Instrumentation Fundamentals for Process Control

Douglas O. J. deSa

• Publisher: Routledge
• Year: 2019
• Print ISBN: 9781560329015
• eBook ISBN: 9781351438070
• Topic: Physical Sciences
• Subtopic: Industrial & Technical Chemistry

A practical introductory guide to the principles of process measurement and control. Written for those beginning a career in the instrumentation and control industry or those who need a refresher, the book will serve as a text or to supercede the mathematical treatment of control theory that will continue to be essential for a well-rounded understanding. The book will provide the reader with the ability to recognize problems concealed among a mass of data and provide minimal cost solutions, using available technology.

PART I

PRIMARY DEVICES AND MEASUREMENTS

CHAPTER 1

Flow Measurement

In almost all process plants, flow is a parameter of prime importance, for the simple reason that most processes involve moving material from one part of the plant to another or from one piece of processing equipment to another. Each movement involves doing work on the material so as to reduce or increase its mass, alter one or several of its properties, add heat, or otherwise change its condition. In this chapter we shall learn the relationship between the volume flow and the differential head created when a restriction such as an orifice plate or a venturi section is placed in the flow stream. Although the use of meters based on this principle is diminishing, there are still a large number in operation today.

The magnetic flowmeter uses the principle of voltage induction, and the vortex meter uses vortex shedding as a means of measuring volumetric flow, and these instruments are gradually replacing the orifice plate and venturi meters. Measuring the flow of a viscous fluid is not possible with the meters just described; hence, we shall also look at methods using a target in the flow stream and a meter having gears forced to rotate by the fluid itself.

Mass flow has always been an essential process measurement but it was only very recently that the means to measure it directly via the Coriolis meter have been available. We shall investigate how this has been achieved. The Doppler effect and the time-of-flight methods are measurements used to determine flow rate, and both of these are discussed. High-accuracy measurements of low-viscosity fluids can be made with turbine meters, and we shall discuss these instruments later in this chapter.

The topics presented in this chapter are not exhaustive; they are only a collection of methods that cover some of the older and newer techniques and give a flavor of the subject.

BASIC THEORY OF FLOW

Any material in motion possesses energy, and this energy is called kinetic energy, from the Greek word for movement. Let us now consider the method of determining the kinetic energy possessed by a body in motion. Note: In this discussion, the mass of the body m is given as W/g, because direct measurement of mass is not generally easily made, whereas the weight of a body can be determined very simply. This statement has to be modified slightly in the light of modern technology, where the mass of liquid fluids can be measured directly using the Coriolis meter, which will be discussed later.

Suppose a body has a weight W and this body attains a velocity v from rest in a time t under the influence of a force F, which causes it to move a distance l. The product of the applied force and the distance over which it moves gives the work done:

$\text{Work}\text{done}\text{=}Fl$

We know that force has been defined as mass times acceleration:

$\begin{array}{l}F=ma\\ =\frac{W}{g}a\end{array}$

where g = acceleration due to gravity and a = acceleration of the body. We also know that the final velocity v of a body equals its initial velocity plus the product of its acceleration and the duration through which the acceleration is applied:

$v=u+at$

from which we can say:

$t=\frac{v-u}{a}$

where u is the initial velocity.

We know that the distance traversed under constant acceleration is the product of the average velocity and the time it took to cover the distance; mathematically:

$l=\left(\frac{u+v}{2}\right)t$

Substituting the expression for v we obtained above into this equation, we have:

$\begin{array}{l}l=\left(\frac{2u+at}{2}\right)t\\ =ut+\frac{1}{2}a{t}^2\end{array}$

Since

$\begin{array}{l}l=\frac{u+v}{2}t\\ =\left(\frac{u+v}{2}\right)\frac{v-u}{a}\\ =\frac{v^2-u^2}{2a}\end{array}$

we can also say

$v^2=u^2+2al$

If we consider the initial velocity to be zero for the body starting from rest, then

$l=\frac{v^2}{2a}$

and substituting this into the equation for work done, we have

$\begin{array}{l}\text{Work}\text{done}=\frac{W}{g}a\frac{v^2}{2a}\\ =\frac{W{v}^2}{2g}\end{array}$

which is the kinetic energy of the body (conforming to the familiar general relationship that energy is proportional to the square of the velocity). We can apply this equation to determine the kinetic energy of a fluid. For the purposes of this discussion, we shall consider a liquid, and let this liquid be a common one: water. If

$\begin{array}{l}W=\text{weight of water flowing}\\ v=\text{velocity of flow}\end{array}$

then as given previously the kinetic energy possessed by this flowing water is given by

$\frac{W{v}^2}{2g}$

which is another way of expressing the general form of kinetic energy of any body:

$\text{Kinetic energy}\text{=}\frac{1}{2}m{v}^2$

where m is the mass and v the velocity.

The mass of the body in the flow form of the equation is shown by W/g; so, to make the flow form similar in appearance to the general form, we can write it as:

$\frac{1}{2}\left(\frac{W}{g}\right)v^2$

Hence, in general terms we can say the velocity head, or kinetic energy per unit weight, of the water in physical dimensions is given by

$\frac{v^2}{2g}=\frac{{\text{length}}^2{\text{/time}}^2}{{\text{length/time}}^2}\text{=}\text{length}$

which is the pressure head due to the fluid velocity or the velocity head.

Since the mass of fluid flowing is constant, any change in flow rate is dependent on the fluid velocity alone. This can be observed when one uses a hosepipe with a jet nozzle fitted to it; the more restricted the nozzle, the faster and further the jet will go.

In order for the water to flow, there must be a force applied to it, and the force necessary is derived from the applied pressure to give the water the acceleration needed to make it flow. We all know that pressure is defined as force per unit area. The required force will vary depending on the type of fluid involved, and more specifically upon the fluid density. Hence, we can redefine pressure in terms that include the density of the fluid. To do this, we shall continue to use water as the fluid and consider a column of water. If we let the column have a cross-sectional area of one square unit, then the volume of the water will be directly proportional to the height of the column, the constant of proportionality being the area of the cross section, in this case, unity, or 1.0. Since water has a density (mass per unit volume), it will exert a force on the base of the column, but we have already said that pressure is force per unit area, and therefore the pressure exerted by the column of water on the base is given by the height of the column multiplied by the density of the water. Thus, if p is the pressure, h is the height of the column, and ρ is the density, then

$p=\rho h$

and this, then, is the pressure energy of the water, or the pressure head.

We all know from experience that if we elevate a tank of water, then the water acquires energy due to its position, and this energy is called the potential energy of the water. Then, the total energy of the water in the general case will be the summation of all the energies involved:

$\text{Total energy = kinetic energy + pressure energy + potential energy}$

or, using symbols:

$\text{Total energy =}\frac{W{v}^2}{2g}+\frac{pW}{gp}+\frac{Wh}{g}$

Since we transmit water from one place to another by pipe, it is easy to calculate the energy available at any point. Remem...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• PREFACE
• INTRODUCTION: CONCEPTS IN INSTRUMENTATION FOR PROCESS CONTROL
• NOTATIONS USED IN THIS BOOK
• PART I PRIMARY DEVICES AND MEASUREMENTS
• PART II PROCESS CONTROL
• PART III APPLICATIONS
• PART V INSTALLATION OF INSTRUMENTATION
• PART VI MODERN CONTROL SYSTEMS
• BIBLIOGRAPHY
• INDEX