Table Of ContentCOMPONENTS FOR
PNEUMATIC
CONTROL INSTRUMENTS
The Static and Dynamic Characteristics of
Pneumatic Resistances^ Capacitances
and Transmission Lines
by
L. A. ZALMANZON
Translated by
R. HARDBOTTLE
Translation edited by
F. P. STAINTHORP
PERGAMON PRESS
OXFORD . LONDON · EDINBURGH . NEW YORK
PARIS · FRANKFURT
Pergamon Press Ltd., Headington Hill Hall, Oxford
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Pergamon Press (Scotland) Ltd., 2 & 3 Teviot Place, Edinburgh 1
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Copyright © 1965
Pergamon Press Ltd.
First edition 1965
Library of Congress Catalog Card No. 64-24301
This book is a translation of the original Russian volume ΠροτοπΗυιβ BACMCHTIA
nHesMaTunecKux npuôopoe κοητροΛΛ u ynpaeAenun (Protochnye elementy pnev-
maticheskikh priborov kontrolya i upravleniya), published in 1961 by the Pub-
lishing House of the Academy of Sciences of the U.S.S.R., Moscow
INTRODUCTION
PNEUMATIC instruments are widely employed in the automation of
production processes and to control various power installations. In the
U.S.S.R. production of a unified pneumatic block system of automatic
control is under way, and instruments for pneumatic control are being
mass produced in all the large industrial countries of the world.
Pneumatic controls are employed in the aircraft industry and in other
specialized branches of engineering. Pneumatic measuring methods
are widely employed.f
All the pneumatic instruments at present being produced by the
industry fall into two types, viz. flow elements, the action of which is
l>ased on the utilization of the various properties of air flow, and flexible
elements, i.e. diaphragms, bellows, etc. With the expansion of auto-
mation by pneumatic instruments the part played by flow elements is
becoming increasingly important. The various properties of air flows are
utilized in the execution, not only of very simple operations but also
of operations such as, e.g. automatically maintaining given ratios of
pressures, differentiation and integration of signals of changes of
pressure, and other operations that become necessary in the automa-
tion of various processes.
The main flow elements encountered in virtually all automatic
pneumatic control instruments, are restrictions or pneumatic resis-
tances, and chambers that act as pneumatic capacitors.
Problems often arise during the development, improvement and use
of pneumatic instruments, that have to do with the characteristics of
restrictions and chambers. In some cases the characteristics of units
in pneumatic instruments, and sometimes of the instruments as a
whole, depend entirely on the properties of the gas flow through the
restrictions and in the pneumatic chambers. Many examples can be
quoted to illustrate this. We will confine discussion here to giving a
t References (1) to (22) in the Bibliography illustrate the wide range of application
>of pneumatic instruments and the recent sharp increase in the number of functions
fulfilled by them in the automation of production processes.
xi
xii INTRODUCTION
list of problems necessitating a detailed study of the characteristics of
restrictions and chambers.
Given operating conditions in the restriction (these will differ depend-
ing on whether flow is laminar or turbulent, and whether the conditions
are sub- or supercritical, etc.) will be suitable for the execution of cer-
tain functions only. For example, in the majority of pneumatic instru-
ments for general industrial use supercritical flows are avoided, but
pneumatic controllers and measuring instruments designed to utilize
the properties of such flows are widely employed in aircraft engineer-
ing. The air flow conditions in valves govern completely the character-
istics of the relays containing nozzle-baffle elements found in many
pneumatic instruments. One of the reasons for the variation in the
characteristics of adjustable slot restrictions of pneumatic controllers,
may be that under laminar conditions the flow of air through such
restrictions can vary within wide limits even though the cross-sectio-
nal area and the pressure differential remain constant (in such cases
the change in the flow is due to differences in the degree of eccentricity-
of the parts making up the restrictions; it is important in practice to
be able to assess the effect of this factor). In selecting the optimum
settings for pneumatic controllers, allowance should be made for the
fact that sometimes the true characteristics of the processes of diffe-
rentiation and integration of the pressures performed by means of
pneumatic chambers, differ from the initial calculated characteristics.
In this connexion it is important to know the laws governing the flow
into and out of the chambers as determined, not by the idealized, but
by the true characteristics of the restrictions. These empirical relation-
ships may be presented in the form of families of curves, each of which
is plotted at set pressures at the inlet or at the outlet. Other problems
are presented by the fact that a change in the supply pressure of pneu-
matic instruments may alter appreciably the times of the transient
processes in the instruments with restrictions of some types but not
when restrictions of other types are used. Special problems arise when
the air flow through the restrictions and chambers takes place at high
temperatures (e.g. in aircraft jet engines, in instruments for measuring
temperatures by means of pneumatic methods, etc.). In some cases
the operating medium is, not air but some other gas, and it is impor-
tant to be able to apply to these cases the findings obtained in the
case of flow of air.
A large number of other problems similar to those listed above, the
solution of which also requires a knowledge of the features of air flow
INTRODUCTION xm
through restrictions of various types and of the characteristics of
pneumatic cylinders, are constantly arising in engineering practice
and in scientific research into automatic pneumatic control.
In studying and calculating the characteristics of the flow of air
through restrictions and in pneumatic chambers, use should be made
of the basic data of theoretical and experimental aerodynamics. How-
ever, the problems arising are specific ones, relating to the problems
encountered in the study and development of pneumatic instruments.
These problems include, for example, problems connected with the need
for obtaining restriction characteristics of a given form, with determin-
ing the conditions in which linearization of the differential equations
describing the processes in pneumatic cylinders is possible, etc.
Hitherto only some of the problems of the theory and calculation
of restrictions and pneumatic chambers have been considered in the
literature. These have been the subject of separate papers that have
appeared at different times and at different places. In view of the rapid
development of automatic pneumatic control and pneumatic measure-
ment methods, a fuller treatment of the subject is required. The pur-
pose of this monograph is to consider the problems mentioned above,
systematically and wherever possible in greater detail.
A special set of problems arises in studying long pneumatic lines
used to transmit signals of changes in pressure in automatic pneuma-
tic control instruments. In some cases the equations derived for long
pneumatic lines also describe the processes of change in pressure in
relatively short tubing and in the channels in the pneumatic instru-
ments themselves. Very often pneumatic tubing can be designed on
the basis of the well-tried methods of the theory of long electric lines
and of the theory of hydraulic systems with distribution parameters.
However, as experience has shown, the problems of designing pneu-
matic lines are not very clearly defined, and this causes complications
in the solution of practical problems. It was thought suitable, there-
fore, to include a section on this subject in the monograph, even though
no new results are reported concerning the theory of long lines.
The layout of the monograph is as follows.
Chapter I deals with the theory and design of restrictions, and
considers the main characteristics of restriction processes, giving the
features of the restrictions used in various pneumatic control and
regulating instruments. Special problems in the theory and design of
restrictions are discussed that arise in the development, improvement
and use of pneumatic instruments (e.g. the above-mentioned problems
XIV IKTBODUCTION
of the effect of the eccentricity of the parts of slot restrictions and
their characteristics, the effect of temperature, etc.). In addition to
simplified methods for the design of restrictions for various combina-
tions of air flow conditions characteristic of the operations of pneu-
matic automatic control instruments, more general design methods
based on the application of data of gas dynamic theory of flow in
pipes are given.
Chapter II deals with the static characteristics of pneumatic cham-
bers with restrictions of various types. Graphs are given for determin-
ing the parameters of steady flow of air in the chambers. It gives
the features of pneumatic chambers used to perform set operations in
control and regulating instruments (discussing the conditions in
which it is possible by means of pneumatic chambers to sum or divide
signals of change in pressure, etc.). Experiments are described that
were made with small chambers positioned between restrictions in
which the air cannot be considered as a homogeneous medium, but
which have to be designed allowing for changes in pressure from one
section of the chamber to the other.
Chapter III considers problems of the dynamics of pneumatic
chambers. Differential equations are derived that describe the law
governing the changes in pressure in various types of chambers.
Graphs are given, by means of which the numerical values of the
coefficients of the above-mentioned differential equations can be
found in each concrete case without the need for calculation. An
estimate is made of the errors due to the simplifying assumptions
usually made in studying the dynamics of pneumatic chambers. In
addition to the general problems of the dynamics of pneumatic cham-
bers, special problems in the study and design of chambers used as
elements with a given functional purpose, are discussed. These prob-
lems include problems of the theory and design of the chambers of
pneumatic regulators, of chambers used as time relays (timers),
equipment for filtering selected pneumatic sinusoidal oscillations
from unharmonic signals.
Chapter IV deals with the characteristics of long pneumatic lines
and of systems with distribution parameters. A short account is given
of methods of designing long lines, such methods being the most
rational ones in the case of pneumatic systems. Here all the equations
are presented in a form convenient for making engineering calcula-
tions on pneumatic tubing. The rated characteristics of long pneumatic
lines are assessed on the basis of comparison thereof with experimental
INTBODUCTION XV
data. By means of approximate equations an analysis is made of the
effect of the basic parameters (length and diameter of tubing, volume
of chamber connected thereto, mean pressure level), on the time and
rate at which control signals are transmitted along long pneumatic
lines.
The Appendix contains brief reference data from aerodynamics,
and explains the derivation of some aerodynamics equations found
in the text of the monograph.
The majority of the problems of the theory and design of elements
of pneumatic control and regulating instruments, are also pressing
problems in other branches of engineering neighbouring on aero-
dynamics (hydrodynamics, etc.).
CHAPTER I
THEORY OF RESTRICTIONS
§1. Basic Data on Restrictions as Elements of Pneumatic Automatic
Control Equipment and Pneumatic Measuring Instruments.
Classification of Restrictions. Problems in the Theory and Design
of Various Types of Restrictions
Among the primary basic elements of pneumatic controllers and
measuring instruments are restrictions, designed to create a resistance
to the flow of air. The simplest restriction is a hole of small cross-
section in a wall separating two chambers, or in a plug mounted in
a channel along which air is flowing (Fig. 1 (a)).
wa) b) c)
'^W/
i \
I l·
.Τ!777Τ7777777λ
W/V// I—« —i
e)
I
FIG. 1. Restrictions for pneumatic devices.
a — very simple cylindrical restriction; 6 — adjustable
annular cylindrical restriction; c — adjustable throat
conical restriction; d — restriction of nozzle-baffle type;
e — restriction with ball valve.
In addition to cylindrical restrictions, many other shapes are used in
pneumatic devices. Together with restrictions of constant cross-
section, there are adjustable or variable restrictions. Figure 1 (b)
shows an annular restriction, the flow cross-section of which consists
l
2 COMPONENTS FOE PNEUMATIC CONTEOL INSTKUMENTS
of a small gap between a cylindrical insert and a cylindrical sleeve;
the restriction shown in Fig. 1 (c) differs, in that the insert and the
sleeve are conical. Figure 1 (d) shows a restriction, the flow cross-
section of which consists of a gap between the end of the nozzle and
a plate; this is the so-called nozzle-baffle restriction. Figure 1 (e)
shows a restriction made in the form of a ball valve.
Restriction leads to an irreversible loss in the mechanical energy
of the air flow, and an irreversible change of mechanical energy into
heat energy. In this connection the difference between restrictions
(Fig. 2 (a)) and nozzles (Fig. 2 (b)), diffusers and other similar elements
also used in pneumatic automatic control equipment, should be
emphasized. The purpose of the latter elements is to convert the
mechanical energy of the air from one form (potential or kinetic
energy) into another, where possible without losses. A clear concep-
tion of this difference is important for a correct understanding of the
operation of pneumatic automatic control equipment.
a) b)
V////////////A 1
m
FIG. 2. Shape of channels in res-
trictions and nozzles.
a — restriction; b — nozzle.
In the following chapters we shall show how elements of pneumatic
controllers for various operations (summing pressures, varying one of
the pressures in proportion to the other, etc.), are made by using
restrictions of various types. The wide range in characteristics of
restrictions is due to the effects of restriction shape and the operating
conditions on the flow pattern. This may be shown by considering
even the simplest restriction (Fig. 1 (a)).
Depending on the geometric dimensions and the pressures before
and after restriction, the predominating losses may be either the
local losses at the inlet and outlet, or the friction losses during flow
of the air along the channel. The flow may be laminar or turbulent,
and depending on this also the basic characteristics will vary sub-
stantially. In addition, in the case of turbulent flow the state of the
surface (degree of roughness) of the walls of the channel affects the
THEORY OF RESTRICTIONS 3
characteristics of the restriction in some cases ; in the case of laminar
flow no such effect is found. When the restriction channel is very
long, supplementary entrance losses occur, where the flow pattern is
formed. The restriction process follows a different pattern depending
on whether there is heat transfer to the external medium or not. In
some cases, when the air issues at low velocities, the phenomena
characterizing the restriction process do not differ from those that
would be found if an incompressible liquid were to flow through the
restriction. In other cases the compressibility of the gas is of great
importance. In the case of high rates of flow of the air, allowance
should be made for change in its density along the length of the
restriction channel. Sometimes the effect on the characteristics of the
restriction of the inertia forces due to change in the rate of flow along
the length of the channel, may be considerable. Novel phenomena
arise when the rate of air flow in the restriction channel attains the
speed of sound (critical and supercritical outflow conditions). Al-
though in this case also the air flow through the restriction depends
on the temperature and pressure of the air before the restriction, it
remains constant on decrease in the pressure after the restriction.
Under supercritical outflow conditions, in some cases at the outlet
of the restriction or in the restriction channel a system of shock waves
is formed, in which an irreversible change of the mechanical energy
of the air current into heat takes place, like that found as a result of
the friction forces in the case of ordinary flow. The losses thus entailed
supplement the other losses characterizing the restriction process.
It is interesting to pick out some cases of operation of the restric-
tions that are typical of pneumatic devices, and study them more closely.
In the following, restrictions will be classified in three categories
according to their operating conditions.
1. Restrictions with a cylindrical channel and a low length/diameter
ratio, where the restriction effect is due to local resistances at the
inlet and losses at the outlet, and the effect of the friction forces during
the flow of air along the restriction channel is not pronounced. The
air flow processes in restrictions of this type resemble those found in
flow from nozzles (Fig. 2 (b)). Usually, flow in restrictions of this type
can be taken as adiabatic, i.e. taking place in the absence of heat transfer
to the external medium. As a rule, it is turbulent. Restrictions of the
first category operating both under sub- and supercritical flow condi-
tions, are used in pneumatic automatic control equipment.
2. Restrictions of cylindrical shape with a high length/diameter
o*
