Osborne Reynolds Centenary Volume || Osborne Reynolds: Scientist, Engineer and Pioneer

Osborne Reynolds: Scientist, Engineer and PioneerAuthor(s): J. D. JacksonSource: Proceedings: Mathematical and Physical Sciences, Vol. 451, No. 1941, Osborne ReynoldsCentenary Volume (Oct. 9, 1995), pp. 49-86Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/52793 .

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Osborne Reynolds: scientist, engineer and pioneer

By J. D. JACKSON

The Manchester School of Engineering, Faculty of Science and Engineering, University of Manchester, Oxford Road, Manchester M13 9PL, UK

The paper seeks to place the landmark paper 'On the dynamical theory of incompressible viscous fluids and the determination of the criterion', published by the Royal Society in 1895, within the broader context of the complete scientific works of its author, Osborne Reynolds. After a short biographical outline, the paper offers a detailed survey of Reynolds's extensive and wide-ranging publications, highlighting those of particular interest in their own right and those serving as noteworthy antecedents of the 1895 paper. Reynolds's contributions are accordingly examined under broad headings of 'Reynolds the scientist' and 'Reynolds the engineer' with particular attention paid to evaluating the 1895 paper before concluding with a consideration of Reynolds's status as a scientific pioneer.

1. Introduction

The occasion of the centenary of the publication by the Royal Society of the paper 'On the dynamical theory of incompressible viscous fluids and the determination of the criterion', which is reprinted in full at the beginning of this volume, is an opportune moment to consider not only the paper itself but its place within the broader context of the complete works of its author, Osborne Reynolds. As a landmark contribution to the development of fluid mechanics the 1895 paper is without question the crowning achievement of Reynolds's long and distinguished career as the first Professor of Engineering at the University of Manchester. Indeed, the fact that 100 years later the ideas contained in his paper remain central to current turbulent research and are widely used in the study of practical flows provides ample cause for celebration and underlines the continued relevance of this contribution.

By means of a detailed examination of his body of work I hope to disclose not only the development and emergence of the lines of thought so definitively realized in 1895, but also give something of an overview of Reynolds's many and diverse scientific interests. Consequently, I have sought to categorize the considerable output of published material Reynolds produced during his 37 years at Manchester (1868- 1905) and to offer a short review, highlighting those contributions that have proved to be of particular importance.

2. Biographical overview

What follows is a very brief biographical outline. Those who are interested to learn more about this may do so by reading the excellent paper by Professor Jack

Proc. R. Soc. Lond. A (1995) 451, 49-86 ? 1995 The Royal Society

Printed jn Great Britain 49 Tg)( Paper



50 J. D. Jackson

Allen (1969), based on the invited lecture which he gave in August 1968 at the Symposium held to celebrate the centenary of Reynolds's appointment to the newly established Chair of Engineering at Manchester. Further insight into his life and work can be gained by viewing a permanent exhibition in the School of Engineering at Manchester featuring original equipment constructed and used by Reynolds. Working reproductions of a number of his experiments are available for 'hands on' use, whilst general display boards provide visitors with additional biographical information.

Osborne Reynolds was born in Belfast on 23 August 1842. He came of a clerical family. His great-grandfather and grandfather were rectors of Debach-with-Boulge, Suffolk, while his father, the Reverend Osborne Reynolds, was a Fellow of Queens' College, Cambridge, Principal of the Belfast Collegiate School, Headmaster of Ded- ham Grammar School, Essex, and finally also Rector of Debach.

Reynolds's early education was undertaken mainly by his father, who in addition to being an extremely able mathematician had a keen interest in mechanics and mechanical matters and took out a number of patents concerned with improvements to agricultural equipment and machinery. The young Osborne Reynolds showed an early aptitude and liking for the study of mechanics and, at the age of 19, entered the workshop of Mr Edward Hayes of Stony Stratford, a well known inventor and mechanical engineer. He remained with Edward Hayes for a year obtaining practical experience in the manufacture and fitting out of coastal steamers. During this period, to use his own words, 'my attention (was) drawn to various mechanical phenomena, for the explanation of which I discovered that a knowledge of mathematics was essential'. He therefore decided to go to Cambridge to take a course in mathematics. His university career was highly successful. He graduated in 1867 and was immediately afterwards elected to a Fellowship at Queens' College. He then entered the office of a civil engineer, Mr John Lawson, of London.

In 1868 he applied for and was elected to the newly instituted Chair of Engineering at Owens College - later to become The Victoria University of Manchester. In his application for the post Osborne Reynolds stated, 'From my earliest recollection I have had an irresistible liking for mechanics and the physical laws on which mechanics as a science are based. In my boyhood I had the advantage of the constant guidance of my father, also a lover of mechanics and a man of no mean attainment in mathematics and their applications to physics'. He remained as Professor of Engineering at the University of Manchester until 1905 and died on 21 February 1912 at Watchet in Somerset at the age of 69.

He was awarded the degree of M.A. by the University of Cambridge in 1880 and elected Honorary Fellow of Queens' College Cambridge in 1882. In 1877, he was elected a Fellow of the Royal Society and in 1888 received the Royal Medal. In 1883, he became a Member of the Institution of Civil Engineers and was awarded the Telford Premium in 1885. The University of Glasgow conferred the Honorary Degree of LL.D. on him in 1884. He was elected President of the Manchester Literary and Philosophical Society in 1888 and received the Dalton Medal in 1903. His collected works were published by Cambridge University Press in three volumes with the title 'Papers on Mechanical and Physical Subjects' (Volume I in 1900, Volume II in 1901 and Volume III in 1903). These contain most of his published papers, over seventy in all.

Osborne Reynolds was one of the most original and independent of men and had strong views as to the character of the training to be offered in this new discipline. He consequently organized a systematic course of lectures extending over three years

Proc. R. Soc. Lond. A (1995)



Osborne Reynolds: scientist, engineer and pioneer 51

which provided a thorough grounding in civil and mechanical engineering. In his view all engineering was one so far as the student was concerned, and the same essential training should be given irrespective of the type of specialization to be pursued afterwards.

Osborne Reynolds's considerable mathematical ability was supplemented by an almost uncanny insight into the physical fundamentals of a problem. Shortly after coming to Manchester, Reynolds began a series of original researches which led, during the next 35 years, to the publication of many papers of outstanding interest. These covered a phenomenally wide range of physical problems and engineering applications and laid the foundations for much of the subsequent work on turbulent flow, hydraulic modelling, hydrodynamic lubrication, friction, heat transfer, and many other rnatters. His experiments on the origins of turbulence, the scaling of estuary models and the determination of the mechanical equivalent of heat remain classics of their kind. One is frequently reminded of the importance of his work in fluid mechanics and heat transfer by the widespread use of terms such as the Reynolds number, Reynolds equations, Reynolds stresses and Reynolds analogy. His study of turbulent transition in pipe flow - 'An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous and of the law of resistance in parallel channels' - was one of the many highlights of Reynolds's research. The original Reynolds Tank experiment, which is still in use at Manchester University for demonstrating this key aspect of fluid mechanics to students, is no less than an object of pilgrimage for visitors.

3. His inaugural lecture and early days at Owens College

It was the custom for the Academic Sessions at Owens College to be inaugurated by an Introductory Address. This task was entrusted to Osborne Reynolds for the opening of the Session 1868-1869, the start of his career at Manchester. In this lecture, revealingly entitled 'The progress of engineering with respect to the social conditions of this country' (Reynolds 1868), he firmly rejects any notion of engineering as an 'ivory tower' abstraction divorced from human context:

The results, however, of the labour and invention of this century are not to be found in a network of railways, in superb bridges, in enormous gulns, or in instan- taneous communication. We must compare the social state of the inhabitants of the country with what it was. The change is apparent enough. The population is double what it was a century back; the people are better fed and better housed, and comforts and even luxuries that were only within the reach of the wealthy can now be obtained by all classes alike ... But with these advantages there are some drawbacks. These have in many cases assumed national imnportance, and it has becorne the province of the engineer to provide a remedy.

Made at the outset of his career these remarks show the youthfuil Reynolds clear in his mind as to what needed to be done, a figure charged with a sense of mission and full of ideas.

The Chair of Engineering at Owens College had been established by eminent local engineers and businessmen with a view to providing a source of well-educated young men trained in science and engineering. The hope was that they would take up employment in the Manchester area and feed ideas and initiatives into the many industrial organizations there to help to combat stiff competition from elsewhere,




52 J. D. Jackson

notably Germany and other parts of Europe. In those places industry was already benefitting as a direct result of the creation of teaching establishments which provided technical education to a high level. The major industrialists Joseph Whitworth, William Fairbairn, Charles Beyer and John Robinson all played a leading role in the foundation of the Chair at Manchester and in the selection of the 25-year-old Osborne Reynolds to fill it.

At the time Reynolds arrived in Manchester in 1868 Owens College was housed in a building in Quay Street which had earlier been the home of Richard Cobden, the renowned former Member of Parliament for nearby Stockport. Little was available to him in the way of laboratory facilities for either teaching or research. Initially, he was restricted to research involving experiments of a very simple kind which could either be done at home or outdoors. We see this clearly reflected in the emphasis of his early work. It was not until much later, well after 1873 when Owens College moved to the present site of the University of Manchester in Oxford Road, that Reynolds was able to undertake experiments using sophisticated apparatus and it was even later before he had laboratory facilities which enabled him to perform tests on engineering plant.

In November 1869, Reynolds became a member of the Manchester Literary and Philosophical Society. At that time the President of the Society was the distinguished scientist James Prescott Joule, a man for whom Reynolds came to have the very highest regard. It was under the latter's encouraging eye that Osborne Reynolds read his first paper to the Literary and Philosophical Society in March 1870 on 'The stability of a ball above a jet of water' (an interesting but rather academic problem). It marked the beginning of a close involvement with the 'Lit. & Phil.' on Reynolds's part and he contributed papers regularly, a total of 26 in all. These were mainly on scientific topics of general interest and broad appeal to members of the Society.

In a successful bid to further extend both his own and the College's contacts with the scientific community of the area, Reynolds also actively involved himself with two other local societies, the Manchester Association of Employers, Foremen and Draughtsmen (a group consisting of men with technical interests and experience, first formed in 1856) and the Manchester Scientific and Mechanical Society (formed in 1870 by William Fairbairn with the intention of linking academics with local industrialists). Between 1871 and 1874 Reynolds addressed the first of these bodies on a number of directly practical topics, as their titles make clear: 'Elasticity and fracture', 'The use of high pressure steam' and 'Some properties of steel as a material for construction.' In contrast, his lectures to the Scientific and Mechanical Society, whom he twice served as President, were of a far more general nature, as indicated by titles such as 'Future progress', 'Engineers as a profession' and 'Mechanical advances'. It is interesting to observe how Osborne Reynolds set out to satisfy the specific needs of the rather different sections of his 'scientific constituency' in the attentions he paid to the various Manchester societies.

4. Reynolds's contribution to science and engineering

The considerable diversity of the problems in both pure and applied science that Reynolds subsequently tackled provides a clear indication of an unusually wide ranging scientific curiosity. Six parallel streams of research falling into two groups and broadly corresponding to the nominal notion of 'Reynolds the scientist' and 'Reynolds the engineer' may be identified.





Figure 1. Apparatus to produce a corona resembling a solar corona.

4.1. Reynolds the scientist

(i) Papers on 'Out-of-door physics' (1870-1881)

This initial stream of Reynolds's work, which was described in the terms used above by his most famous student, J. J. Thomson, clearly stemmed from interests developed as a result of his background and experience before coming to Manchester. It was convenient as an initial area for research in view of the fact that little was available to him at that time in the way of laboratory and workshop facilities at Owens College. In addition it provided ideal material for lectures of general interest and popular appeal for presentation to the Manchester Literary and Philosophical Society.

The papers on this aspect of his work, which are all to be found in Volume I of the Collected Works (Reynolds 1900), deal with matters concerned with comets; the solar corona and the aurora; terrestrial magnetism; the electrical properties of clouds; the bursting of trees struck by lightning; the destruction of sound by fog; the refraction of sound by the atmosphere; the action of rain to calm the sea; the action of oil on water in preventing wind waves; surface tension and capillary action.

Solar and cometary matters

The earliest of these, papers 2, 3A and 3B (1870-1872), are all closely related. In papers 2 and 3A the tails of comets, the solar corona and the aurora are considered as electrical phenomena. In paper 3B (1872), a corona resembling the solar corona produced by discharging electricity from a brass ball in a partially evacuated receiver is described (see figure 1). In paper 4 (1872), the induction of static electricity on the part of the sun is proposed as a probable cause of terrestrial magnetism and in paper 5 (1872) the inductive action of the sun on the electrical properties of clouds is considered with respect to thunderstorms. Paper 7 (1873) 'On the bursting of trees and other objects struck by lightning' reports an experiment showing that the explosive effect of a lightning strike is due to the rapid evaporation of moisture into steam.

Proc. R. Soc. Lornd. A (1995)



54 J. D. Jackson

., /

Figure 2. Apparatus to illustrate the action of rain to calm the sea.

Natural phenomena

In paper 7A (1873) Reynolds deals with the destruction of sound by fog explaining it in terms of the resistance to motion of air when charged with small droplets of water.

Paper 16 (1874) and paper 22 (1876) are likewise concerned with the refraction of sound by the atmosphere. In these Reynolds considers the effects due to the difference of wind velocity near the surface of the ground and at a height above it. This causes sound to be lifted when the waves move into the wind and to fall when waves move with the wind. He goes on to examine the effect of the variation of temperature in the atmosphere and explains that this causes sound waves to rise. Experiments are reported in which he studied these various effects but the papers are particularly noteworthy for the keenness of Reynolds's observations and revealing of his interest in outdoor pursuits. Thus:

It has often astonished me, however, when shooting, that a wind which did not appear to me to make the least difference to the direction in which I could hear small sounds distinctly, should yet be sufficient to cover one's approach to partridges, and more particularly to rabbits, even until one was within a few feet of them - a fact which shows how much more effectively the wind obstructs sound near the ground than even a few feet above it.

In a presentation to the Manchester Literary and Philosophical Society, 'On the action of rain to calm at sea' (paper 15, 1875), Reynolds showed by experiment that vortex rings produced by droplets of rain cause water to be carried well below the surface in appreciable amounts leading to the damping of wave motion (see figure 2).

Papers 29 (1875) and 30 (1877) deal with the formation of raindrops, hailstones and snowflakes. Reynolds points out that hailstones are formed by the aggregation of small frozen particles resulting from coalescence with more rapidly descending larger particles. To prove it he ingeniously produced artificial hailstones by chilling a flow of air laden with tiny droplets of water through the use of an ether spray (see figure 3).

In a paper read to the British Association in 1880 'On the effect of oil in destroying waves on the surface of water' (paper 38), Reynolds attributes this to the surface tension varying inversely with the thickness of the oil film as the wind flows over it. This introduces tangential stiffness which prevents the surface taking up the motion of the water beneath. The effect is a dynamic one; instead of wave motion occurring in





Figure 3. Apparatus to produce hailstones in the laboratory.

the water, eddies are formed below the surface. At the centennial British Association meeting held at York the following year Reynolds developed his ideas 'On surface- tension and capillary action' still further (paper 39).

On 4 October 1881 Reynolds made a short presentation to the Manchester Literary and Philosophical Society 'On the floating of drops on the surface of water depending only on the purity of the surface' (paper 40). In this Reynolds reported experiments using powder in the form of flowers of sulphur to determine the circumstances under which such d:rops are suspended.

(ii) Papers on the physics of gases, liquids and granular materials (1874-1903)

This is a part of Osborne Reynolds's work which is not as widely appreciated now as it deserves to be. It was, however, of considerable interest within the Victorian scientific community and it was for his early efforts in this area that Reynolds was elected a Fellow of the Royal Society in 1877. Featuring in both Volumes I and II of the Collected Works, his papers deal with forces at a surface caused by evaporation; condensation and heat transfer; the transpiration of gases through porous media; the internal cohesion of liquids; the dilatancy of granular materials and the general properties of matter. Almost all of Reynolds's post-1877 publications on these matters were presented to the Royal Society.

Kinetics of gaseous fluzids

In paper 11 (1874) Reynolds is concerned with the forces due to the evaporation or condensation of a liquid at a surface. Experiments conducted by him showed that evaporation caused a force tending to drive the surface back and condensation a force tending to drive the surface forward. The explanation of these effects is given using the kinetic theory model of gases.




56 J. D. Jackson

Figure 4. The Crookes light mill.

Papers 12 (1874) and 23 (1876) deal with forces exerted by the communication of heat to a surface immersed in a rarefied gas. Such forces are attributed to molecular influences and used to afford an explanation of the operation of the Crookes light mill (figure 4), again using the kinetic theory model. The ideas involved led Reynolds to invent a simple photometer. Experiments on a light mill performed in collaboration with a colleague at Owens College, Arthur Schuster, demonstrated conclusively that the force which turns the vanes is not directly due to thermal radiation.

Reynolds's interest in the Crookes light mill was perhaps the initial stimulus for his thoughts on the 'transpiration' of gases. Graham had applied this term to the passage of gases through capillary tubes. Reynolds re-applied it to describe the motion of gases through minute channels including porous plugs and apertures in thin plates as well as capillary tubes. The results of his 1879 investigation are presented in one of the longest and most original of his papers entitled 'On certain dimensional properties of matter in the gaseous state' (paper 33). In this, he showed by theory and experiment (using the apparatus shown in figure 5) that not only would a difference of pressure cause a gas to flow from one side of a porous plate to the other, but so also would a difference of temperature, even when initially the pressures on the two sides were equal. To this phenomenon he gave the name 'thermal transpiration'.

In the same paper Reynolds also demonstrated that the extremely low pressure of the gas in the light mill was necessary because of the comparatively large size of the vanes and that similar results ought to be obtainable with smaller vanes at higher pressure. This he proved by experiments on fibres of silk and a 'spider line' using the apparatus in figure 6. He showed that, provided the pressure in the vessel containing the fibre was not more than approximately one-quarter of an atmosphere, the fibre moved towards an external source of heat.





vlt-~~~~

a e~~~~~~~~~~~~ ~~~~~~~~ 3:F um p

Figure 5. Apparatus to measure thermal transpiration of gas through a porous material.

Figure 6. Apparatus to detect the surface force experienced by a silk thread due to heating.

Reynolds considered his investigation as a whole to have very profound implications, affording a proof that gas is not a continuous medium but possesses a 'dimensional structure'. His description and explanation introduced the dependence of the density of the gas in relation to the size of the passages in the porous medium or the vanes of the light mill, and so involved what he called the 'dimensional properties of gases'. This he believed could have more than philosophical importance:




58 J. D. Jackson

The actions only become considerable within extremely small spaces, but then the work of construction in the animal and vegetable world, and the work of destruction in the mineral world, are carried on within such spaces. The varying action of the sun must be to cause alternate inspiration and expiration of air, promoting continual change of air within the interstices of the soil as well as within the tissue of plants. What may be the effects of such changes we do not know, but the changes go on; and we may fairly assume that in the processes of nature the dimensional properties of gas play no unimportant part.

Advancement of the kinetic theory of gases was a notable feature of the science of the 1870s and one to which Reynolds made a significant contribution alongside more established figures such as Maxwell. A short note by Reynolds on thermal transpiration (paper 34) written in response to a criticism of his ideas by Maxwell and communicated to the Royal Society by its Secretary Sir George Stokes in 1879, provides an intriguing insight into the very formal manner in which the scientific establishment operated.

Reynolds's work on the surface forces due to heating and on thermal transpiration provided valuable experimental support for the developing kinetic theory (i.e. that 'heat' is a manifestation of the molecules of which a gas is composed). Widespread acceptance of the theory by the scientific community did not come until much later. Reynolds's experiments and theoretical contributions in the period 1874 to 1879 were many years in advance of the time. It is of interest that one of Reynolds's students in his last years at Manchester, Sidney Chapman, was later to make further important advances in this field.

Physics of liquids

Reynolds's interest in the physics of fluids extended to liquids. In papers 31 (1877) and 35 (1880) delivered to the Manchester Literary and Philosophical Society he reported experiments on the internal cohesion of mercury and water. By careful exclusion of air he was able to suspend a column of mercury to a height of more than double that of the barometer (see figure 7).

Properties of granular media

A few years later he turned his attention to the properties of granular media. Reynolds's first announcement of the property of such media to which he attached the name 'dilatancy' was made to Section A of the British Association at its meeting in Aberdeen in 1885. The paper attracted sufficient attention for him to be asked to read it again to Section B a few days later, and a printed version (paper 50) appeared in the Philosophical Magazi'ne in December of the same year with the title 'On the dilatancy of media composed of rigid particles in contact'. A version also appeared in Nature due to the extent of interest. The British Association audiences must have been greatly intrigued by the strikingly simple but ingenious experiments which he performed and equally startled by the conclusions which he drew from them.

He applied the term 'dilatancy' to the property possessed by a mass of granular material to alter its volume in accordance with a change in the arrangement of its grains. His illustration of this in terms of the piling of spheres in two different ways is shown in figure 8: the pile of spheres in cubical formation occupies a volume greater than that of the same number and size of spheres when piled in the second way.

Reynolds went on to illustrate this by characteristically simple means. If an india-




Osborne Reynolds: scientist, engineer and pioneer 59 A

C?~~~~

Figure 7. Apparatus to study the internal cohesion of mercury.

Figure 8. Diagram to illustrate the dilatancy of granular materials.

rubber bottle with a glass neck is filled with water and the bag is then squeezed, water will be forced up the neck. But if the bottle is full of granular material and water, the effect of squeezing, up to a point, is to draw water down from the neck into the bag, because the grains have adopted an arrangement in which the volume of the interstices has been increased. In Reynolds's words, 'the result, but for the knowledge of dilatancy, would appear paradoxical, not to say magical ... Sand presents many striking phenomena well known but not hitherto explained, which are now seen to be simply evidence of dilatancy'. A familiar phenomenon explained by Reynolds was that observed when a foot is planted on firm moist sand on the sea-shore: an area around the foot appears to become dry, however, when the foot is raised, the sand beneath is found to be abnormally wet. The pressure of the foot has increased the volume of the interstices between the grains of sand below it and water has been drawn in to occupy the additional voids.

Reynolds stated that the recognition of this property of dilatancy would, from a practical point of view, place the theory of earth-pressures on a true foundation, but that 'the greatest results are likely to follow in philosophy, and it was with a view to these results that the investigation was undertaken'. He goes on to declare that




60 J. D. Jacckson

the recognition of this property of dilatancy places a hitherto unrecognized mechanical contrivance at the command of those who would explain the fundamental arrangement of the Universe, and one which, so far as I have been able to look into it, seems to promise great things, besides possessing the inherent advantage of extreme simplicity.

These were the thoughts in his mind in 1885. Indeed, the title of his discourse to the Royal Institution in February, 1886 (paper 51), on the same property of granular material, contained the significant words 'possibly connected with gravitation". Seven years previously, a paragraph concluding his paper on dimensional properties of matter in the gaseous state had shown that his thoughts were turning towards the possibility of solving the riddle of the luminiferous ether. However, it was not until February 1902, that his memoir 'On the sub-mechanics of the Universe' was communicated to the Royal Society.

(iii) Papers on fluid motion and turbulence (1872-1894)

Osborne Reynolds is without doubt best known for his papers on fluid motion and turbulence which are to be found in both Volumes I and II of the Collected Works. The matters dealt with include: the progression of groups of waves; vortex motion; laminar and turbulent flow in pipes; the dynamical theory of fluid flow and, hydrodynamic lubrication. Among the papers are a number which have received universal recognition.

Wave motion

Paper 27 (1877) is concerned with the progression in deep water of groups of dispersive surface waves and the rate at which energy is transmitted by them. Here Reynolds showed not only that the velocity of the group is one half that of an individual wave, as was already known, but that the group velocity also gives the rate of transmission of energy.

Vortex motion

In the same year Reynolds described methods for rendering the internal motions of a fluid visible by means of colour bands, a technique which he was to use later in his renowned experiments on transition (see below). This he did with particular reference to vortex motion, considering the vortex lines behind an oblique wave, the vortex ring behind an inclined disc, vortex rings caused by drops falling into water and by a 'puff' of water.

Laminar and turbulent flow in pipes: the Reynolds number In 1883, Osborne Reynolds published his famous paper entitled 'An experimental

investigation of the circumstances which determine whether motion of water shall be direct or sinuous and of the law of resistance in parallel channels' (paper 44). This paper, published in the Philosophical Transactions of the Royal Society, proved to be a classic in the literature of the science of fluid motion and had a profound effect on the development of fluid mechanics in the widest sense. It contained the enunciation of the dimensionless group, the Reynolds number.

The first step in Reynolds's discovery of this fundamental parameter appears to have been his observation that 'the tendency of water to eddy becomes much greater as the temperature rises'. It occurred to him that this might be related to the well-





known fact that the viscosity of water diminishes as the temperature rises, and moreover, that the physical property, kinematic viscosity, 'is a quantity of the nature of the product of a distance and a velocity'.

He procee(led to consider the equations of motion and to establish that the forces per unit mass are of two distinct types, inertial and viscous, and further that the ratio of these is related to the dimensionless group DUmjv, in which Ur is the mean velocity of the flow, D is the tube diameter and v the kinematic viscosity. In his paper he states:

This is a definite relation of the exact kind for which I was in search. Of course without in-tegration the equations only gave the relation without showing at all in what way the motion might depend upon it. It seemed, however, to be certain, if the eddies were due to one particular cause, that integration would show the birth of eddies to depend on some definite value of DUmjv.

The story of his experiments using colour bands in glass tubes is well-known. His final apparatus, so effectively portrayed by the well known illustration shown in figure 9, consisted of a glass-sided tank, 6 feet long, 18 inches deep and 18 inches wide. Inside it was a glass tube with 'a trumpet mouth of varnished wood, great care being taken to make the surface of the wood continuous with that of the glass'. On the right-hand side, the tube was connected to an iron pipe equipped with a valve which could be controlled by means of a long lever. On the left-hand side is the device for introducing a streak of dye into the trumpet, while a float and dial was used to register the water-level in the tank and hence the volume being discharged through the glass tube. The experiments, made in 1880, consisted of filling the tank with water, allowing several hours for conditions to become steady, then opening the valve, at first only slightly. Referring to figure 10 the colour-band established itself as a beautifully steady streak (10a) but a point was reached on increasing the flow along the tube by opening the valves till further, when 'the colour band would all at once mix up with the surrounding water, and fill the rest of the tube with a mass of coloured water' (lOb). 'On viewing the tube by the light of an electric spark, the mass of colour resolved itself into a mass of more or less distinct curls, showing eddies' (lOc).

Reynolds proceeded to measure the critical velocity for onset of eddies using three tubes of different diameter and in each case varying the water temperature. To a first approxirnation, the Reynolds numbers based on these critical values of velocity were found to be the same (about 13000) for each of the tubes and for all water temperatures. He then set out to find the critical condition for an eddying flow to change into non-turbulent flow, referring to this as the 'inferior limit'. To do this, he allowed water to flow in a disturbed state from the mains through a length of pipe and measured the pressure-drop over a five-foot distance near the outlet (see figure 11).

Starting with low flows and gradually increasing them, he found that at a certain point the fluid levels in the differential manometer connected to the pressure-holes began to fluctuate: this coincided with the change in the character of the flow and provided visual evidence of the attainment of the critical velocity which he later determined by plotting the mean velocity against the pressure-gradient. Two sizes of pipe were tested. The result was to demonstrate that the critical velocities for the two pipes were in fact so related as to imply the same critical value of the Reynolds number (about 2000).




62 J. D. Jackson

Figure 9. Final apparatus for studying direct and sinuous motion in a tube: the Reynolds Tank.

(a)

(b)

_____________________________________ (c)

Figure 10. Illustration of direct (laminar) and sinuous (turbulent) motion in a tube.

In this renowned contribution to the development of fluid mechanics, Reynolds not only evolved the number to which his name was later attached and determined the critical value below which flow in a pipe is always stable and laminar, but also provided a detailed picture of the resistance to flow in pipes. In addition, he took the further step of showing that, for given conditions of surface roughness, the friction coefficient is a unique function of the Reynolds number. The following year (1884) in his Presidential Address to the British Association in Montreal, Lord Rayleigh paid this tribute:

Professor Reynolds has traced with much success the passage from the one state of things to the other, and has proved the applicability under these complicated conditions of the general laws of dynamical similarity as adapted to viscous fluids by Professor Stokes. In spite of the difficulties which beset both the theoretical and experimental treatment, we may hope to attain before long to a better understanding of a subject which is certainly second to none in scientific as well as practical interest.

Stokes himself, in his capacity as President of the Royal Society, also singled out this exceptional paper in his statement of 30 November 1888 on the occasion of





Figure 11. Apparatus for mneasuring friction in pipe flow.

the presentation of a Royal Medal to Osborne Reynolds 'for his investigations in mathematical and experimental physics, and on the application of scientific theory to engineering.'

In a subsequent shorter contribution entitled 'On the two manners of motion of water', paper 48 (1883), Reynolds compared the characteristics of flow in converging and diverging channels, pointing out that whereas in the former the conditions are favourable for producing steady flow, in the latter the flow is likely to be turbulent and unsteady. This he contrasted with flow in parallel channels where below a certain flow rate steady streamline conditions prevail and above that turbulence is encountered.

The dynamical theory of fluid flow

Eleven years were to elapse before the major breakthrough in the understanding of turbulent flows anticipated by Lord Rayleigh in his Montreal address was made. It came with Reynolds's contribution 'On the dynamical theory of incompressible viscous fluids and the determination of the criterion' (paper 62), the publication of which by the Royal Society is celebrated in the centenary volume. This remarkable development was of very great significance, dealing as it did with matters which Reynolds considered:

... must be of a general and important kind, such as the unexplained laws of the resistance of fluid motions, the laws of universal dissipation of energy and the second law of thermo-dynamics




64 J. D. Jackson

It was the culmination of 25 years of research and came as a result of Reynolds conducting 'a more rigorous examination and definition of the geometrical basis on which the analytical method of distinguishing between molar-motions and heat- motions in the kinetic theory of matter is founded; and of the application of the same method of analysis, thus definitely founded, to distinguish between the mean-molar- motions and relative-molar-motions, where, as in the case of steady-mean (turbulent) flow along a pipe, the more rigorous definition of the geometrical basis shows the method to be strictly applicable.' Its origins date back to Reynolds's interests in the properties of gases at the outset of his career.

Section I of the paper is a lengthy introduction which sketches the background to the work to be reported, states the objectives, outlines the approach adopted and summarizes the findings. He begins by tracing the development between 1822 and 1845 of the equations governing fluid motion, the Navier-Stokes equations. He refers to the comparisons reported by Stokes in 1857 between theoretical solutions of the equations and certain experimental observations, which seemingly proved the assumptions made in the formulation of the equations. These were restricted to the drag on slowly moving objects of small size and the resistance to the flow of liquid at low rates through long tubes of small bore. These he contrasts with examples where theoretical results were found to be directly at variance with common experience in the case of the motion of larger bodies at higher velocity and the discharge of fluid through large tubes at greater flow rates. He points to the fact that Stokes was aware that the discrepancies resulted from the presence of eddies which rendered the actual motion other than that to which the theoretical solutions referred.

Reynolds then goes on to discuss his own contribution in 1883 in identifying the dimensionless parameter, the Reynolds number, which governs whether the flow in tubes will be direct (laminar) or unsteady (turbulent), and establishing by experiment the value of 'the inferior limit', above which transition can occur. He asserts that:

These experimental results completely removed the discrepancy previously noticed, showing that whatever may be the cause, in those cases in which the experimental results do not accord with those obtained by the singular solution of the equations, the actual motions of the water are different. But in this there is only a partial explanation, for there remains the mechanical or physical significance of the existence of the criterion to be explained

Reynolds then flatly states 'my object in this paper is to show that the theoretical existence of an inferior limit to the criterion follows from the equations of motion,' before continuing, 'I also show that the limit to the criterion obtained by this method of analysis, and by integrating the equations of motion in space, appears as a geometrical limit to the possible simultaneous distribution of certain quantities in space, and in no wise depends on the physical significance of these quantities.'

Expressed in modern terms, Reynolds sought to write the components of velocity in a turbulent flow in terms of mean and fluctuating quantities and to perform averaging of the momentum equations. This showed that these equations contained additional terms which could be thought of as apparent stresses due to turbulence. He then derived equations for the kinetic energy of the mean motion and the kinetic energy of the turbulent motion and noticed that they contained terms, the turbulent energy production terms, which represent the total exchange of energy between the mean motion and the kinetic energy of the turbulence.





To explain the occurrence of transition in channel flows Reynolds examined the conditions under which the turbulence energy could be sustained. Using the turbulence energy equation and considering a control volume for which the turbulent diffusion of turbulent energy would integrate to zero, he arrived at a condition for 'the inferior limit' based on the idea that the total turbulence production must equal the total turbulence dissipation. He analysed the particular case of flow between parallel walls driven by a pressure gradient. Using an analytical function to describe a small disturbance superimposed on a fully developed laminar flow he evaluated the total turb-ulence production and the total turbulence dissipation. The result was that they were in balance at a particular value of the Reynolds number of 517 based on the bulk mean velocity and the distance between the walls.

It is clear that Reynolds's historic paper contained the foundations of modern turbulence modelling. The concept of turbulent stress, the role of the turbulent production terms in the exchange of energy between the mean motion and the turbulence and the dissipation of turbulence are matters which remain of central importance in the subject of turbulence. In essence he conceived the idea of the energy cascade in turbulent flows. One can take his equations for the kinetic energy of the mean motion and for turbulence energy and with little modification derive the corresponding equations currently in use. A century later the basic ideas contained in Reynolds's paper are still used in almost all our numerical predictions of practical turbulent flows, at least in situations close to industrial applications.

Hydrodynamic lubrication

We come next to a very different contribution, namely, Reynolds's theory of hydrodynamic lubrication. The stimulus for this was the important experimental research on 'The friction of lubricated journals' carried out for the Institution of Mechanical Engineers by Beauchamp Tower, first reported in 1883 and 1884.

This showed that it was possible for a journal to drag oil between itself and the bearing, causing a rise of pressure sufficient to support the shaft. Reynolds realized that the maintenance of a film of oil between the shaft and its bearing might be explained by hydrodynamics on the assumption that the centre of the rotating shaft shifted away from the centre of the bearing in such a direction as to make the film of oil thicker on the ingoing than on the outgoing side.

Excited by Tower's results and after a preliminary reference to them at the 1884 British Association meeting, he pursued the subject with such energy that his famous contribution 'On the theory of lubrication...' appeared in the Philosophical Trans- actions of the Royal Society in 1886 (paper 52). In this very lengthy and detailed paper, Reynolds not only formulated and integrated the hydrodynamic equations but also, by allowing for the variation of viscosity with temperature, obtained close agreement with the observed pressures.

The paper provides a very good example of Reynolds's approach of discussing the physical or mechanical picture of things before proceeding with the mathematics. Under the heading 'General view of the action of lubrication', he evolves the basic concepts involved by first considering two plane surfaces. In Case 1 (figure 12) they are parallel to one another but AB is moving to the left with a velocity U and 'pumping' fluid between itself and the stationary surface CD. The sloping lines show how the velocity varies between U at AB and zero at CD. The pressure is constant between D and C although there are tangential viscous stresses on the two surfaces.

Next, he considers the same plates without tangential motion with the upper




66 J. D. Jackson

Case 1 c s

Case2 -> C1I%Ve ~~~~of Pe0

Case 3

Cas 4:

A ~ ~ ~ ~ ~~/ A7,7'.Z B

Figure 12. Diagrams to illustrate the action of lubrication.

one being forced downwards to squeeze out the fluid. A pressure distribution is then created, reaching its highest value at the centre (Case 2, figure 12). He then combines the two: tangential motion and squeezing of the surfaces together (Case 3, figure 12). In this instance, the distribution of pressure resembles that of Case 2, while the mean viscous stress on CD is similar to that of Case 1.

To account for the case of lubricated surfaces which are not approaching one another, but which nevertheless are capable of sustaining a transverse load, it only remains to visualize Case 4, figure 12, where one surface is inclined to the other. At the section P1Q1, there is the same uniform distribution of velocities as if the surfaces were parallel to one another and at a distance P1Q1 apart. But to either side of P1Qj, the velocities must be modified to preserve continuity and so they adopt a shape similar to those of Case 3. Correspondingly, the pressure follows the general shape of the curve shown in figure 12, with its maximum value at the section P1Q1. 'This', Reynolds concludes, 'is the explanation of continuous lubrication. The pressure of the intervening film of fluid would cause a force tending to separate the surfaces.'

Ever practical, Reynolds then considers the question of a cylindrical surface, de-





veloping the detailed mathematics and comparing the implications with Tower's observations:

... The result of the whole research is to point to a conclusion (important in Natural Philosophy) that not only in cases of intentional lubrication, but wherever hard surfaces under pressure slide over each other without abrasion, they are separated by a film of some foreign matter, whether perceivable or not. And that the question as to whether this action can be continuous or not, turns on whether the action tends to preserve the matter between the surfaces at the points of pressure, as in the apparently unique case of the revolving journal, or tends to sweep it to one side, as is the result of all backwards and forwards rubbing with continuous pressure ...

An interesting postscript to this giant among Reynolds's papers is provided by paper 67 (1899), the final one which he read to the Manchester Literary and Philo- sophical Society. This is entitled 'On the slipperiness of ice'. In it he proposes that an explanation of the phenomenon is afforded by the ideas on lubrication contained in paper 52.

Visualization of the internal motion of fluids

In 1893, we find Osborne Reynolds with an established reputation presenting an interesting and authoritative discourse to the Royal Institution (paper 61) on an experimental technique which he had put to very good use earlier, namely, 'Study of fluid motion by means of coloured bands'. In this he demonstrated many examples of the internal motion of fluids. At the outset of the address he produced a box with a hinged door on one side and a circular aperture on the one opposite. This he used to project invisible vortex rings of air in the direction of balloons suspended in the lecture theatre and exclaimed:

Now I will ask you to look at these balloons. They are familiar objects enough, and yet they are most sensitive anemometers, more sensitive than anything else in this room; but even they do not show any motion; each of them forms an internal bounding surface of the air. I send an aerial messenger to them, and a small but energetic motion is seen by which it acknowledges the message, and the same message travels through the rest, as if a ghost touched them. It is a wave that moves them. You do not feel it, and, but for the surfaces of the air formed by the balloons, would have no notion of its existence.

He then repeated the experiment but added smoke to the vortex-generating box:

I will now fulfil my promise to reveal the silent messenger I sent to those balloons. The messenger appears in the form of a large smoke ring, which is a vortex ring in air rendered visible by smoke instead of colour ... These are, if I may say so, the phenomenal instances of internal motion of fluids. Phenomenal in their simplicity, they are of intense interest, like the pendulum, as furnishing the clue to the more complex. It is by the light we gather from their study that we can hope to interpret the parallel of the vortex wrapped up in the wave, as applied to the wind of heaven, and the grand phenomenon of the clouds, as well as those things which directly concern us, such as the resistance of ships.




68 J. D. Jackson

4.2. Reynolds the engineer

(i) Papers on applied fluid dynamics and hydraulics (1872-1894) Osborne Reynolds had developed an interest in problems connected with the dy-

namics of ships, particularly screw steamers, a number of years before coming to Manchester, probably dating back to his apprenticeship with Edward Hayes at Stony Stratford. This further parallel stream of research led to publications in the Trans- actions of the Institution of Naval Architects and later to a long involvement in work concerned with the safety of ships. Much of the work was carried out under the auspices of a specially formed committee of the British Association for the Advance- ment of Science which included, among others, Kelvin, Froude and Rayleigh, and for which Reynolds produced a series of important lengthy reports. His attention later turned to waves and currents and the laws relating the scaling of experiments to study flow in rivers, estuaries and foreshores. A further series of reports for the British Association followed.

Ship propulsion and dynamics The first fruits of the interest in ships inculcated at Stony Stratford were his

publications in 1873 and 1874 on the racing of screw propellers (papers 9 and 14). By showing this to be the result of the admission of air Reynolds was among the first to recognize the important influence which air can exert on a mass of water in which it is dissolved or occluded. From his studies, he deduced that it is more important to ensure that a propeller is sufficiently submerged than to increase its diameter and that it seemed likely that some of the advantage of twin screws was derived from their depth of immersion being generally greater than that for a single screw.

The conclusions which he reached later colncerning the racing of screws and the steering of screw-steamers, paper 19 (1875), were largely based on pioneering experiments made with two models, one 2 feet 6 inches long driven by a spring and the other 5 feet 6 inches, driven by steam. He contended that

the reversing of the screw of a vessel with full way on very much diminishes her steering-power, ... so that where a collisiQon is imminent, to reverse the screw and use the rudder as if the ship would answer to it in the usual manner is a certain way of bringing about the collision'.

His model experiments indicated, moreover, that the influence of reversing the screw to turn the vessel independently of her rudder was most pronounced when the screw was not deeply submerged.

Reynolds went so far as to suggest, paper 26 (1876), that models in the form of steam-launches should be used for training navel officers in the manoeuvring of ships. This proposal was not adopted, but Reynolds's views had aroused so much interest and concern that the British Association appointed a committee, with Reynolds as Secretary, to collect and examine evidence concerning the steering qualities of steamships. In addition to having tests made on actual ships, the Committee received reports from ships' masters who had carried out similar experiments on their own merchant vessels. Reynolds produced three detailed reports for the Committee on this work (papers 28, 32 and 37). In their 1878 Report, the British Association Committee affirmed that 'the conclusions drawn by Professor Reynolds from experiments on models have been fully confirmed by the experiments on full-sized ships'.

Reynolds returned to the subject of ship-models some years later after a disaster





4 B

Figure 13. Diagram illustrating flow through a multi-stage hydraulic machine.

had occurred with the St. Annes and Southport lifeboats. Within a week of this tragic occurrence, he read his paper 'On methods of investigating the qualities of lifeboats' to the Manchester Literary and Philosophical Society, paper 54 (1886), in which he urged that scale-models should be used to test the sea-going qualities of lifeboats.

Pumps and turbines

From the dynamics of ships we turn next to the development of hydraulic machinery and in particular pumps and turbines. In matters of innovation and invention Reynolds was never motivated by financial gain and it is doubtful whether he ever had any monetary reward from any of his inventions. He did, however, take out a number of patents. These are listed in the appendix to this paper. The patent for 'improvements in turbines and centrifugal pumps', the specification for which is dated 1875, is reprinted as paper 20 in Volume I of the Collected Works. It reads, in many respects, like a research-paper and at the same time demonstrates Reynolds's great powers as an engineer and inventor.

His proposal envisaged the use of a succession of stages, such that:

on emerging from the moving passages the fluid shall not, as in the case of the ordinary turbine, have spent the whole or nearly the whole of its available pressure, but that it shall still have sufficient pressure to carry it through one or more additional sets of passages ... that is to say, on emerging from the first moving passages, it shall again be received into other fixed passages, so that on being forced through them it shall emerge with a velocity of whirl or rotary motion round an axis - not necessarily the same as before - with a reduced pressure, and again be received into another set of moving passages from which it may emerge with no velocity of whirl ... On emerging from the last set of passages the fluid will be allowed to flow away into such receptacle, channel or tail-race as may be provided'.

Reynolds describes how these sets of passages may be arranged side by side as in a parallel (axial) flow turbine or one set within the other in radial fashion. Figure 13 is taken from his specification which goes on to state that the inverse arrangement could serve as a multi-stage centrifugal pump and that the invention 'applies to all fluids, liquids, vapours and gases.' He further incorporated the idea of guide-vanes and divergent passages surrounding the impeller of a centrifugal pump for the improved recovery of dynamic head and the concept of movable gulde-vanes for regulating the inflow to water turbines.

The first multi-stage, or 'turbine pump' as it is rather ambiguously described, was




70 J. D. Jackson

successfully installed in Reynolds's own laboratories. Prototypes of his pumps and turbines are on display in the exhibition referred to earlier.

A. H. Gibson (1946) has pointed out that in his 1875 patent specification, Reynolds anticipated both the multi-stage turbine of the Parsons type and the turbine with opposite rotation of the two elements as in the Ljungstrom turbine. About this time (1875-1876), Reynolds did in fact experiment with a two-stage small radial-flow steam turbine with a wheel-diameter of 6 inches which ran at 12 000 revolutions per minute. While it worked successfully, its consumption of steam was high, probably because of relatively large losses between the blades and the casing.

Modelling of rivers and estuaries

1887 marked another of Reynolds's pre-eminent contributions. In that year he addressed the Manchester meeting of the British Association 'On certain laws relating to the regime of rivers and estuaries, and on the possibility of experiments on a small scale' (paper 55).

Reynolds's first scale model was of the Mersey and covered the region between Liverpool Narrows and a point some distance below Runcorn; it had a flat bed and vertical sides representing the shape of the estuary at high tide; the horizontal scale was 2 inches to a mile (1/31800) and the vertical scale 1 inch to 80 feet (1/960), giving a vertical exaggeration of approximately 33:1. Tides were generated by a hinged tray at the seaward side of the model. Reynolds noticed that only one period - about 40 seconds - gave a correct imitation of the tidal phenomena in the actual Mersey: 'a result', he says,

that might have been foreseen from the theory of wave motions, since the scale of velocities varies as the square roots of the scales of wave heights, so that the velocities in the model which would correspond to the velocities in the channel would be as the square roots of the vertical scales ... and the ratios of the periods would be the ratio of horizontal scales divided by this ratio of velocities.

Reynolds had, therefore, established the rule that if the horizontal scale is 1/x and the vertical scale is 1/y, the logical corollary is that the velocity-scale should be 1/V/y and the timescale for tidal periods V/y/x. This was a major advance and opened up great possibilities for modelling flow in rivers and estuaries.

In addition Reynolds astutely observed that his tide-generator also accurately shaped the sand he had placed in the model (to ensure the correct mean depth of water at high tide) to mirror the principal features of the natural estuary.

As a direct consequence of this he produced a larger version with a horizontal scale of 6 inches to a mile (1/10560) and a vertical scale of one inch to 33 feet (1/396) which underwent 6000 tides. This model he showed to the British Association alongside charts of the real estuary and invited fellow members to note the 'remarkable resemblance in the general features to the charts of the Mersey.' Reynolds went on:

From my present experience in constructing another model, I should adopt a somewhat greater exaggeration of the vertical scale. In the meantime I have called attention to these results, because this method of experimenting seems to afford a ready means of investigating and determining beforehand the effects of any proposed estuary or harbour works; a means which, after what I have seen, I should feel it madness to neglect before entering upon any costly undertaking.

So strong was the evidence presented by Reynolds that the British Association





____ .

~~~~~~~~~~~~ i~~~~~~~~~~~~~~~~~~~t

14~ ~~~44-4--4H-

_ II./ "P1PV AU

Figure 14. Bed formation and other features of models of estuaries.

Proc. R. Soc. Lornd. A (1995)



72 J. D. Jackson

Figure 15. Apparatus to demonstrate the boiling of water at ordinary temperature: cavitation.

immediately acted to establish a committee to investigate the action of waves and currents on the beds and foreshores of estuaries by means of working models. The research was planned and carried out by Reynolds in the Whitworth Engineering Laboratory at Owens College, and three Reports were issued, papers 57, 58 and 59 (1889, 1890, 1891). These were written by Reynolds himself and described in great detail the experiments made on model estuaries of hypothetical shape: rectangular, V-shaped, and V-shaped with straight tidal rivers added at the upper ends. Figure 14 gives some idea of the bed formation and other features of one of these models.

Cavitation

To conclude this review of Reynolds's work on hydraulics we come to a short paper presented at a meeting of the British Association at Oxford entitled 'Experiments concerned with the boiling of water in an open tube at ordinary temperatures', paper 63 (1894). The paper begins with a description of the processes involved in the boiling of water by heating it. However, it is really about the phenomenon of cavitation, a common problem in hydraulic machinery involving the production of vapour bubbles in flowing water as a result of the pressure being reduced locally to the point where nucleation occurs.

In experiments exhibited at the meeting he used a glass tube of internal diameter half an inch and length six inches drawn down to a neck in the middle, something less than a tenth of an inch bore. Coupling one end of this to the water main and inclining the open end downwards into a vessel filled with water (see figure 15), he proceeded to turn on the water very slowly so as to fill the tube, then increased the flow until at a particular velocity a distinct sharp hiss was heard. Reynolds described the situation thus:

as the bubbles of air and vapour would be carried with great velocity from the low pressure at the neck, where they formed, into the higher pressure in the wider portion of the expanding tube; so that the pressure being greater than the vapour tension, condensation would ensue and the bubbles would collapse

Nowhere in the paper does Reynolds use the word 'cavitation', yet both here and in his investigation of the racing of screw propellers, he was patently demonstrating his understanding of it.





(ii) Papers on heat transfer and thermal power (1873-1897)

This area of work interested Osborne Reynolds throughout his career. There can be no doubt that the presence in Manchester of the eminent scientist Joule was an important influence at the outset. To this can be added the influence of Rankine, whose texts Reynolds frequently referred to.

Reynolds's early contributions on the effect of air on the rate of condensation of steam at a su:rface and on the extent and action of heating surfaces for steam boilers were followed after a gap of about ten years by detailed studies on the steam engine indicator and trials on a large triple expansion steam engine, culminating in 1897 in a classical experiment using that equipment to determine the mechanical equivalent of heat. The later studies highlight Reynolds's outstanding practical ability and his interest in experimentation using full scale engineering plant. His papers are to be found in both Volumes I and II of the Collected Works. Some were published by the Institution of Civil Engineers and others by the Royal Society.

Condensation of steam

In Paper 10 (1873) Reynolds states that he was interested to discover 'how far the presence of a small quantity of air affects the power of a cold surface to condense steam.' The means by which he did so were characteristically simple. The equipment consisted of a glass flask in which a 'surface condenser' took the form of a copper pipe passing in and out of the cork. Water was forced through the pipe to keep it cool. From experiments using this apparatus Reynolds deduced that, while there is no limit to the rate at which pure steam will condense but the power of the surface to carry off the heat, the rate of condensation diminishes rapidly as the quantity of air present increases. He concludes:

that in consequence of this effect of air it is necessary for the size of a surface- condenser for a steam-engine to increase very rapidly with the quantity of air allowed to be present within it; ... and that by mixing air with the steam before it is used, the condensation at the surface of a cylinder may be greatly diminished, and consequently the efficiency of the engine increased.

Analogy between heat transfer and momentum transfer

In 1874 (some nine years before the appearance of the famous paper on laminar and turbulent flow) Reynolds produced a short and farsighted paper, 'On the extent and action of the heating surface of steam boilers', in which he pointed out that heat is removed from such a surface not only through molecular action but also by the turbulent eddies present in the flow which mix hotter fluid with cooler fluid. He argued and demonstrated experimentally that if hot gas flowed at sufficiently high speed through a tube, the temperature of which was maintained constant, the temperature of the gas emerging from the end of the tube would be sensibly independent of any further increase of speed. This effect he related to the fact that under such conditions the resistance to flow is sensibly proportional to the square of the velocity, thereby inferring an analogy between heat-transfer and skin-friction. Almost half a century was to pass before these ideas were taken up and the analogy extended by later authorities such as Taylor, Prandtl and von Kairmain.




74 J. D. Jackson

Thermodynamics and heat and work

In an address entitled 'On the general theory of thermo-dynamics' delivered to the Institution of Civil Engineers in November 1883 (paper 47), Reynolds began by amusingly acknowledging the challenge he faced:

In lecturing on any subject, it seems to be a natural course to begin with a clear explanation of the nature, purpose, and scope of the subject. But in answer to the question 'What is thermo-dynamics?' I feel tempted to reply 'It is a very difficult subject, nearly, if not quite, unfit for a lecture'.

Reynolds then proceeded to describe what he saw as the real difficulty in the appreciation of thermo-dynamics:

It deals with a thing or entity (if I may so call heat) which, although we can recognise and measure its effects, is yet of such a nature that we cannot with any of our senses perceive its mode of operation.

To assist his audience in understanding the ideas involved he went on later to use a simple mechanical contrivance to demonstrate the problem of converting heat into work. It is indicative of his approach that not a single equation or even a mathematical symbol appears anywhere in his paper.

Thermodynamics of gas flow

In a paper read before the Manchester Literary and Philosophical Society in November 1885 (paper 53), Reynolds considered the thermodynamics of fluid flow in the case of a gas or vapour discharging from one vessel into another through an orifice or nozzle. He called attention to the fallacy of the assumption that the pressure in the receiving vessel is the same as that at the orifice, and went on to consider the observation that the rate of flow was only affected by the pressure in the receiver if that were greater than about half of the pressure in the upstream vessel. Moreover, he established that the reason for this lay in the fact that a limit to the flow is reached when the velocity at the orifice becomes equal to the velocity of sound at that point.

Steam enrgine trials

In Paper 56 read to the Institution of Civil Engineers in December 1889, Reynolds described with some pride the large triple-expansion steam engine which had been installed under his close supervision in the Whitworth Engineering Laboratory at Owens College (see figures 16 and 19). Characteristically, Reynolds ensured that this new test facility was extremely flexible. The engine could be operated as a triple- expansion condensing engine or run in a variety of other ways.

In his address he defined the purpose of the engines as two-fold; (i) to afford students practice in making the many measurements involved in steam engine trials, to give them an insight into the action of the steam and the mechanical components and to familiarize them with good design; (ii) to supply a means of research by which the knowledge of the steam-engine could be extended.

The detailed design and the construction of the engines and the boiler were undertaken by Messrs Mather and Platt, whose 'zeal and liberality' Reynolds gratefully acknowledged. It was decided to have the three engines on separate brakes and that these should be hydraulic devices rather than ones dependent on mechanical friction.

William Froude had earlier developed a radically new design for a compact hy-





Scal ev t$

Figure 16. Section of the steam engine.




76 J. D. Jackson

Figure 17. Dynamometer details.

draulic brake for determining the power of large engines. Accordingly, Reynolds tested a 4 inch diameter model of the new design. He found that when the speed exceeded a certain limit, the brake partially emptied itself of water and the resistance correspondingly decreased. To overcome this defect, Reynolds had radial holes drilled through the metal of the fixed vanes in such a way as to maintain the water in the brake at atmospheric pressure or above it under all conditions of operation. Having tested this idea out using his model, Reynolds adopted it successfully on the 18 inch wheels which became the hydraulic brakes for his three-cylinder steam engine. The dynamometer is illustrated in figure 17.

Determination of the mechanical equivalent of heat

As a result of these efforts Reynolds had brought into being a large-scale apparatus suitable for the most accurate determination yet of Joule's mechanical equivalent of heat. Reynolds recognized that the attraction lay not only in the magnitude of the quantities to be measured but also in the possibility of using two physically fixed points of temperature by measuring the quantity of work required to heat a known mass of water from freezing point to boiling point. This could be achieved by feeding water continuously at freezing temperature to the brake in which the internal fluid friction would heat it to boiling point.

This classic investigation was described in great detail in paper 66, the Bakerian Lecture to the Royal Society in May 1897. The apparatus is shown in figure 18. Figure 20 shows the brake and some associated equipment. One of the striking features of the study is the thorough consideration given to the circumstances which might affect the accuracy of the results. Twenty five possible sources of error are tabulated, together with an assessment of the limits of relative errors to which they could give rise.





IA= ~~~~~~~~~I

Figure 18. Apparatus to measure the mechanical equivalent of heat.

Five years earlier, in 1892, Reynolds had produced a brilliant biography for the Manchester L,iterary and Philosophical Society simply entitled 'Memoir of James Prescott Joule' (Reynolds 1892), but his re-determination of the mechanical equivalent of heat perhaps represented the ultimate tribute Reynolds was able to pay to him.

(iii) Papers on the dynamics of machines and the mechanics of materials (1872-1902)

This lesser known side of Reynolds's work encompassed a wide variety of topics mainly of a rather practical nature. These include: elasticity and fracture; properties of steel; stress concentration; inertial forces and stresses; friction; slipping of belts and straps; rolling friction; vibration measurement; and last but not least, the fatigue of materials subjected to repeated loading. We do not have to look far to detect the incentive for such work. In the city of Manchester Reynolds was surrounded by intensive mechanical engineering activity with all its attendant problems.

A number of his papers on these themes were published in The Engineer. His pioneering work on rolling friction was presented to the Royal Society as was his collaborative work on repeated stresses and fatigue.

Rolling friction

In Paper 17 'On the efficiency of belts or straps as communicators of work' (1874), Reynolds explained the slipping of the strap used for a belt-drive between two pulleys. The elasticity of the belt caused the tight side to be stretched more than the slacker side and correspondingly the tight side had to move faster. Some months later, in the Philosophical Transactions of the Royal Society, paper 18 (1875), he




78 J. D. Jackson

Figure 19. Triple-expansion steam engine used in the measurement of the mechanical equivalent of heat.

extended this concept to a detailed study of rolling friction, arguing and demonstrating experimentally that, as in the case of endless belts over pulleys, there would be an 'analogous slipping when a hard roller rolls on a soft surfac'e or when an india- rubber wheel rolls on a hard surface'. He found that 'an iron roller rolled through something like three-quarters of an inch less in a yard when rolling on india-rubber than when rolling on wood or iron'. He proceeded to show that, whatever the nature of the materials, the deformation at the point of contact must cause slipping to occur, even though this would be difficult to measure with hard materials. In this way, he accounted for the resistance to the motion of a roller, and further explained the disquieting phenomenon of the scaling of wrought-iron railway rails as being a consequence of the slipping which attends the rolling.

Dynami'cs Of machi'nes

Reynolds's four articles in The Engi'neer (1881 1882) on the 'Fundamental limits to speed' (paper 41) remind us that what is common knowledge today was not at all clearly understood before he expounded it. He defines one limit to possible speeds as the limited strength of materials in relation to their weight, but also points to the fact that the properties of materials are essentially restricted in other respects, for example by the limited temperature at which a material retains its strength. He then

Proc. R. Soc. Lod. A. (1995)




part of the structure. Reynolds c ludes by refl g o. te pssi y o-.: ..........i.. .f. ....

.... . .. .. .. ... .. . ... .,.. ..

thegwhoe or0a portion ofei the movingemasest in ah locomotivel eqialnd point ouat.tat

whnier the preoblvn part mibayin bed cmlthel balanifoced, iet isipossible teipoachtieve

complete balance of the oscillating masses.

Repeated stresses and fatigute

Although rnot included among the Collected papers, an investigation of the fatigue of materials subjected to repeated stresses deserves notice as a contribution of some significance. The research was conceived by Reynolds and carried out in his laboratories. It is described in a paper with J. H. Smith published in the Philosophical Transactions of the Royal Society (Reynolds & Smith 1902).

5. Overview: Reynolds the pioneer

Osborne Reynolds's 37-year tenure at Owens College coincided with major changes in the scientific world, as the age of the gentleman-scientist and the self-taught devo- tee, embodied at its best in the form of Joule, gave way to that of the university- educated, research group leader such as Rutherford who took up his appointment in Manchester in 1907. Any overview of Reynolds's contribution must be made with this in mind together with the realization that the ever more refined specialization




80 J. D. Jackson

of today's complex science was a development that had scarcely started. The not unexpected consequence of this is that the range of Reynolds's interests and involve- ments has rather escaped general notice, and thus it is with a short summary of his achievements that I propose to conclude.

Firstly, although his name is not widely associated with the furtherance of the kinetic theory of gases, Reynolds's papers dealing with the communication of surface forces due to heating, taken together with his work on the transpiration of gases, ar- guably provided the first substantive experimental support for the ideas involved. If we add to this his detailed theoretical treatment of the problem of thermal transpiration, the contributions he made in the period 1874 to 1879 to the early advancement of the kinetic theory of gases were clearly of fundamental importance.

A classic example of Reynolds's pioneering work in a sphere far from that of turbulent flow are the two papers he produced on the dilatancy of granular materials, long acknowledged by practitioners of geotechnics but not so well known by those outside the field. The beautifully simple explanation of the mechanism involved in the property of dilatancy provided those working in soil mechanics with an understanding of the behaviour of granular materials which greatly assisted the subsequent development of this particular branch of engineering.

Nonetheless, it is within the field of fluid motion, and in particular, turbulent flow that Osborne Reynolds has received his fullest recognition from the scientific frater- nity. His success in identifying the fundamental dimensionless parameter which char- acterises the behaviour of flowing fluids was unquestioningly a pioneering achievement and is what many people regard as Osborne Reynolds's most valuable scientific legacy. Linked as it is to the stability of flow and the occurrence of turbulence, it is of immense importance. His development of a dynamical theory of turbulent flow coupled with the experimental work on the circumstances under which flow is laminar or turbulent have together provided the true foundations for the subsequent development of the subject. Indeed it is difficult to exaggerate the importance of Reynolds's achievement in engineering fluid mechanics.

Similarly, Reynolds's contribution to another aspect of fluid flow, namely hydrodynamic lubrication, has also had far-reaching consequences. His lengthy and detailed paper on this topic provided a theoretical basis for the understanding and design of bearings which 32 years later (in 1918) Lord Rayleigh felt able to assert 'includes most of what is now known on the subject'. Taken together, Reynolds's fundamental work on rolling friction and his theory of hydrodynamic lubrication provide ample justification for 'the claim that he was indeed the dominant figure in the evolution of the subject of Tribology' (Barwell 1969).

As we have seen, Reynolds's work in fluid mechanics was not merely confined to fundamental topics. His applied investigations into aspects of marine engineering and naval architecture had considerable impact in their own right. Reported as they were to a Committee of the British Association for the Advancement of Science composed of some of the most distinguished scientists and engineers of the day, Reynolds's conclusions concerning the propulsion and steering of ships had immediate and literally far-reaching consequences. His fundamental and innovative research into the modelling of water flow and sediment transport in rivers and estuaries has likewise had a profound effect, setting the scene for much of the work which has followed in this area.

However, for the earliest and perhaps the most directly practical of Reynolds's contributions we must turn to a little known publication entitled 'On sewer gas and





how to keep it out of houses' (Reynolds 1876) which first appeared in 1872. This could possibly be connected with his time in London at the offices of John Lawson where he was engaged on matters connected with a sewage system for Croydon. His short monograph is a handbook on house drainage which provides the reader with clear and detailed guidance on sanitary systems designed to isolate sewers from houses. A new preface written for the 1876 reprint offers an invaluable insight into its author's practical side:

The principal part of this book was written nearly four years ago. It has only been waiting in order that some suggestions it contains might have a thorough practical trial, and this being accomplished, it is now published in the hope that it may hell) those people who are in doubt and trouble with the drainage of their houses. It would be a public calamity if ... wide-spread alarm ... were allowed to subside without producing a beneficial effect; but there is danger that such will be the case, simply for the want of definite information as to what is amiss, and how it is to be set right.

The booklet rapidly went through four editions and undoubtedly Reynolds's pro- vision of 'definite information' had an important impact on subsequent practice.

In the world of engineering heat transfer and thermal hydraulics too, Osborne Reynolds must also be viewed as a pioneer. His very simple experiments on the effect of the presence of air on the condensation of steam had important contemporary implications for the design of engines. Today the topic remains one which occupies the attention of power engineers. Turning next to convective heat transfer, if we take Reynolds's short but extremely important paper on heat transfer in the boiler tubes of steam locomotives, which contains the essence of the analogy between heat transfer and fluid friction, and link it with his study of frictional pressure drop in tubes, we have the basis of the empirical equations currently used in thermal design. Moreover, his invaluable contribution to this field was not simply limited to his own efforts, for his student T. E. Stanton went on to have a major impact on the subject.

Again, if we consider Reynolds 'the inventor' then once more we are obliged to recognize a man who consistently went to the 'heart' of scientific matter. Nowhere is this better seen than in his 1875 patent, 'Improvements in apparatus for obtaining motive power from fluids and also for raising or forcing fluids'. Not only did his inno- vations provide ideas for the commercial multi-stage hydraulic pumps and turbines which subsequently came into widespread use, but they also led ultimately to today's steam turbines. The simple two-stage steam turbine which Osborne Reynolds designed and ran successfully in 1875 stands today in a showcase at the University of Manchester as a testament to this truly pioneering endeavour.

Reynolds's lifelong pursuit of scientific truth is particularly evident in his final contribution published in 1903 under the auspices of the Royal Society. His paper 'On the sub--mechanics of the Universe' in which he used his ideas on dilatancy to construct a mechanical theory of the ether was certainly a bold and ambitious one. It well illustrates the wide-ranging nature of his interests, his dedication to science and his confidence that the most fundamental of matters could ultimately be explained in simple mechanical terms. Figure 21 shows the very fine portrait of Osborne Reynolds painted by John Collier in 1904 which depicts him holding a tray containing a number of spheres, one of the illustrations used in his Rede lecture on the subject (Reynolds 1902). Sadly, the contents of this intriguing final paper proved




82 J. D. Jackson

_~~~~~~~~~~~~~~~~~~~ . .. _____,_. .... ... , _ . | , | | _ ~~~~~~~~~~~~~~~. ___. . _. . ......

! l 1|111

~~~~~. IEGSB z>x.................. - ,.,.'.. :.111111 _** *_

_ E _ _ _ __ se l _ sg~~~~~~~~~~~~~~~~

........................ .. .a :'''.Er::....E'B -

- l- - | - | i- -> B "B'':.B....................... ''.':''t.B'::0':B'.:'B"'.tE"g:a,........*..*. |

Figure 2 1. Portrait of Osborne Reynolds painted in 1904 by John Collier.

to be extremely difficult to appraise and the timing of its publication was such that the ideas contained in it were overtaken by events in the development of Physics. At the beginning of this paper I made reference to the excellent, but little known, paper by Professor Jack Allen on 'The Life and Work of Osborne Reynolds'. Professor Allen was the Principal Speaker at the International Symposium held in Manchester in 1968 to mark the centenary of the appointment of Osborne Reynolds to the Chair of Engineering at Owens College. In my capacity as Organising Secretary for the Centenary Symposium, I gave Professor Allen what help I could in gathering material for his lecture. In turn he gave me much encouragement in the course of the preparations for the Symposium. I recall with great pleasure the contact which I had with him at that time.

Professor Allen approached the task of preparing his lecture with great dedication and produced what remains today the authoritative work on the life and work of Osborne Reynolds. Jack Allen's paper has been of considerable help to me in the preparation of the present paper. I have made extensive use of his material and acknowledge this fact. I also acknowledge the very considerable assistance which I have had from Dr Ian Fishwick in researching material used in this paper and also in editing the final version. Finally, I also thank Linda Jefferies, Pei An and Malcolm Firth for their invaluable help in producing the manuscript and diagrams.

Proc. Rt. Soc. Lond. A (1995)




Appendix A. Original sources for the collected works

Paper 1. On the suspension of a ball by a jet of water. Manchester Literary and Philosophical Society, Memoirs, Series 3, Vol. 4, Session 1869-1870.

Paper 2. The -tails of comets, the solar corona, and the aurora, considered as electrical phenomena. Manchester Literary and Philosophical Society, Memoirs, Series 3, Vol. 5, Session 1870-1871.

Paper 3A. On cometary phenomena. Manchester Literary and Philosophical Society, Memoirs, Series 3, Vol. 5, Session 1871-1872.

Paper 3B. On an electrical corona resembling the solar corona. Manchester Literary and Philo- sophical Society, Memoirs, Series 3, Vol. 5, Session 1871-1872.

Paper 4. On the electro-dynamic effect which the induction of statical electricity causes in a moving body. This induction on the part of the sun a probable cause of terrestrial magnetism. Manchester Literary and Philosophical Society, Memoirs, Series 3, Vol. 5, Session 1871-1872.

Paper 5. On the electrical properties of clouds and the phenomena of thunder storms. Manchester Literary and Philosophical Society, Proceedings, Vol. 12, Session 1872-1873.

Paper 6. On the relative work spent in friction in giving rotation to shot from guns rifled with an increasing, and a uniform twist. Manchester Literary and Philosophical Society, Proceedings, Vol. 13, Session 1873-1874.

Paper 7. On the bursting of trees and objects struck by lightning. Manchester Literary and Philosophical Society, Proceedings, Vol. 13, Session 1873-1874.

Paper 7A. On t;he destruction of sound by fog and the inertness of a heterogeneous fluid. Manch- ester Literary and Philosophical Society, Proceedings, Vol. 13, Session 1873-1874.

Paper 8. On the effect of acid on the interior of iron wire. Manchester Literary and Philosophical Society, Proceedings, Vol. 13, Session 1873-1874.

Paper 9. The causes of the racing of the engines of screw steamers investigated theoretically and by experiment. Institution of Naval Architects, Trans., 1873.

Paper 10. On the condensation of a mixture of air and steam upon cold surfaces. Proceedings of the Royal Society, No. 144, 1873.

Paper 11. On the forces caused by evaporation from, and condensation at a surface. Proceedings of the Royal Society, No. 153, 1874.

Paper 12. On the surface-forces caused by the communication of heat. Philosophical Magazine, November 1874.

Paper 13. On the effect of immersion on screw propellers. Institution of Naval Architects, Trans., 1874.

Paper 14. On the extent and action of the heating surface of steam boilers. Manchester Literary and Philosophical Society, Proceedings, Vol. 14, Session 1874-1875.

Paper 15. On the action of rain to calm the sea. Manchester Literary and Philosophical Society, Proceedings, Vol. 14, Session 1874-1875.

Paper 16. On t;he refraction of sound by the atmosphere. Proceedings of the Royal Society, No. 155, 1874.

Paper 17. On the efficiency of belts or straps as communicators of work. The Engineer, Nov. 27, 1874.

Paper 18. On rolling friction. Philosophical Transactions of the Royal Society, Vol. 166, Pt. 1. Paper 19. On the steering of screw-steamers. British Association Report, 1875. Paper 20. Improvements in turbines and centrifugal pumps. Specification of Patent No. 724,

1875. Paper 21. On the unequal onward motion in the upper and lower currents in the wake of a

ship; and the effects of this unequal motion on the action of the screw-propeller. Institution of Naval Architects, Trans., 1876.

Paper 22. On the refraction of sound by the atmosphere. Philosophical Transactions of the Royal Society, Vol. 166, Pt. 1.

Paper 23. On the forces caused by the communication of heat between a surface and a gas; and




84 J. D. Jackson

on a new photometer. Philosophical Transactions of the Royal Society, Vol. 166, Pt. 2. Paper 24. On various forms of vortex motion. Manchester Literary and Philosophical Society,

Proceedings, Feb. 1877. Paper 25. On vortex motion. Royal Institution of Great Britain, Proceedings, Feb. 1877. Paper 26. On the investigation of the steering qualities of ships. British Association Report,

1876. Paper 27. On the rate of progression of groups of waves and the rate at which energy is trans-

mitted by waves. Nature, Vol. 16, Aug. 23, 1877. Paper 28. On the effect of propellers on the steering of vessels. British Association Report, 1877. Paper 29. On the manner in which raindrops and hailstones are formed. Manchester Literary

and Philosophical Society, Memoirs, Series 3, Vol. 6, Session 1876-1877. Paper 30. On the formation of hailstones, raindrops, and snowflakes. Manchester Literary and

Philosophical Society, Memoirs, Series 3, Vol. 6, Session 1877-1878. Paper 31. On the internal cohesion of liquids and the suspension of a column of mercury to

a height more than double that of the barometer. Manchester Literary and Philosophical Society, Memoirs, Series 3, Vol. 7, Session 1877-1878.

Paper 32. On the steering of screw steamers. Report of the Committee, consisting of James R. Napier, F.R.S., Sir W. Thomson, F.R.S., J.T. Bottomley and Osborne Reynolds, F.R.S. (Secretary), appointed to investigate the effect of Propellers on the Steering of Vessels. British Association Report, 1878.

Paper 33. On certain dimensional properties of matter in the gaseous state. Philosophical Trans- actions of the Royal Society, Pt. 2, 1879.

Paper 34. Note on thermal transpiration. (In a letter to Professor Stokes, Sec. R.S. Communi- cated by Professor G.G. Stokes.) Philosophical Transactions of the Royal Society, No. 203, 1880.

Paper 35. Some further experiments on the cohesion of water and mercury. Manchester Literary and Philosophical Society, Proceedings, Vol. 20, Session 1880-81.

Paper 36. On the bursting of the gun on board The Thunderer. Manchester Literary and Philo- sophical Society, Proceedings, Vol. 18, Session 1878-1879.

Paper 37. On the steering of ships. British Association Report, 1880. Paper 38. On the effect of oil in destroying waves on the surface of water. British Association

Report, 1880. Paper 39. On surface-tension and capillary action. British Association Report, 1881. Paper 40. On the floating of drops on the surface of water depending only on the purity of the

surface. Manchester Literary and Philosophical Society, Proceedings, Vol. 21, Session 1881- 1882.

Paper 41. On the fundamental limits to speed. 1, 11, III and IV. The Engineer, Oct. 28, 1881; Nov. 18, 1881; Dec. 9, 1881; March 17, 1882.

Paper 42. On the elementary solution of the dynamical problem of isochronous vibration. Manch- ester Literary and Philosophical Society, Proceedings, Vol. 22, Session 1882-1883.

Paper 43. The comparative resistances and stresses in the cases of oscillation and rotation with reference to the steam engine and dynamo', 1, 11, III and IV. The Engineer, Jan. 5, 1883; Jan. 19, 1883; Feb. 2, 1883; Feb. 16, 1883.

Paper 44. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Philosophical Transactions of the Royal Society, 1883.

Paper 45. The transmission of energy. 1, 11 and III. Society of Arts, Cantor Lectures, April 23, 1883; April 30, 1883; May 7, 1883.

Paper 46. On the equations of motion and the boundary conditions for viscous fluids, British Association, Section A, 1883.

Paper 47. On the general theory of thermo-dynamics. Institution of Civil Engineers, Proceedings, November 15, 1883.





Paper 48. On the two manners of motion of water. Royal Institution, Proceedings, March 1884.

Paper 49. On the theory of the steam-engine indicator. Joint paper with A.W. Brightmore, Institution of Civil Engineers, Proceedings, 1885.

Paper 50. On the dilatancy of media composed of rigid particles in contact. With experimental illustrations. Philosophical Magazine, December, 1885.

Paper 51. Experiments showing dilatancy, a property of granular material, possibly connected with gravitation. Royal Institution, Proceedings, February 12, 1886.

Paper 52. On the theory of lubrication and its application to Mr Beauchamp Tower's experiments, including an experimental determination of the viscosity of olive oil. Philosophical Transactions of the Royal Society, Pt. 1, 1886.

Paper 53. On the flow of gases, Philosophical Magazine, March 1886.

Paper 54. On methods of investigating the qualities of lifeboats. Manchester Literary and Philo- sophical Society, Proceedings, Vol. 26, Session 1886-1887.

Paper 55. On certain laws relating to the regime of rivers and estuaries, and on the possibility of experiments on a small scale. British Association Report, 1887.

Paper 56. On the triple-expansion engines and engine-trials at the Whitworth Engineering Lab- oratory, Owens College, Manchester. Instittution of Civil Engineers, Proceedings, 1889-1890.

Paper 57. Report of the committee appointed to investigate the action of waves and currents on the beds and foreshores of estuaries by means of working models. British Association Report, 1889.

Paper 58. Second report of the committee appointed to investigate the action of waves and currents on the beds and foreshores of estuaries by means of working models. British Association Report, 1890.

Paper 59. Third report of the committee appointed to investigate the action of waves and currents on the beds and foreshores of estuaries by means of working models. British Association Report, 1891.

Paper 60. On two harmonic analyzers. Manchester Literary and Philosophical Society, Memoirs and Proceedings, Series 4, Vol. 4, Session 1890-1891.

Paper 61. Study of fluid motion by means of coloured bands. Royal Institution, Proceedings, June 2, 1893.

Paper 62. On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Philosophical Transactions of the Royal Society, 1895.

Paper 63. Experiments showing the boiling of water in an open tube at ordinary temperatures. British Association, Section A, 1894.

Paper 64. On the behaviour of the surface of separation of two liquids of different densities. Manchester Ltterary and Philosophical Society, Memoirs and Proceedings, Series 4, Vol. 9, Session 1894-1895.

Paper 65. On nmethods of determining the dryness of saturated steam and the condition of steam gas. Manchester Literary and Philosophical Society, Memoirs and Proceedings, Vol. 41, Pt. 1, Session 1896-1897.

Paper 66. Bakerian Lecture. On the mechanical equivalent of heat. Joint paper with W. H. Moorby. Philosophical Transactions of the Royal Society, London, 1897.

Paper 67. On the slipperiness of ice. Manchester Literary and Philosophical Society, Memoirs and Proceedings, Vol. 43, Session 1898-1899.

Appendix B. Patent specifications by Professor Osborne Reynolds

No. 1878, dated 2nd July 1870. Improvements in machinery for propelling ships or vessels.

No. 724, dated 27th February 1875. Improvements in apparatus for obtaining motive power from fluids and also for raising or forcing fluids.

No. 9603, dated 7th July 1887. Improvements in friction clutches.

No. 9604, dated 7th July 1887. Improvements in yielding couplings for rotating shafts.




86 J. D. Jackson

No. 10482, dated 28th July 1887. Improvements in hydraulic or liquid brakes for causing and measuring resistances on rotating shafts.

No. 781227, dated 31st January 1905. United States Patent Office. Packing for pistons.

References

Allen, J. 1969 The life and work of Osborne Reynolds. Paper no. 1, Proc. Osborne Reynolds Centenary Symposium, Manchester. In Osborne Reynolds and engineering science today (ed. D. M. McDowell & J. D. Jackson). Manchester University Press.

Barwell, F. T. 1969 The founder of modern tribology. Paper no. 10, Proc. Osborne Reynolds Centenary Symposium, Manchester. In Osborne Reynolds and engineering science today (ed. D. M. McDowell & J. D. Jackson). Manchester University Press.

Gibson, A. H. 1946 Osborne Reynolds and his work in hydraulics and hydrodynamics. Published by Longmans Green, for the British Council.

Reynolds, 0. 1868 The progress of engineering considered with respect to the social conditions of this country. Cambridge: Macmillan.

Reynolds, 0. 1876 Sewer gas and how to keep it out of houses - a handbook on house drainage, 3rd edn. London: Macmillan.

Reynolds, 0. 1892 Memoir of James Prescott Joule. Mem. Proc. Manc. Lit. Phil. Soc., 4th Series, vol. 6.

Reynolds, 0. 1900 Papers on mechanical and physical subjects 1870-1880. Collected Works, vol. I. Cambridge University Press.

Reynolds, 0. 1901 Papers on mechanical and physical subjects 1881-1900. Collected Works, vol. II. Cambridge University Press.

Reynolds, 0. 1902 On an inversion of ideas as to the structure of the Universe. Rede Lecture, 10th June 1902. Cambridge University Press.

Reynolds, 0. 1903 Papers on mechanical and physical subjects - the sub-mechanics of the Universe. Collected Works, vol. III. Cambridge University Press.

Reynolds, 0. & Smith, J. H. 1902 On a throw-testing machine for reversals of mean stress. Phil. Trans. R. Soc. Lond. A 199, 265.




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