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How Derivatives and Integrals Relate to One Another

How Derivatives and Integrals Relate to One Another

First, let us review some of the properties of differentials and derivatives, referencing the expression and…


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Mathematical Problem-solving Techniques

Mathematical Problem-solving Techniques

Some problem-solving techniques are unique to quantitative problems, involving mathematical calculations. In…


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Valve Seat Leakage

Valve Seat Leakage

In some process applications, it is important that the control valve be able to completely stop fluid flow…


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Auxiliary and Lockout (86) Relays

Auxiliary and Lockout (86) Relays

An important type of “accessory” relay, especially for legacy electromechanical protective relays,…


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Metering Pumps

Metering Pumps

A very common method for directly controlling low flow rates of fluids is to use a device known as a metering…


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Pressure-based Flowmeters

Pressure-based Flowmeters

All masses require force to accelerate (we can also think of this in terms of the mass generating a reaction…


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Using Manometers for Measuring Pressure

Using Manometers for Measuring Pressure

A very simple device used to measure pressure is the manometer: a fluid-filled tube where an applied gas…


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the Negative Consequences of Poor PID Controller Tuning

the Negative Consequences of Poor PID Controller Tuning

Much has been written about the benefits of robust PID control. Increased productivity, decreased equipment…


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Limit, Selector, and Override Controls

Limit, Selector, and Override Controls

Another category of control strategies involves the use of signal relays or function blocks with the ability…


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Velocity-based Flowmeters

Velocity-based Flowmeters

The Law of Continuity for fluids states that the product of mass density (\(\rho\)), cross-sectional pipe area…


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Symbolic Versus Numerical Calculus

Symbolic Versus Numerical Calculus

Calculus has a reputation for being difficult to learn, and with good reason. The traditional approach to…


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Self-balancing Pneumatic Instruments Principles

Self-balancing Pneumatic Instruments Principles

A great many precision instruments use the principle of balance to measure some quantity. Perhaps the simplest…


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Dispersive Spectroscopy

Dispersive Spectroscopy

The dispersion of visible light into its constituent colors goes all the way back to the 17th century with…


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Radiative Temperature Measurement

Radiative Temperature Measurement

Temperature measurement devices may be classified into two broad types: contact and non-contact. Contact-type…


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On/off Shut-off Valves

On/off Shut-off Valves

An on/off valve is the fluid equivalent of an electrical switch: a device that either allows unimpeded flow or…


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Introduction to Calculus

Introduction to Calculus

Few areas of mathematics are as powerfully useful in describing and analyzing the physical world as calculus:…


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Classified Areas and Electrical Safety Measures

Classified Areas and Electrical Safety Measures

Any physical location in an industrial facility harboring the potential of explosion due to the presence of…


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2-wire (“loop-powered”) Transmitter Current Loops

2-wire (“loop-powered”) Transmitter Current Loops

It is possible to convey electrical power and communicate analog information over the same two wires using 4…


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Error Corrections

Error Corrections

Abdelaziz, Ahmed (June 2014) Identified numerous typographical errors throughout the book, mostly repeated…


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Practical PID Controller Features

Practical PID Controller Features

In order for any PID controller to be practical, it must be able to do more than just implement the PID…


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