Instrumentation in Industrial Applications

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Questions and Answers

What is the primary purpose of instrumentation in industrial applications?

  • To enhance the visual aesthetics of machinery
  • To reduce operational costs of machinery
  • To measure, monitor or control industrial processes (correct)
  • To improve workforce efficiency

Which type of instrument could potentially compromise product or process quality if it does not meet specifications?

  • Operational Instrument
  • Critical Instrument (correct)
  • Reference Only Instrument
  • Non-critical Instrument

What defines a measurement instrument?

  • A device only used during equipment installation
  • An instrument utilized for aesthetic purposes
  • A device capable of detecting changes and converting them into information (correct)
  • A device used only in laboratory settings

In what way does process control contribute to a plant process?

<p>By controlling variables and executing emergency actions during upsets (A)</p> Signup and view all the answers

Which of the following best characterizes automatic control?

<p>Operates independently without human intervention (C)</p> Signup and view all the answers

What is the primary characteristic of a reference only instrument?

<p>Used for operational significance but not quality decisions (A)</p> Signup and view all the answers

What is the role of a control system in industrial applications?

<p>To regulate and direct various aspects of the process (A)</p> Signup and view all the answers

Which of the following describes manual control?

<p>Involves human intervention to manage processes (C)</p> Signup and view all the answers

What principle do differential capacitance sensors operate on?

<p>Change in capacitance (C)</p> Signup and view all the answers

What is the role of the electrically insulating fill fluid in a differential capacitance sensor?

<p>To transfer motion from the isolating diaphragms to the sensing diaphragm (D)</p> Signup and view all the answers

Which of the following is a feature of differential pressure transmitters?

<p>They output a signal based on the difference in pressure between two ports (B)</p> Signup and view all the answers

What is the primary principle of vapor filled systems in temperature sensors?

<p>Liquid and vapor combination creating a temperature-dependent pressure change (C)</p> Signup and view all the answers

Why are differential capacitance sensors considered effective for pressure measurement?

<p>They utilize flexible diaphragms to sense pressure changes (A)</p> Signup and view all the answers

What aspect makes strain gauges useful aside from pressure measurement?

<p>They can be calibrated to measure various other quantities. (D)</p> Signup and view all the answers

Which filling fluid is commonly used in gas filled systems?

<p>Nitrogen (A)</p> Signup and view all the answers

Which part of the differential pressure transmitter is labeled 'high'?

<p>The port that is not required to be at a higher pressure than the other (B)</p> Signup and view all the answers

What distinguishes mercury filled systems from other liquid filled temperature sensors?

<p>Mercury offers a wider range of operational temperatures compared to others (C)</p> Signup and view all the answers

How do gas filled systems sense temperature changes?

<p>Through the variation of pressure in response to absolute temperature (B)</p> Signup and view all the answers

What is the primary advantage of using a Rosemount model 1151 differential pressure transmitter?

<p>It allows for high flexibility and responsiveness in pressure measurement. (C)</p> Signup and view all the answers

What happens in a vapor filled system when the temperature decreases?

<p>Condensation of vapor occurs resulting in reduced pressure (A)</p> Signup and view all the answers

How do capacitance sensors differ from strain gauges in their measurement approach?

<p>Capacitance sensors use change in capacitance while strain gauges measure a change in resistance. (B)</p> Signup and view all the answers

What is a characteristic of bistate/phase change sensors?

<p>They use solid materials that change phase color at set temperatures (A)</p> Signup and view all the answers

What is a limitation of using mercury in temperature sensors?

<p>It can interfere with some industrial processes due to its toxicity (C)</p> Signup and view all the answers

At what temperature range can bistate/phase change sensors operate?

<p>From 100°F to 3000°F (B)</p> Signup and view all the answers

What is the primary reason for measuring liquid levels in boilers?

<p>To prevent dangerous states from developing (A)</p> Signup and view all the answers

Which of the following describes the interface that level measurement determines?

<p>The position of an existing interface between two media (D)</p> Signup and view all the answers

In the context of level measurement, what does the direct method primarily rely on?

<p>Direct measurement of distance from a datum line (B)</p> Signup and view all the answers

What is NOT an objective of level measurement in the oil and gas industries?

<p>Controlling finance and marketing operations (C)</p> Signup and view all the answers

Why is monitoring the level in bulk storage tanks necessary?

<p>To allocate costs accurately (A)</p> Signup and view all the answers

Which of the following best describes indirect methods of level measurement?

<p>They utilize calculations based on measurements from a distance (D)</p> Signup and view all the answers

What is one of the historical uses of level measurement mentioned?

<p>For the storage and release of water in agricultural settings (B)</p> Signup and view all the answers

What can excessive build-up of solids in hoppers lead to?

<p>Higher clearing costs and operational inefficiencies (C)</p> Signup and view all the answers

What is a significant drawback of using dip sticks and lead lines for level measurement?

<p>They cannot measure levels in pressurized vessels. (C)</p> Signup and view all the answers

How does a sight glass function in level measurement?

<p>It indicates the level by showing liquid in a transparent tube. (C)</p> Signup and view all the answers

Which accuracy level can be expected from the dipstick and lead line methods?

<p>0.1% (D)</p> Signup and view all the answers

What principle do float type measurement devices utilize?

<p>They depend on the buoyancy of a floating element. (A)</p> Signup and view all the answers

In which aspect are sight glasses and manometers similar?

<p>Both provide continuous visual indication for monitoring. (D)</p> Signup and view all the answers

What makes the float gauge a preferred option in level measurement?

<p>Its simplicity and dependability. (A)</p> Signup and view all the answers

What is the main rationale for using level gauges in conjunction with other measuring instruments?

<p>To serve as a backup in case of instrument failure. (C)</p> Signup and view all the answers

Why might operators prefer level gauges over manual gauging tapes?

<p>Level gauges offer continuous measurement. (B)</p> Signup and view all the answers

What is the customized linear equation for the temperature transmitter using the given values?

<p>y = x - 3.67 (C)</p> Signup and view all the answers

At what temperature will the transmitter output a pressure of 6.86 psi?

<p>79 °F (A)</p> Signup and view all the answers

What indicates that the current-to-pressure transducer is configured for reverse action?

<p>Pressure output at 4 mA is 15 psi. (D)</p> Signup and view all the answers

To determine the current signal at a flow rate of 204 GPM, which formula is applied?

<p>% = (Flow rate / Max flow) x 100% (A)</p> Signup and view all the answers

What is the output signal range of the pH transmitter mentioned in the examples?

<p>4-20 mA (C)</p> Signup and view all the answers

If the current output of an electronic loop controller is 8.55 mA, how open is the control valve?

<p>28.44% (A)</p> Signup and view all the answers

What is the lower pressure output at 4 mA for the current-to-pressure transducer?

<p>15 psi (A)</p> Signup and view all the answers

How is the necessary current signal value to produce an output pressure of 12.7 psi determined?

<p>By reversing the action values based on output psi. (D)</p> Signup and view all the answers

Flashcards

Instrumentation

A collection of instruments, devices, hardware, or functions used to measure, monitor, or control industrial processes or machines.

Instrument

A device that measures, monitors, or controls a variable, including indicators, controllers, annunciators, and switches.

Measurement Instrument

A device that detects changes (physical or otherwise) in a process and converts them into understandable information.

Critical Instrument

An instrument whose failure can jeopardize product quality or safety.

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Non-critical Instrument

An instrument whose failure doesn't directly affect product quality or safety, but is important for operations.

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Process Control

The regulation, command, or direction of all aspects of a process.

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Process

The methods used to change or refine raw materials into end products.

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Control System

A collection of connected components that regulates, directs, or commands itself or another system.

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Calculating Transmitter Output (Linear Equation)

To find the output of a temperature transmitter (or similar device), plug the measured input value (like temperature) into a linear equation. The equation is custom-fit to the transmitter's specific calibration.

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Linear Equation for Transmitter Output

A linear equation in the form y = mx + b, where 'y' is the output, 'x' is the input (like temperature), 'm' is the slope, and 'b' is the y-intercept.

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Finding Transmitter's Output Pressure

Use the calculated linear equation for a specific transmitter to find the output pressure (y) at a given input temperature or another similar variable (x).

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4-20mA Output Signal

A common electronic signal range used in industrial process control instruments, indicating a process variable. 4mA represents the lowest value, and 20mA the highest.

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Flow Transmitter Calibration

A flow transmitter is calibrated using a known range of flow rates (e.g., 0-350 gallons per minute) to determine the corresponding output signal, usually in terms of current (e.g. 4-20 mA).

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Direct Responding

A control system where the output (e.g., valve position) directly correlates with the input (e.g., measured flow rate or pressure).

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Calculating Current Signal (mA)

The calculation formula to use depends on the type of transmitter and its calibration . It's used to determine the current signal needed to reach a specific output value.

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Percentage Calculation

Determining a percentage of a measured value using a formula that compares the current reading with the upper and lower range values.

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Bourdon Tube

A curved, hollow tube that expands or contracts in response to pressure changes, used in pressure gauges.

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Xylene

A colorless liquid hydrocarbon commonly used as a filling fluid in Bourdon tube pressure gauges.

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Vapor Filled System

A temperature sensor that uses a volatile liquid/vapor combination to generate a pressure change based on temperature.

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Gas Filled System

A temperature sensor that uses the direct relationship between gas pressure and temperature to measure temperature.

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Mercury Filled System

A temperature sensor that uses the expansion of mercury to indicate temperature.

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Bistate Sensor

A low-cost temperature sensor that changes color at a specific temperature, indicating whether the temperature is above or below that point.

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Fusible Solid

A solid material that melts or changes state at a specific temperature, used in bistate sensors.

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Steam Trap

A device that removes condensate from steam lines, often using a bistate sensor to indicate when it's functioning correctly.

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Level Measurement

Determining the position of the interface between two different media (usually fluids, but can be solids or combinations).

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Direct Level Measurement

Simple and economical method where the distance (usually height) from a reference point is directly measured.

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Why Measure Level?

Level measurement is critical for safety, economy, and monitoring in various industries.

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Level Measurement in Oil & Gas

Used to manage tank inventories, protect equipment, prevent spills, and control processes across the oil and gas industry.

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Interface

The boundary between two different media, such as liquid and vapor, or two liquids.

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Level Control

Maintaining a desired level of a substance within a container or process.

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Local Indication

Providing a direct reading of the level at the measurement point.

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Datum Line

A reference point from which the level is measured.

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Strain Gauge

A sensor that measures changes in resistance due to applied force, used for stress analysis of materials.

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Differential Capacitance Sensor

A pressure sensor that uses a change in capacitance to infer pressure. It works by measuring the change in capacitance between two plates as a diaphragm flexes under pressure.

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Capacitance

The ability of a device to store electrical charge. It depends on the geometry of the conductive plates and the insulator between them.

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Diaphragm

A thin, flexible membrane that moves under pressure. Used in many sensors and instruments to convert pressure into a measurable change.

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Differential Pressure Transmitter

A device that measures the difference in pressure between two ports and outputs a signal proportional to the difference.

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High and Low Ports

The two ports on a differential pressure transmitter, labeled 'high' and 'low'. These labels indicate the relative pressure at each port, NOT necessarily that the 'high' port must always have higher pressure.

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Pressure Measurement

The act of determining the amount of force applied over a specific area.

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Pressure Conversion

Transforming pressure values from one unit to another (e.g., psi to kPa).

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Dip Stick Method

A simple level measurement technique using a marked stick inserted into a tank to gauge liquid depth.

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Lead Line

A weighted line used to measure water depth, often used for centuries by sailors.

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Sight Glass

A clear tube connected to a tank, allowing visual observation of liquid level.

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Level Gauge

A simple instrument that provides a direct visual indication of liquid level in a vessel.

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Float Type Measurement

A method that uses a buoyant element floating on the liquid surface, whose position indicates level changes.

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Limitations of Dip Stick & Lead Line

These methods require manual action, cause interruptions, and are unsuitable for pressurized vessels.

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Advantages of Sight Glass

Provides continuous visual indication, is more convenient than dip sticks, and offers a simple way to monitor liquid level.

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Level Gauge Application

Even when other level-measuring instruments exist, level gauges are often used as a direct indicator for operators.

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Study Notes

Introduction to Instrumentation and Control Engineering

  • The objectives of this course include gaining understanding of basic concepts and principles in instrumentation and control engineering, explaining instrument classifications, and recognizing control loop elements.
  • Measurement is the science of determining physical variable values. It involves comparing an unknown quantity to a predefined standard and expressing the result numerically.

Measurement

  • Measurement (also called metrology) is the science of determining values of physical variables.
  • It's a method of obtaining information about physical values of a variable.
  • Measurement of a given quantity is fundamentally an act or result of comparison between the quantity (whose magnitude is unknown) and predefined standards. The result is expressed numerically.

Why do we measure?

  • Students to think of answers to this question and prepare to share it with the class.

The Needs for Measurement

  • Carat was initially the weight of carob beans, and today is standardized as 0.2 grams. This is used to measure precious stones like diamonds.

Metric System

  • A table of prefixes, symbols, and multiplying factors for the metric system is provided.

SI Units: Systemes Internationales d'Unites

  • A table defining the seven fundamental quantities of the International System of Units (SI) is present, detailing their names, symbols and SI units

Derived Quantities and their SI Units

  • A second table shows common derived quantities, their symbols and SI units, with formulas for some.

Standards

  • Various standards organizations are listed, including ISO, IEC, ANSI, SCC, BS, and TSE.

Standard Bodies

  • International standards are defined by international agreements.
  • Primary standards are maintained at institutions around the world, their primary function is to check the accuracy of secondary standards.

Instrumentation

  • Instrumentation is used in almost every industrial process and generating system.
  • Instrumentation provides the means of monitoring, recording, and controlling a process to maintain it at a desired state.
  • A typical industrial plant, like an electric generating station, generates many process variables that must be measured and manipulated.

Process Variables

  • Variables such as boiler level, temperature, pressure, turbine speed, and generator output require prudent control for a plant's safe and effective operation.
  • Instrumentation provides automatic control of those processes, allowing for the indication of process conditions, enabling corrective action if necessary.

Instrumentation based on industrial application

  • A collection of instruments, devices, and functions are used to measure, monitor, or control industrial processes and machines.

What is an instrument?

  • A device for direct or indirect measurement, monitoring, and/or control of a variable.
  • Includes indicators, controllers, and other devices like annunciators, buttons, and switches.

Measurement Instrument

  • A device that detects various physical changes in a process and converts them into a usable form of information for the user.

Instrument Examples

  • Images/diagrams of various instruments are provided.

Classification of Instruments

  • Critical instruments are essential for product quality and safety, and a failure in specifications can compromise these.

  • Non-critical instruments are vital for operational significance, but not directly related to product quality and safety.

  • Reference-only instruments have functions that are not critical to the operation and are not involved in quality decisions.

Control Systems and Process Control

  • Control in process industries refers to the regulation, command, and direction of all process aspects.
  • Two primary types of control systems are manual control and automatic control.

System

  • Arrangement of physical components linked/connected so they behave or act as an entire unit.
  • A system refers to the methods of changing or refining raw materials to create final products.

Process Control

  • Process Controls are essential for maintaining plant processes at their desired states.
  • Process control range from simple manual actions to sophisticated computer logic controllers.

Control Systems

  • A system whose output can be regulated by altering its input is a control system.
  • Control systems are often built with multiple smaller control systems.

Block Diagram of Control System

  • A diagram illustrating the input-processing-output sequence in a control system is provided.

Mathematical Equation of Control System

  • A simple control system can be illustrated using a mathematical formula (X + 5 = Y), where X is the input, Y is the output, and 5 is acting as the control system.
  • The system's output (Y) can be altered by changing the input parameter value (X).

Explain the shown example of a simple Control System

  • A diagram of a water level control system (with components like pulleys, cords, a stopper, water container, a ball float, and stopcock) is provided.

Open Control Loop

  • A process variable isn't compared against a setpoint.
  • Actions are taken independently of the current status of the process.

Closed Control Loop

  • A process variable is measured and compared to a set point.
  • Actions are taken in response to deviations from the set point.

In Open Loop Control Systems

  • Three components are present: Input, Controller, and Output signals
  • The input signal is directly fed to the controller.
  • The output signal from the controller has no effect on the input signal.

Example of an Open Loop Control Systems

  • The operation of a clothes dryer, where the dryer stops after a set time, is an example, regardless of whether the clothes are completely dry.

Block Diagram of a Cloth Dryer Control System (Example)

  • A block diagram of a clothes dryer system showing the input (Desired Time), controller (Timer), output (Heating Elements), and process (Clothes Drying) is shown.

Example of Open Loop Traffic Light Control System

  • The operation of a traffic light system is a further example of open loop system.

Closed Loop Control System

  • An advanced automated system that generates desired outputs using inputs, controllers, and feedback elements.

  • Output is fed back to the controller, allowing for comparison against input signal to determine errors.

Example of an Closed Loop Air Conditioner System

  • The operation of air conditioners adjusting room temperature by sensing and responding to variations is an illustration of closed loop control, using feedback loop to maintain desired temperature.

Four Basic Elements of a Control Loop:

  • Primary Element/Sensor
  • Secondary Element/Signal-Generating Element
  • Controlling Element/Controller
  • Final Control Element

Primary Elements/Sensors

  • Measure process parameters and variables based on unique physical, chemical, thermo-electrical phenomena.
  • They generate an output signal indicative of the process variable.
  • Process Variables sensed are not transmittable unless converted to an electric (or pneumatic) signal by a secondary element

Primary Element Examples

  • Sensors
  • Detectors (detect presence of something like flammable gases or discrete parts)..

Secondary Elements/Signal-Generating Element

  • Primarily transduce to convert different physical quantities into electrical/electronic signals
  • They convert readings from sensors into standard signals for monitoring and control applications.

Transmitter Examples

  • Converters
  • Transmitters

Types of Signal

  • Analog Signals (no discrete positions or states, value changes) :
  • Pneumatic (3-15 psi)
  • Electrical (4-20 mA (Current) or 1-5 VDC (Voltage))
  • Digital Signals (binary digit signals to represent continuous values or discrete states)

Controlling Element/Controller

  • The brain of the control system.
  • Receives data from the measurement instrument, compares it to setpoints, and signals control elements for action, if necessary.

Common examples of controller

  • Programmable Logic Controller (PLC)
  • Distributed Control System (DCS)

Final Control Element

  • The component of a control system that physically alters the manipulated variable (such as increasing/decreasing fluid flow)
  • Actuators and Control Valves are common examples

Common Final Control Elements

  • Actuators: Component in a final control device which causes a physical change.
  • Control Valves: Manipulates the flow rate of fluid/gases; Control switches manipulate the electric energy entering the system

Instrument applications

  • Factory automation instruments
  • Plant safety instruments
  • Product quality instruments
  • Environmental condition instruments
  • Process variable measurement and control instruments

Piping & Instrumentation Diagram Fundamentals

  • A P&ID is a design document showing equipment interconnected with control instrumentation.
  • P&IDs use standardized symbols for elements like mechanical equipment, valves, and instrumentation
  • Tag numbers associate specific devices and their functions

Objectives: Understanding a P&ID Layout

  • Symbology, Piping (that connects equipment), Lines and instruments (to monitor and control processes).
  • Tag numbers and functional identifiers are essential for recognizing specific components..

Piping and Instrumentation Diagram

  • An overall process plant design document.
  • Shows how process equipment and instrumentation are interconnected.
  • Utilizes symbols to depict mechanical equipment like piping components, valves, and instrumentation.

P&IDs

  • Piping and instrumentation drawings, or P&IDs, are the schematics used within instrumentation and control systems

Process Flow Diagram

  • A fundamental representation of how raw materials transform into finished products.
  • Shows material and utility flows, with pressure and temperature ratings for each piece of equipment.

Instrument List

  • An alphanumeric list of instrumentation in a facility and its related functional details.
  • References other documents for installation details.

Logic Diagrams

  • Illustrate on-off/sequential functions of a process plant.

Instrument Loop Diagrams

  • Schematic representations of control loops, including their hydraulic, electric, magnetic, and pneumatic components.

Installation Details

  • Outline how instrumentation/control system components are connected to the process.
  • Details the requirements for correct instrumentation/control component installation

Location Plans

  • Provide orthographic views of the plant at scale, showing instrument and control system component placement.
  • Display other critical plant elements including instrument racks, control panels, power panels etc.

Different Engineering Documents

  • Process Flow Diagram, Piping & Instrumentation Diagram (P&ID), Instrument List, Logic Diagrams, Instrument Loop Diagram, Installation Details, and Location Plans summarize all information needed for the process.

Instrument Ranges/Spans

  • Instrument range refers to an instrument’s capacity to measure variables.
  • Calibration range identifies the output and measures variables within the range.
  • Instrument span is the difference (or distance) between the upper and lower range limit values.

Discrete Process Measurement

  • Measurement of true-or-false conditions
  • Discrete sensors use "switches" to indicate when a measured quantity exceeds or falls below a specified value.

"Normal" Status of a Switch

  • The electrical status of a switch's contacts under minimal stimulus.
  • Conditions are normally classified as "normally open" (NO) or "normally closed" (NC).

Hand Switches

  • Electric switches operated manually via toggle, pushbutton, or rotary actions.

Limit Switches

  • Detect physical object movement through direct contact.
  • Status as "normal" when not in contact.

Proximity Switches

  • Detect proximity to an object without physical contact.
  • Use magnetic, electric, or optical methods for detection.

Pressure Switches

  • Detect the presence of fluid pressure using diaphragms or bellows.

Level Switches

  • Detect liquid or solid level in a vessel using floats as level sensing elements.

Temperature Switch

  • Detect the temperature using bimetallic strips (two dissimilar metals).

Flow Switches

  • Detect fluid flow through pipes using "paddles" as the flow sensing elements.

Discrete Control Elements

  • On/Off Valves are the equivalent of an electrical switch.

On/Off Valves

  • Regulate, direct, or control fluid flow by opening, closing, or partially obstructing passageways.

Process Valve Types

  • Various valve types illustrated include ball, globe, butterfly, Saunders, angle, check, diaphragm, pressure relief, ball check valves.

Valve Actuator Types

  • Devices that provide the motive force to operate the valve mechanism.
  • Common types include pneumatic, hydraulic, electric motor, and hand (manual) actuators.

Control Valve Actuators

  • Provide motive force to control valve mechanisms.

Hydraulic Actuators

  • Use liquid pressure to move valve mechanisms.
  • High pressure ratings are useful for overcoming friction in piston-type actuators.

Electric Actuators

-Use electric motors to actuate large valves. -Often used for on-off ("shut-off") and throttling valves. -Worm gear sets are typical to reduce high rotational speed for efficient valve movement.

Solenoid Actuators

  • Utilized in small-sized valves (typically up to 1-inch).
  • Employ the magnetic field of a solenoid.

Hand Actuators

  • Use hand power for valve actuation.

Valve Failure Modes

  • Ways in which a valve may not function as intended when power is lost or other issues arise.

Fail-Safe Concepts

  • A mechanism that automatically mitigates harm to equipment or people should the primary system fail.

Fail-Open

  • Indicates a valve will open if a system signal is lost/interrupted.

Fail-Closed Concept

  • Indicates a valve will close if system signal is lost/interrupted.

Fail-Locked

  • Indicates a valve will remain in its current position during a system failure.

Fail-Indeterminate

  • Indicates that the valve's position cannot be determined during a failure.

FL/Drift Open and FL/Drift Closed

  • Valves operate as in "Fail-last" for safety.
  • They are locked in their last (open or shut) position during air or signal failure.

Applications of the Strain Gauges

  • Measure strain (for analyzing internal forces on items) -Measure other related quantities from the change in resistance due to applied force like pressure, displacement, and acceleration.

Differential Capacitance Sensors

  • Another type of pressure sensor based on the change of capacitance with applied pressure
  • A capacitor is used as a component to store electrical charge.
  • Two metal plates are separated by an insulator (forming a capacitor) in the sensor

Differential Pressure Transmitters

  • Common method of measuring differential pressures in industry
  • Outputs an electrical signal proportional to the pressure differential between two inputs.

Other Valve Types

  • Check valves prevent backflow, opening when pressure moves forward and closing against backflow.
  • Plug valves have a rotating plug inside the valve body. Valves are commonly used to control liquid or gas flow.

Indicators

  • Materials specifically designed to change color with different pH values.
  • Used to visually determine if a measured substance is more or less acidic or alkaline.

Colorimeter

  • Device used for measuring pH using chemical reaction of a supplied reagent
  • Involves adding the supplied reagent and then comparing color to a reference wheel/chart to determine pH value.

Potentiometric pH Measurement

  • Based on electrochemical measurements. -Special pH-sensitive electrodes are used for measuring the voltage of the solution and this voltage is dependent on the pH value.

pH Measurement Methods

  • Indicators, use of chemical reagents which change color based on pH of substance measured.
  • Colorimetry, a device to measure color change of a test subject in correlation to a reference chart.
  • Potentiometry, an electrochemical method using electrodes with standard potentials to measure pH value, according to Nernst equation

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