the signal from the DP mon- itoring the flow of liquid A. The difference between the two signals (error signal) is used to control the valve, so that the flow rate of liquid B (manipulated variable) is directly proportional to that of liquid A, and then the two liquids are combined. Manipulated Feedback Valve variable (Flow) Measured Fluid in variable (Level) Pivot Float (Level Sensor) Figure 1.2 Automated control system. Liquid A DP Controller DP Mixture out Liquid B Figure 1.3 Continuous control for liquid mixing. 4 Introduction to Process Control 1.3 Definition of the Elements in a Control Loop In any process, there are a number of inputs (i.e., from chemicals to solid goods). These are manipulated in the process, and a new chemical or component emerges at the output. To get a more comprehensive look at a typical process control system, it will be broken down into its various elements. Figure 1.4 is a block diagram of the elements in a continuous control process with a feedback loop. Process is a sequence of events designed to control the flow of materials through a number of steps in a plant to produce a final utilitarian product or material. The process can be a simple process with few steps, or a complex sequence of events with a large number of interrelated variables. The examples shown are single steps that may occur in a process. Measurement is the determination of the physical amplitude of a parameter of a material; the measurement value must be consistent and repeatable. Sensors are typ- ically used for the measurement of physical parameters. A sensor is a device that can convert the physical parameter repeatedly and reliably into a form that can be used or understood. Examples include converting temperature, pressure, force, or flow into an electrical signal, measurable motion, or a gauge reading. In Figure 1.3, the sensor for measuring flow rates is a DP cell. Error Detection is the determination of the difference between the amplitude of the measured variable and a desired set reference point. Any difference between the two is an error signal, which is amplified and conditioned to drive a control element. The controller sometimes performs the detection, while the reference point is nor- mally stored in the memory of the controller. Controller is a microprocessor-based system that can determine the next step to be taken in a sequential process, or evaluate the error signal in continuous process control to determine what action is to be taken. The controller can normally condi- tion the signal, such as correcting the signal for temperature effects or nonlinearity in the sensor. The controller also has the parameters of the process input control element, and conditions the error sign to drive the final element. The controller can monitor several input signals that are sometimes interrelated, and can drive sev- eral control elements simultaneously. The controllers are normally referred to as programmable logic controllers (PLC). These devices use ladder networks for pro- gramming the control functions. Set point Error Control signal Comparator signal Controller Variable amplitude Feedback signal Manipulated Controlled variable variable Control Measuring Process element Output element Input Figure 1.4 Block diagram of the elements that make up the feedback path in a process control loop. 1.4 Instrumentation and Sensors 5 Control Element is the device that controls the incoming material to the process (e.g., the valve in Figure 1.3). The element is typically a flow control element, and can have an On/Off characteristic or can provide liner control with drive. The con- trol element is used to adjust the input to the process, bringing the output variable to the value of the set point. The control and measuring elements in the diagram in Figure 1.4 are oversim- plified, and are broken down in Figure 1.5. The measuring element consists of a sen- sor to measure the physical property of a variable, a transducer to convert the sensor signal into an electrical signal, and a transmitter to amplify the electrical signal, so that it can be transmitted without loss. The control element has an actuator, which changes the electrical signal from the controller into a signal to operate the valve, and a control valve. In the feedback loop, the controller has memory and a summing circuit to compare the set point to the sensed signal, so that it can generate an error signal. The controller then uses the error signal to generate a correction signal to control the valve via the actuator and the input variable. The function and opera- tion of the blocks in different types of applications will be discussed in a later chap- ter. The definitions of the terms used are given at the end of the chapter. 1.4 Instrumentation and Sensors The operator’s control function has been replaced by instruments and sensors that give very accurate measurements and indications, making the control function totally operator-independent. The processes can be fully automated. Instrumenta- tion and sensors are an integral part of process control, and the quality of process control is only as good as its measurement system. The subtle difference between an instrument and a sensor is that an instrument is a device that measures and displays the magnitude of a physical variable, whereas a sensor is a device that measures the amplitude of a physical variable, but does not give a direct indication of the value. The same physical parameters normally can be applied to both devices. 1.4.1 Instrument Parameters The choice of a measurement device is difficult without a good understanding of the process. All of the possible devices should be carefully considered. It is also important to understand instrument terminology. ANSI/ISA-51.1-R1979 (R1993) From Controller To Comparator Transmitter Measuring = Control Actuator element Transducer = element Valve Sensor Material flow Material flow Figure 1.5 Breakdown of measuring and control elements. 6 Introduction to Process Control Process Instrumentation Terminology gives the definitions of the terms used in instrumentation in the process control sector. Some of the more common terms are discussed below. Accuracy of an instrument or device is the error or the difference between the indicated value and the actual value. Accuracy is determined by comparing an indi- cated reading to that of a known standard. Standards can be calibrated devices, and may be obtained from the National Institute of Standards and Technology (NIST). The NIST is a government agency that is responsible for setting and maintaining standards, and developing new standards as new technology requires it. Accuracy depends on linearity, hysteresis, offset, drift, and sensitivity. The resulting discrep- ancy is stated as a plus-or-minus deviation from true, and is normally specified as a percentage of reading, span, or of full-scale reading or deflection (% FSD), and can be expressed as an absolute value. In a system where more than one deviation is involved, the total accuracy of the system is statistically the root mean square (rms) of the accuracy of each element. Example 1.1 A pressure sensor has a span of 25 to 150 psi. Specify the error when measuring 107 psi, if the accuracy of the gauge is (a) ±1.5% of span, (b) ±2% FSD, and (c) ±1.3% of reading. a. Error = ±0.015 (150 −25) psi = ±1.88 psi. b. Error = ±0.02 × 150 psi = ±3 psi. c. Error = ± 0.013 × 103 psi = ±1.34 psi. Example 1.2 A pressure sensor has an accuracy of ±2.2% of reading, and a transfer function of 27 mV/kPa. If the output of the sensor is 231 mV, then what is the range of pressures that could give this reading? The pressure range = 231/27 kPa ± 2.2% = 8.5 kPa ± 2.2% = 8.313 to 8.687 kPa Example 1.3 In a temperature measuring system, the transfer function is 3.2 mV/k ± 2.1%, and the accuracy of the transmitter is ±1.7%. What is the system accuracy? System accuracy = ±[(0.021) + (0.017) ] = ±2.7% 2 2 1/2 Linearity is a measure of the proportionality between the actual value of a vari- able being measured and the output of the instrument over its operating range. The deviation from true for an instrument may be caused by one or several of the above factors affecting accuracy, and can determine the choice of instrument for a particu- lar application. Figure 1.6 shows a linearity curve for a flow sensor, which is the out- put from the sensor versus the actual flow rate. The curve is compared to a best-fit straight line. The deviation from the ideal is 4 cm/min., which gives a linearity of ±4% of FSD. 1.4 Instrumentation and Sensors 7 10 Actual curve 8 Output (volts) 6 Best fit linear 4 2 4 0 0 20 40 60 80 100 Flow cm/min Figure 1.6 Linearity curve or a comparison of the sensor output versus flow rate, and the best-fit straight line. Sensitivity is a measure of the change in the output of an instrument for a change in the measured variable, and is known as a transfer function. For example, when the output of a flow transducer changes by 4.7 mV for a change in flow of 1.3 cm/s, the sensitivity is 3.6 mV/cm/s. High sensitivity in an instrument is desired, since this gives a higher output, but has to be weighed against linearity, range, and accuracy. Reproducibility is the inability of an instrument to consistently reproduce the same reading of a fixed value over time under identical conditions, creating an uncertainty in the reading. Resolution is the smallest change in a variable to which the instrument will respond. A good example is in digital instruments, where the resolution is the value of the least significant bit. Example 1.4 A digital meter has 10-bit accuracy. What is the resolution on the 16V range? 10 Decade equivalent of 10 bits = 2 = 1,024 Resolution = 16/1,024 = 0.0156V = 15.6 mV Hysteresis is the difference in readings obtained when an instrument approaches a signal from opposite directions. For example, if an instrument reads a midscale value beginning at zero, it can give a different reading than if it read the value after making a full-scale reading. This is due to stresses induced into the mate- rial of the instrument by changing its shape in going from zero to full-scale deflec- tion. A hysteresis curve for a flow sensor is shown in Figure 1.7, where the output 8 Introduction to Process Control 10 Actual curve 8 decreasing readings Output (volts) 6 Best fit linear 4 Actual curve increasing readings 2 0 0 20 40 60 80 100 Flow cm/min Figure 1.7 Hysteresis curve showing the difference in readings when starting from zero, and when starting from full scale. initiating from a zero reading and initiating from a maximum reading are different. For instance, the output from zero for a 50 cm/min is 4.2V, compared to 5.6V when reading the same flow rate after a maximum reading. Time constant of a sensor to a sudden change in a measured parameter falls into two categories, termed first-order and second-order responses. The first-order response is the time the sensor takes to reach its final output after a transient change. For example, a temperature measuring device will not change immediately follow- ing a change in temperature, due to the thermal mass of the sensor and the thermal conductivity of the interface between the hot medium and the sensing element. The response time to a step change in temperature is an exponential given by: ( A(t ) = A 0 + A f − A 0 )(1 − e ) −t τ (1.1) where A(t) is the amplitude at time t, A0 is the initial amplitude, Af is the final ampli- tude, and τ is the time constant of the sensor. The second-order response occurs when the effect of a transient on the monitor- ing unit is to cause oscillations in the output signal before settling down. The response can be described by a second-order equation. Other parameters used in instrumentation are Range, Span, Precision, Offset, Drift, and Repeatability. The definitions of these parameters are given at the end of the chapter. Example 1.5 A linear pressure sensor has a time constant of 3.1 seconds, and a transfer function of 29 mV/kPa. What is the output after 1.3 seconds, if the pressure changes from 17 to 39 kPa? What is the pressure error at this time? 1.5 Control System Evaluation 9 Initial output voltage A0 = 17 × 29 mV = 493 mV Final output voltage Af = 29 × 39 mV = 1,131 mV −1.3/3.1 A(1.3) = 493 + (1131 − 493) (1 − e ) A(1.3) = 493 + 638 × 0.66 = 914.1 mV Pressure after 1.3 sec = 914.1/29 kPa = 31.52 kPa Error = 39 − 31.52 = 7.48 kPa 1.5 Control System Evaluation A general criterion for evaluating the performance of a process control system is dif- ficult to establish. In order to obtain the quality of the performance of the control- ler, the following have to be answered: 1. Is the system stable? 2. How good is the steady state regulation? 3. How good is the transient regulation? 4. What is the error between the set point and the variable? 1.5.1 Stability In a system that uses feedback, there is always the potential for stability. This is due to delays in the system and feedback loop, which causes the correction signal to be in-phase with the error signal change instead of out-of-phase. The error and correc- tion signal then become additive, causing instability. This problem is normally cor- rected by careful tuning of the system and damping, but this unfortunately comes at the expense of a reduction in the response time of the system. 1.5.2 Regulation The regulation of a variable is the deviation of the variable from the set point or the error signal. The regulation should be as tight as possible, and is expressed as a per- centage of the set point. A small error is always present, since this is the signal that is amplified to drive the actuator to control the input variable, and hence controls the measured variable. The smaller the error, the higher the systems gain, which nor- mally leads to system instability. As an example, the set point may be 120 psi, but the regulation may be 120 ± 2.5 psi, allowing the pressure to vary from 117.5 to 122.5 psi. 1.5.3 Transient Response The transient response is the system’s reaction time to a sudden change in a parame- ter, such as a sudden increase in material demand, causing a change in the measured variable or in the set point. The reaction can be specified as a dampened response or as a limited degree of overshoot of the measured variable, depending on the process, 10 Introduction to Process Control in order to return the measured variable to the set point in a specified time. The topic is covered in more detail in Chapter 16. 1.6 Analog and Digital Data Variables are analog in nature, and before digital processing evolved, sensor signals were processed using analog circuits and techniques, which still exist in many processing facilities. Most modern systems now use digital techniques for signal processing. 1.6.1 Analog Data Signal amplitudes are represented by voltage or current amplitudes in analog sys- tems. Analog processing means that the data, such as signal linearization, from the sensor is conditioned, and corrections that are made for temperature variations are all performed using analog circuits. Analog processing also controls the actuators and feedback loops. The most common current transmission range is 4 to 20 mA, where 0 mA is a fault indication. Example 1.6 The pressure in a system has a range from 0 to 75 kPa. What is the current equiva- lent of 27 kPa, if the transducer output range is from 4 to 20 mA? Equivalent range of 75 kPa = 16 mA Hence, 27 kPa = (4 + 16 × 27/75) mA = 9.76 mA 1.6.2 Digital Data Signal amplitudes are represented by binary numbers in digital systems. Since vari- ables are analog in nature, and the output from the sensor needs to be in a digital for- mat, an analog to digital converter (ADC) must be used, or the sensor’s output must be directly converted into a digital signal using switching techniques. Once digitized, the signal will be processed using digital techniques, which have many advantages over analog techniques, and few, if any, disadvantages. Some of the advantages of digital signals are: data storage, transmission of signals without loss of integrity, reduced power requirements, storage of set points, control of multiple variables, and the flexibility and ease of program changes. The output of a digital system may have to be converted back into an analog format for actuator control, using either a digi- tal to analog converter (DAC) or width modulation techniques. 1.6.3 Pneumatic Data Pressure was used for data transmission before the use of electrical signals, and is still used in conditions where high electrical noise could affect electrical signals, or in hazardous conditions where an electrical spark could cause an explosion or fire haz- ard. The most common range for pneumatic data transmission is 3 to 15 psi (20 to 100 kPa in SI units), where 0 psi is a fault condition. 1.7 Process Facility Considerations 11 1.6.4 Smart Sensors The digital revolution also has brought about large changes in the methodology used in process control. The ability to cost-effectively integrate all the controller functions, along with ADCs and DACs, have produced a family of Smart Sensors that combine the sensor and control function into a single housing. This device reduces the load on the central processor and communicates to the central processor via a single serial bus (Fieldbus), reducing facility wiring requirements and making the concept of plug-and-play a reality when adding new sensors. 1.7 Process Facility Considerations The process facility has a number of basic requirements, including well-regulated and reliable electrical, water, and air supplies, and safety precautions. An electrical supply is required for all control systems, and must meet all stan- dards in force at the plant. The integrity of the electrical supply is most important. Many facilities have backup systems to provide an uninterruptible power supply (UPS) to take over in case of the loss of external power. Power failure can mean plant shutdown and the loss of complete production runs. Isolating transformer should be used in the power supply lines to prevent electromagnetic interference (EMI) generated by devices, such as motors, from traveling through the power lines and affecting sensitive electronic control instruments. Grounding is a very important consideration in a facility for safety reasons. Any variations in the ground potential between electronic equipment can cause large errors in signal levels. Each piece of equipment should be connected to a heavy cop- per bus that is properly grounded. Ground loops also should be avoided by ground- ing cable screens and signal return lines at only one end. In some cases, it may be necessary to use signal isolators to alleviate grounding problems in electronic devices and equipment. An air supply is required to drive pneumatic actuators in most facilities. Instru- ment air in pneumatic equipment must meet quality standards. The air must be free of dirt, oil, contamination, and moisture. Contaminants, such as frozen moisture or dirt, can block or partially block restrictions and nozzles, giving false readings or causing complete equipment failure. Air compressors are fitted with air dryers and filters, and have a reservoir tank with a capacity large enough for several minutes of supply in case of system failure. Dry, clean air is supplied at a pressure of 90 psig (630 kPa-g), and with a dew point of 20°F (10°C) below the minimum winter operating temperature at atmospheric pressure. Additional information on the quality of instrument air can be found in ANSI/ISA – 7.0.01 – 1996 Standard for Instrument Air. A water supply is required in many cleaning and cooling operations and for steam generation. A domestic water supply contains large quantities of particulates and impurities, and while it may be satisfactory for cooling, it is not suitable for most cleaning operations. Filtering and other operations can remove some of con- taminants, making the water suitable for some cleaning operations, but if ultrapure water is required, then a reverse osmosis system may be required. 12 Introduction to Process Control Installation and maintenance must be considered when locating devices, such as instruments and valves. Each device must be easily accessible for maintenance and inspection. It also may be necessary to install hand-operated valves, so that equip- ment can be replaced or serviced without complete plant shutdown. It may be neces- sary to contract out maintenance of certain equipment, or have the vendor install equipment, if the necessary skills are not available in-house. Safety is a top priority in a facility. The correct materials must be used in container construction, plumbing, seals, and gaskets, to prevent corrosion and failure, leading to leakage and spills of hazardous materials. All electrical equip- ment must be properly installed to Code, with breakers. Electrical systems must have the correct fire retardant. More information can be found in ANSI/ISA – 12.01.01 – 1999, — “Definitions and Information Pertaining to Electrical Appara- tus in Hazardous Locations.” 1.8 Summary This chapter introduced the concept of process control, and the differences between sequential, continuous control and the use of feedback loops in process control. The building blocks in a process control system, the elements in the building blocks, and the terminology used, were defined. The use of instrumentation and sensors in process parameter measurements was discussed, together with instrument characteristics, and the problems encountered, such as nonlinearity, hysteresis, repeatability, and stability. The quality of a process control loop was introduced, together with the types of problems encountered, such as stability, transient response, and accuracy. The various methods of data transmission used are analog data, digital data, and pneumatic data; and the concept of the smart sensor as a plug-and-play device was given. Considerations of the basic requirements in a process facility, such as the need for an uninterruptible power supply, a clean supply of pressurized air, clean and pure water, and the need to meet safety regulations, were covered. Definitions Absolute Accuracy of an instrument is the deviation from true expressed as a number. Accuracy of an instrument or device is the difference between the indicated value and the actual value. Actuators are devices that control an input variable in response to a signal from a controller. Automation is a system where most of the production process, movement, and inspection of materials are performed automatically by specialized testing equipment, without operator intervention. Definitions 13 Controlled or Measured Variable is the monitored output variable from a process, where the value of the monitored output parameter is normally held within tight given limits. Controllers are devices that monitor signals from transducers and keep the process within specified limits by activating and controlling the necessary actuators, according to a predefined program. Converters are devices that change the format of a signal without chang- ing the energy form (e.g., from a voltage to a current signal). Correction Signal is the signal that controls power to the actuator to set the level of the input variable. Drift is the change in the reading of an instrument of a fixed variable with time. Error Signal is the difference between the set point and the amplitude of the measured variable. Feedback Loop is the signal path from the output back to the input, which is used to correct for any variation between the output level and the set level. Hysteresis is the difference in readings obtained when an instrument approaches a signal from opposite directions. Instrument is the name of any various device types for indicating or mea- suring physical quantities or conditions, performance, position, direction, and so forth. Linearity is a measure of the proportionality between the actual value of a variable being measured and the output of the instrument over its operating range. Manipulated Variable is the input variable or parameter to a process that is varied by a control signal from the processor to an actuator. Offset is the reading of the instrument with zero input. Precision is the limit within which a signal can be read, and may be some- what subjective. Range of an instrument is the lowest and highest readings that it can measure. Reading Accuracy is the deviation from true at the point the reading is being taken, and is expressed as a percentage. Repeatability is a measure of the closeness of agreement between a num- ber of readings taken consecutively of a variable. Reproducibility is the ability of an instrument to repeatedly read the same signal over time, and give the same output under the same conditions. Resolution is the smallest change in a variable to which the instrument will respond. Sensitivity is a measure of the change in the output of an instrument for a change in the measured variable. Sensors are devices that can detect physical variables. 14 Introduction to Process Control Set Point is the desired value of the output parameter or variable being monitored by a sensor; any deviation from this value will generate an error signal. Span of an instrument is its range from the minimum to maximum scale value. Transducers are devices that can change one form of energy into another. Transmitters are devices that amplify and format signals, so that they are suitable for transmission over long distances with zero or minimal loss of information. References Battikha, N. E., The Condensed Handbook of Measurement and Control, 2nd ed., ISA, 2004, pp. 1–8. Humphries J. T., and L. P. Sheets, Industrial Electronics, 4th ed., Delmar, 1993, pp. 548–550. Sutko, A., and J. D. Faulk, Industrial Instrumentation, 1st ed., Delmar Publishers, 1996, pp. 3–14. Johnson, C. D., Process Control Instrumentation Technology, 7th ed., Prentice Hall, 2003, pp. 6–43. Johnson, R. N., “Signal Conditioning for Digital Systems,” Proceedings Sensors Expo, October 1993, pp. 53–62.  CHAPTER 2 Units and Standards 2.1 Introduction The measurement and control of physical properties require the use of well-defined units. Units commonly used today are defined in either the English system or the Systéme International d’Unités (SI) system. The advent of the Industrial Revolu- tion, developing first in England in the eighteenth century, showed how necessary it was to have a standardized system of measurements. Consequently, a system of measurement units was developed. Although not ideal, the English system (and U.S. variants; see gallon and ton) of measurements became the accepted standard for many years. This system of measurements has slowly been eroded by the develop- ment of more acceptable scientific units developed in the SI system. However, it should be understood that the base unit dimensions in the English or SI system are artificial quantities. For example, the units of distance (e.g., feet, meter), time, and mass, and the use of water to define volume, were chosen by the scientific commu- nity solely as reference points for standardization. 2.1.1 Units and Standards As with all disciplines’ sets of units and standards have evolved over the years to ensure consistency and avoid confusion. The units of measurement fall into two dis- tinct systems: the English system and the SI system. The SI units are sometimes referred to as the centimeter-gram-second (CGS) units and are based on the metric system but it should be noted that not all of the metric units are used. The SI system of units is maintained by the Conférence Genérale des Poids et Measures. Because both systems are in common use it is neces- sary to understand both system of units and to understand the relationship between them. A large number of units (electrical) in use are common to both systems. Older measurement systems are calibrated in English units, where as newer systems are normally calibrated in SI units The English system has been the standard used in the United States, but the SI system is slowly making inroads, so that students need to be aware of both systems of units and be able to convert units from one system to the other. Confusion can arise over the use of the pound (lb) as it can be used for both mass and weight and also its SI equivalent being. The pound mass is the Slug (no longer in common use as a scientific unit) The slug is the equivalent of the kg in the SI system of units, where as the pound weight is a force similar to the Newton, which is the unit of force in the SI system. The practical unit in everyday use in the English system of units is the lb 15 16 Units and Standards weight, where as, in the SI system the unit of mass or kg is used. The conversion fac- tor of 1 lb = 0.454 kg which is used to convert mass (weight) between the two sys- tems, is in effect equating 1 lb force to 0.454 kg mass this being the mass that will produce a force of 4.448 N under the influence of gravity which is a force of 1 lb. Care must be taken not to mix units from the two systems. For consistency some units may have to be converted before they can be used in an Equation. The Instru- ment Society of America (ISA) has developed a complete list of symbols for instru- ments, instrument identification, and process control drawings, which will be discussed in Chapter 17. Other standards used in process control have been devel- oped in other disciplines. 2.2 Basic Units Table 2.1 gives a list of the base units used in instrumentation and measurement in the English and SI systems. Note that the angle units are supplementary geometric units. 2.3 Units Derived from Base Units All other units are derived from the base units. The derived units have been broken down into units used in both systems (e.g., electrical units), the units used in the Eng- lish system, and the units used in the SI system. 2.3.1 Units Common to Both the English and SI Systems The units used in both systems are given in Table 2.2. 2.3.2 English Units Derived from Base Units Table 2.3 lists some commonly used units in the English system. The correct unit for mass is the slug, which is now not normally used. The English system uses weight to infer mass, which can lead to confusion. The units for the pound in energy and horsepower are mass, whereas the units for the pound in pressure is a force. Note that the lb force = lb mass (m) × g = lb (m) ft s−2. Table 2.1 Basic Units Quantity English Units English Symbol SI Units SI Symbol Length foot ft meter m Mass pound (slug) lb kilogram kg Time second s second s Temperature rankine °R Kelvin K Electric current Ampere A ampere A Amount of substance mole mol Luminous intensity candle c lumen lm Angle degree ° radian rad Solid angle steradian sr 2.3 Units Derived from Base Units 17 Table 2.2 Electrical Units Common to the English and SI Systems Quantity Name Symbol Units Frequency hertz Hz s−1 Wavelength meter λ m Resistance ohm Ω kg m2 s−3 A−2 −2 −1 3 2 Conductance siemens S A/V, or m kg s A 2 −3 −1 Electromotive force volt V A Ω, or m kg s A Electronic quantity coulomb C As 4 2 −1 −2 Capacitance farad F s A kg m 3 −1 −2 Energy density joule per cubic meter J/m kg m s −1 Electric field strength volts per meter V/m Vm 3 −3 Electric charge density coulombs per cubic meter C/m Cm 2 −2 Surface flux density coulombs per square meter C/m Cm 2 −2 Current density amperes per square meter A/m Am −1 Magnetic field strength amperes per meter A/m Am 2 4 −3 −1 Permittivity farads per meter F/m A s m kg 2 −2 −2 Inductance henry H kg m s A −2 −2 Permeability henrys per meter H/m m kg s A 2 −2 −1 Magnetic flux density tesla T Wb/m , or kg s A 2 −2 −1 Magnetic flux weber Wb V s, or m kg s A Table 2.3 English Units Derived from Base Units Quantity Name Symbol Units Frequency revolutions per minute r/min s−1 −1 Speed ft/s ft s —Linear feet per second −1 —Angular degrees per second degree/s degree s 2 −2 Acceleration ft/s ft s —Linear feet per second squared 2 −2 —Angular degrees per second degree/s degree s squared 2 −2 Energy foot-pound ft-lb lb (m) ft s −2 Force pound lb lb (m) ft s −1 −2 Pressure pounds per square in psi lb (m) ft s 2 −3 Power horsepower hp lb (m) ft s 3 −3 Density pound (slug) per cubic lb (slug)/ft lb (m) ft foot 3 −2 −2 Specific weight pound per cubic foot lb/ft lb (m) ft s −2 Surface tension pound per foot lb/ft lb (m) s Quantity of heat British thermal unit Btu lb (m) ft2 s−2 2 -2 −1 Specific heat Btu/lb (m) °F ft s °F −3 −1 Thermal conductivity Btu/ft h °F lb (m) ft s °F 2 −3 −1 Thermal convection Btu/h ft °F lb (m) s °F 2 4 −3 −4 Thermal radiation Btu/h ft °R lb (m) s °R −1 −2 Stress σ lb (m) ft s Strain ε dimensionless Gauge factor G dimensionless Young’s modulus lb/ft 2 lb (m)ft−1 s−2 −1 −1 Viscosity dynamic poise P lb (m) ft s 2 −1 Viscosity kinematic stoke St ft s 2 −2 Torque (moment of force) lb ft lb (m) ft s 18 Units and Standards Conversion between English units is given in Table 2.4. This table gives the con- version between units of mass, length, and capacity in the English system. Note the difference in U.S. and English gallon and ton. 2.3.3 SI Units Derived from Base Units The SI system of units is based on the CGS or metric system, but not all of the units in the metric system are used. Table 2.5 lists the metric units used in the SI system. It should be noted that many of the units have a special name. Conversion between SI units is given in Table 2.6. This table gives the conver- sion between mass, length, and capacity in the SI system. 2.3.4 Conversion Between English and SI Units Table 2.7 gives the factors for converting units between the English and SI systems. Example 2.1 How many meters are there in 2.5 miles? 2.5 miles = 2.5 × 5,280 × 0.305m = 4,026m = 4.026 km Example 2.2 What is the weight of 3.7-lb mass in newtons? 3.7 lb mass = 3.7 × 32.2 lb weight = 119.1 lb 119.1 lb = 4.448 × 119.1N = 530N Example 2.3 2 What is the pressure equivalent of 423 Pa in lb/ft ? 423 Pa = 0.423/6.897 psi = 0.061 psi 0.061 psi = 0.061 × 12 × 12 psf = 8.83 psf Table 2.4 Conversion Between Mass, Length, and Capacity in the English System Quantity Name Symbol Conversion Length mile 1 mi 5,280 ft Capacity to volume gallon (U.S.) 1 gal 0.1337 ft3 3 imperial gallon 1 imp gal 0.1605 ft Capacity to weight 1 gal (U.S.) 8.35 lb (water) 1 imp gal 10 lb Weight ton (U.S.) ton short 2,000 lb imperial ton ton long 2,240 lb 2.3 Units Derived from Base Units 19 Table 2.5 SI units Derived from Base Units Quantity Name Symbol Other Units Base Units Frequency hertz Hz s−1 s −1 −1 Speed — Linear meters per second m/s ms −1 — Angular radians per second rad/s rad s −2 Acceleration — Linear meters per second squared m/s2 ms 2 −2 — Angular radians per second squared rad/s rad s −1 −1 Wave number per meter m m 3 −3 Density kilograms per cubic meter kg/m kg m 3 −2 −2 Specific weight weight per cubic meter kN/m kg m s 3 −3 Concentration of mole per cubic meter mol/m mol m amount of substance 3/ −1 3 Specific volume cubic meters per kilogram m kg kg m 2 −2 Energy joule J Nm kg m s 2 −2 Force newton N m kg/s kg m s 2 −1 −2 Pressure pascal Pa N/m kg m s 2 −3 Power watt W J/s kg m s 2 −2 Luminance lux lx lm/m m cd sr Luminous flux lumen lm cd sr cd sr 2 −2 Quantity of heat joule J Nm kg m s 2 −3 Heat flux density watts per square meter W/m kg s irradiance Heat capacity entropy joules per kelvin J/K kg m2 s−2 K−1 2 −2 −1 Specific heat entropy J/kg K m s K Specific energy joules per kilogram J/kg m2 s−2 Thermal conductivity W/m K kg m s−3 K−1 2 −3 −1 Thermal convection W/m K kg s K −3 −4 Thermal radiation kg s K −1 −2 Stress σ Pa kg m s Strain ε δm/m Dimensionless Gauge Factor G δR/R per ε Dimensionless 2 −1 −2 Young’s modulus N/m kg m s −1 −1 Viscosity dynamic Poiseuille Po kg/m s kg m s 2 2 −1 Viscosity kinematic Stokes St cm /s m s −2 Surface tension newtons per meter N/m kg s 2 −2 Torque (moment) newton meter Nm kg m s 2 −2 Molar energy joules per mole J/mol kg m s −1 mol Molar entropy, joules per mole kelvin J/(mol K) kg m2 s−2 −1 −1 heat capacity K mol −1 Radioactivity Becquerel Bq per sec s 2 −2 Absorbed radiation Gray Gy J/kg m s Table 2.6 Conversion Between Mass, Length, and Capacity and Other Units in the SI System Quantity Name Symbol Conversion Capacity liter L 1L = 1 dm3 (1,000L = 1 m3) Weight liter L 1L water = 1 kg 2 Area hectare ha 1 ha = 10,000 m −19 Charge electron volt eV 1 eV = 1.602 × 10 J −27 Mass unified atomic mass unit µ 1.66044 × 10 kg 20 Units and Standards Table 2.7 Conversion Between English and SI Units Quantity English Units SI Units Length 1 ft 0.305m Speed 1 mi/h 1.61 km/h 2 2 Acceleration 1 ft/s 0.305 m/s Mass 1 lb (m) 14.59 kg Weight 1 lb 0.454 kg Capacity 1 gal (U.S.) 3.78 L Force 1 lb 4.448N Angle 1 degree 2π/360 rad Temperature 1°F 5/9°C Temperature 1°R 5/9K Energy 1 ft lb 1.356J Pressure 1 psi 6.897 kPa Power 1 hp 746W Quantity of heat 1 Btu 252 cal or 1,055J Thermal conduction 1 Btu/hr ft °F 1.73 W/m K Specific heat 1 Btu/lb (m) °F J/kg K 2 2 Thermal convection Btu/h ft °F W/m K 2 4 2 4 Thermal radiation Btu/h ft °R W/m K Expansion 1 α/°F 1.8 α/°C 3 3 Specific weight 1 lb/ft 0.157 kN/m 3 3 Density 1 lb (m)/ft 0.516 kg/m 2 Dynamic viscosity 1 lb s/ft 49.7 Pa s (4.97 P) 2 2 Kinematic viscosity 1 ft /s 9.29 × 10−2 m /s (929 St) Torque 1 lb ft 1.357 N m Stress 1 psi 6.897 kPa Young’s modulus 1 psi 6.897 kPa Example 2.4 A steam boiler generates 7.4 kBtu/h. The steam is used to drive a 47% efficient steam engine. What is the horsepower of the engine? 7.4 kBtu/h = 7,400 × 1,055/60W = 130 kW 130 kW @ 47% = 130,000 × 0.47/746 = 81.97 hp Example 2.5 A 110V electric motor uses 5.8A. If the motor is 87% efficient, then how many horsepower will the motor generate? Watts = 110 × 5.8 × 0.87W = 555.1W hp = 555.1/746 = 0.74 hp 2.3.5 Metric Units not Normally Used in the SI System There are a large number of units in the metric system, but all of these units are not required in the SI system of units because of duplication. A list of some of the units not used is given in Table 2.8. 2.4 Standard Prefixes 21 Table 2.8 Metric Units not Normally Used in the SI System Quantity Name Symbol Equivalent Length Angstrom Å 1Å = 0.1 nm Fermi fm 1 fm = 1 femtometer X unit 1 X unit = 100.2 fm 3 Volume Stere st 1 st = 1 m 3 Lambda λ 1 mm Mass metric carat 1 metric carat = 200 mg