The Measurement of Air Flow

373 Pages·1977·21.628 MB·English

by  E. Ower and R. C. Pankhurst (Auth.)

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THE MEASUREMENT
OF AIR FLOW
5th Edition (in SI Units)
BY
E. OWER, BSC, A.C.G.L, C ENG.
AND
R. C. PANKHURST,
PH.D., A.R.C.S., C ENG., F.R.A.E.S.
PERGAMON PRESS
OXFORD NEW YORK TORONTO
SYDNEY PARIS FRANKFURT
U. K. Pergamon Press Ltd., Headington Hill Hall,
Oxford OX3 OBW, England
U. S. A. Pergamon Press Inc., Maxwell House, Fairview Park,
Elmsford, New York 10523, U.S.A.
CANADA Pergamon of Canada Ltd., 75 The East Mall,
Toronto, Ontario, Canada
AUSTRALIA Pergamon Press (Aust.) Pty. Ltd., 19a Boundary
Street, Rushcutters Bay, N.S.W. 2011, Australia
FRANCE Pergamon Press SARL, 24 rue des Ecoles,
75240 Paris, Cedex 05, France
WEST GERMANY Pergamon Press GmbH, 6242 Kronberg-Taunus,
Pferdstrasse 1, West Germany
Copyright © 1977 E. Ower and R. C. Pankhurst
All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system or transmitted in
any form or by any means: electronic, electrostatic,
magnetic tape, mechanical, photocopying, recording or
otherwise, without permission in writing from the
publishers
First published 1927 by Chapman & Hall
Second edition 1933 by Chapman & Hall
Third edition 1949 by Chapman & Hall
Fourth edition 1966 revised
Reprinted with corrections and amendments 1969
Fifth edition completely revised 1977
Library of Congress Cataloging in Publication Data
Ower, Ernest, 1894-
The measurement of air flow.
Includes bibliographies and indexes.
The measurement of air flow.
1. Air flow—Measurement. I. Pankhurst, R. C,
joint author. II. Title.
TJ1025.08 1977 620.1Ό74 76-27372
ISBN 0-08-021282-4 (Hardcover)
ISBN 0-08-021281-6 (Flexicover)
Typeset by Cotswold Typesetting Ltd, and printed in
Great Britain by Page Bros (Norwich) Ltd.
PREFACE
As STATED in the prefaces to earlier editions, this book is intended to serve as a
textbook both for students and for engineers and other practitioners concerned
with the measurement of the speed of air in motion relative to solid boundaries
or surfaces, and of the associated pressures.
For the first time, the entire text now appears in metric units. We have
adopted throughout the units of the Système International (S.I.) and have used
its abbreviations except that we have preferred to retain "sec" as the abbrevia-
tion for "second" instead of "s". Brief notes on the S.I. are provided in Appen-
dix 1. Recognizing that instruments reading in British units are likely to remain
in use for some time to come, we have included in this Appendix the numerical
values of the conversion factors for the units that occur most commonly in the
measurement of air flow.
The change to metric units necessitated the re-working of much of Chapter
XIII (Examples from Practice), but the principal result of using the S.I. is
general simplification. In particular, the S.I. removes the risk of confusion
between units of mass and force, provided that no attempt is made to use the
kilopond (kilogram-force) in place of the proper S.I. unit (the newton): this
point is emphasized in Appendix 2.
Appendix 2 also discusses the numerical evaluation of non-dimensional
quantities : the task of metrication served to drive home once again the great
advantages of expressing results in this form.
We have taken the opportunity to replace several physical terms by their
equivalents in modern terminology, notably "specific gravity" (nowadays
called "relative density") and "specific heat" (now "specific heat capacity");
and, in view of the increasing use of pressure transducers in place of liquid-
column manometers, we have tried to avoid referring to pressures as "heads"
except where this term is specially appropriate or convenient.
We have also re-written much of Chapter VI (which deals with flow measure-
ments by pitot-traverse methods) so as to conform with the complete overhaul
of the relevant part of British Standard 1042 (Part 2A) issued in 1973; and
reference is made throughout the book to a number of significant developments
that have taken place in air-flow measurement techniques since the fourth
edition was reprinted in 1969.
vu
Vlll PREFACE
Extract from Preface to Fourth Edition
The title under which the book has established itself since the first edition
appeared in 1927 has been retained; but we recognize that the text does not
cover all matters that a modern interpretation of the title might be expected to
include. As in past editions, our aim has been to concentrate on aspects, both
practical and theoretical, primarily of interest to engineers. We have, therefore,
not dealt with problems of measuring the flow of air at hypersonic speeds, when
such high temperatures can be attained that dissociation and ionization effects
change the physical character of the air ; or at very low pressures, when the mean
free path of the molecules becomes comparable with the dimensions of the
measuring instruments. Both these states concern physicists or space scientists
rather than engineers dealing with air-flow measurements in typical industrial
situations.
E.O.
January, 1977 R.C.P.
ACKNOWLEDGEMENTS
TAKEN together, many of the measurement methods described in this book
constitute an important part of the experimental resources of wind-tunnel
technique, to which one of us (R.C.P.) devoted a Sabbatical term at Cambridge
in 1970. He is glad of this opportunity to acknowledge his indebtedness to the
Master and Fellows of Emmanuel College for the award of the Fellow-
Commonership which enabled him to do so.
We are both deeply indebted to Dr. E. A. Spencer and Dr. F. C. Kinghorn
of the National Engineering Laboratory and to Mr. R. W. F. Gould of the
National Physical Laboratory for their valuable co-operation in answering
our numerous queries, mainly concerning measurements with pitot-static
tubes and orifices. We wish also to record our special appreciation to Mrs.
Sheila Bradshaw of the Aeronautical Research Council Library for her help
in supplying us with books, papers, and reports we wished to consult.
Our thanks are also due to the following for providing material from which
a number of illustrations have been made :
Air Flow Developments Ltd., Fig. 10.2; Mr. A. M. Binnie, Fig. 5.16; C. F.
Casella & Co. Ltd., Fig. 10.8; G.E.C. Elliott Process Instruments Ltd., Figs.
11.5 and 11.6; Willh. Lambrecht K.G., Göttingen, Fig. 11.10; Lowne Instru-
ments Ltd., Fig. 8.1 ; Salford Electrical Instruments Ltd., Fig. 11.7; H. Tinsley
& Co. Ltd., Fig. 9.4.
Figures 3.14, 4.3,t 4.4, t and 10.10 have been reproduced with permission
from publications of H.M. Stationery Office, and Crown Copyright is reserved.
Figs. 3.15, 5.10, and 5.12 have been reproduced by permission of the Royal
Aeronautical Society; and Fig. 3.20 by permission of Aircraft Engineering.
t With slight modifications due to the change from British to S.I. units.
ix
ABBREVIATIONS USED IN LISTES OF
REFERENCES
Aero. Aeronautical
AGARD Advisory Group for Aerospace Research and Development
A.I.A.A. Aircraft Industries Association of America
Aircr. Aircraft
App. Applied
A.S.M.E. American Society of Mechanical Engineers
B.S.I. British Standards Institution
Chem. Chemical
Engr(s) Engineer(s)
Engng Engineering
f. für
Forsch. IngWes Forschung auf dem Gebiete des Ingenieurwesens
I.C.A.O. International Civil Aviation Organization
Inst. Institute or Institut
Instn. Institution
Instrum. Instruments
I.S.A. Instrument Society of America
I.S.O. International Organization for Standardization
J. Journal
Jb. Jahrbuch
Mag. Magazine
Mech. Mechanical
Mechs Mechanics
Mitt. Mitteilungen
N.A.C.A. (American) National Advisory Committee for Aeronautics
NASA National Aeronautics and Space Administration
NAVORD Naval Ordnance Laboratory (U.S.A.)
N.E.L. National Engineering Laboratory
N.P.L. National Physical Laboratory
Phil. Philosophical
Phys. Physics
Proc. Proceedings
R.A.E. Royal Aircraft Establishment
R. & M. Reports and Memoranda of the Advisory Committee for Aeronautics
(1909-20), or the Aeronautical Research Committee (1920-44), or the
Aeronautical Research Council (1945 onwards)
Rep. Report
Rev. Review
Roy. Royal
Scient. Scientific
Soc. Society
Tech. Technical
T.M.T. Technische Mechanik und Thermodynamik
Trans. Transactions
u. und
V.D.I. Verein(es) deutscher Ingenieure
Z. Zeitschrift
XI
CHAPTER I
INTRODUCTION
ALTHOUGH this book deals primarily with the measurement of air flow, the
methods to be described will in general apply also to the flow of other gases
with little, if any, modification, except as regards the numerical values of the
various physical properties occurring in the equations. Further, much of the
theory will apply to the flow of liquids as well as gases, although, for practical
reasons, the methods of measurement may not always be applicable. Two-
phase flows are excluded.
When physical measurements have to be made, a choice of methods is often
available; and the experimenter must then decide which of these is best suited
to his particular purpose. His choice will be guided by considerations of sim-
plicity, directness, and the degree of accuracy he requires; he should always
avoid a complicated method when a simpler one will equally serve his ends. Let
us therefore consider what means are available for the problem with which we
are here concerned, namely the measurement of the speeds of streams of gases,
with particular reference to the motion of air along pipes or ducts. A search for
a simple, direct method yields disappointing results. Perhaps the most accurate
method of measuring the mean rate of water flowing along a pipe is to weigh
the quantity passing in a given time or to measure its volume. Weighing can
obviously not be used for air; volume measurements, on the other hand, can,
and they form the basis of the common gas meters described in Chapter XI.
But unfortunately the use of gas meters is severely limited because both the two
existing standard types can measure only rates of flow much smaller than those
that usually concern engineers. Moreover, one of these types is not designed for
high accuracy.
The only other direct method that suggests itself is to introduce some indi-
cator, such as a small, light body or a puff of smoke, which will be carried along
by the stream and can be timed over a measured distance. The prima facie
attraction of this method — its simplicity — disappears on examination. In the
first place, the duct or pipe must be transparent if the indicator is to be visible;
in the second, the rate of flow varies from point to point across a pipe section,
and this will make the determination of the mean rate of flow difficult even
without the additional complication due to the diffusion across the stream of an
indicator such as smoke. The first difficulty, invisibility, but not the second, can
1
2 MEASUREMENT OF AIR FLOW
be overcome by the use of a radioactive tracer or a hot spot in the gas produced
by an electric spark and subsequently made visible by an optical method such
as Schlieren. These and other techniques (see, for example, refs. 1-3) have been
tried, but so far have not been developed into practical engineering methods.
Broadly, we can say that indicator methods are suitable only in particular
cases, such as ventilation surveys in which the flow can be observed visually ; and
that most of them would usually be difficult to apply to the measurement of
flowrates in pipes.
Thus, for most air-flow measurements they have to make, engineers cannot
use direct methods, but have to resort to the measurement of some physical
effect arising from the motion. Three such effects have been found by experience
to be suitable: pressure changes associated with the motion; consequent
mechanical effects, such as the rate of rotation induced in a rotor made up of
light vanes mounted in the stream; and the rate of cooling of a hot body, such
as an electrically heated wire, introduced into the air current. Of these, the first
is of the greatest importance, since, as we shall see later, a properly designed
instrument, suitably inserted in the stream, records a pressure difference which
is entirely characteristic of the motion, and can be measured with a pressure
gauge. If such an instrument is constructed in accordance with certain well-
established principles, which are explained in Chapters III and IV, it may be
used without calibration as a standard for the measurement of air speed. This
is not true of anemometersf that depend for their action either on mechanical
or on electrical effects ; instruments of both these types are subject to individual
variations difficult to control, and usually require calibration against a standard
instrument of the pressure-measuring type.
Instruments that depend on the measurement of pressure can be subdivided
into two distinct groups according to whether air does or does not flow through
them. If there is no flow, we have what we shall term a pressure-tube anemo-
meter, the characteristic feature of which is two independent and differently
shaped tubes, each containing, in the end exposed to the air current, an orifice
or a group of orifices at which a pressure is established by the motion of the
stream. These tubes are connected at their other ends to opposite sides of a
differential pressure gauge, which prevents all flow through the anemometer
and measures the difference between the pressures at the two groups of orifices.
Differential pressure is also measured in pressure anemometers through which
there is flow. In both types the measured pressure difference depends on the
speed and density of the air and also on the geometry of the instrument itself.
It is obviously desirable that the geometry shall affect the readings as little as
possible or, at any rate, with as little variation as possible over a wide speed
range; and one variety of pressure-tube anemometer — the pitot-static tube
t The term anemometer, as its derivation implies, includes all types of instruments used for
the measurement of air speed.
INTRODUCTION 3
discussed in Chapters III and IV — has been devised which possesses this
property more than any other type so far developed. The remarks made in the
previous paragraph about the possibility of constructing anemometers that
can be used to measure air speed without calibration apply to this type of
instrument above all others; and it is by virtue of this property that the pitot-
static tube has been adopted universally as the standard against which practic-
ally all other types of anemometer are ultimately checked.
Pressure anemometers through which there is a flow are more sensitive to
small differences in shape than is a good pressure-tube anemometer. Neverthe-
less, within their limitations, such instruments have many useful applications.
Commonly used examples are the plate orifice, the nozzle, and, to a smaller
extent, the venturi tube. For accurate work they must be used under strictly
controlled conditions.
Mechanical anemometers are of two main types. In the first, the working
element is a rotor maintained in continuous rotation by the air at a rate depend-
ing on the air speed; in the second, the air deflects a plate or a vane controlled
by gravity or a spring. The rotary type can be subdivided into the vane anemo-
meter and the cup anemometer. The first of these is a most useful instrument
which is widely used by engineers; it is discussed in some detail in Chapter
VIII. The cup anemometer is used mainly by meteorologists and little by
engineers, and, beyond the following brief description, will not be considered
in this book.
In its original form, the cup anemometer consists of four hemispherical cups
carried, with their bases vertical, at the outer ends of four light arms, which are
symmetrically disposed in a horizontal plane and are attached to a central
sleeve free to rotate about a vertical axis. The cups are arranged in pairs so that
the concave side of one member of a pair is presented to the air current at the
same time as the convex side of the diametrically opposite cup. Thus at any
instant the air on one side of the median plane through the vertical axis of the
instrument will be blowing into the interior of one or two cups and, on the other
side of this plane, on the exterior of the opposite cup or cups. Hence, since the
aerodynamic force on a cup with its concave side presented to the wind is
greater than when the wind is blowing on its convex face, rotation ensues at a
rate depending on the air speed. Instruments of this type are bulky and not
easily portable.
In 1926 Patterson(4) claimed certain advantages for a three-cup type which
was adopted to some extent in Canada. Later Sheppard(5) developed a much
improved three-cup instrument with conical instead of hemispherical cups.
Extreme lightness of construction and the use of an elegant indicating mechan-
ism with little friction have resulted in a very sensitive instrument — it responds
to an air speed as low as 0-2 m/sec — and one that behaves satisfactorily in a
fluctuating wind,(6) in which the older types tend to overestimate the mean
speed considerably. Sheppard's instrument has been used in investigations of