September 15, 1898] 



NATURE 



467 



LETTERS ^ TO THE EDITOR 



The Editor does not hold himself responsible for opinions ex- 

 pressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymous communications,']. 



Flow of Water Shown by Colour Bands. 

 I SHALL be obliged if you will publish, as soon as possible, 

 the enclosed correspondence under the heading given above. 

 Osborne Reynolds. 

 28 Marine Terrace, Criccieth, N.W. 

 Copy. 



September 2, 1898. 

 Dear Osborne Reynolds.— I do not know whether you 

 are going to the British Association at Bristol. In any case you 

 may like to have the enclosed. 



I am just re-reading the Royal Institution discourse you ^yere 

 kind enough to send me some time ago, and from several things 

 I see in it, I am sure you would like to see Prof. Stokes' proof, 

 especially in view of the doubt you had at one time as to the 

 distance at which viscosity would dominate the flow. 



I enclose a photograph which will give you an idea of the 

 sort of effects obtained with glycerine. 



Yours truly, 

 Prof. Osborne Reynolds, F.R.S. H. S. Hele-Shaw. 



Dear Prof. Hele-Shaw,— I have to thank you for your 

 letter of the second inst., and the copy of Sir George Gabriel 

 Stokes' paper " On the viscous flow between parallel surfaces." 

 I think it was in June 1896 that you asked me to show you 

 the appliances and experiments, which I have introduced during 

 the last twenty-five years, for studying and demonstrating the 

 manners of motion of water by the method of colour bands, 

 which I introduced in 1875, in order that you might have 

 similar demonstrations introduced at University College, to 

 which request I had great pleasure in responding as far as your 

 time would allow. I was glad when I heard shortly afterwards 

 from you that you had already begun experimenting, and I had 

 great pleasure in furnishing (you with copies and references to 

 all my publications bearing on the subject, as well as any verbal 

 information I could give you in several interviews. When, 

 however, you sent me a copy of a paper you proposed to read, 

 and subsequently read, before the Institution of Naval Architects, 

 being deeply engaged in other work, I felt it necessary to put 

 it aside, and this I did with less reluctance as I felt that any 

 criticism suggested by experience would tend to discourage 

 rather than to encourage you in your work, which reason I gave 

 shortly afterwards on your pressing me for an opinion, and in 

 this opinion I remained until this last summer, when the widely 

 published and striking photographs were brought before me in 

 so many ways as to force my attention in spite of my reluctance. 

 I then apprehended for the first time the method you had 

 employed as described in your first paper, and the conclusion 

 you had formed from results you had obtained by this method ; 

 which conclusion, I see from your last letter, you still maintain, 

 namely, that with water in sinuous motion and air bubbles as 

 indices of the manner of motion, the light bands adjacent to the 

 surfaces of the solids, which show absence of bubbles adjacent 

 to the solid, prove that the, once air charged, water has not 

 been carried by sinuous motion sufficiently near to the solid 

 surface to displace the initially adjacent water ; and hence 

 prove that the sinuous motion does not extend up to the solid 

 surface. 



With this conclusion I am entirely unable to agree for reasons 

 which are as follows : — 



(i) The photographs show that the air-clear bands adjacent 

 to the solid surfaces are in a sense permanent ; that is to say, 

 these bands do not get thinner and ultimately vanish as the 

 experiment is continued even when the solid surface is dis- 

 continuous fore and aft, and that the light bands on the sides of 

 the object are thicker at the bows than at the stern, which facts 

 cannot be explained by the maintenance of initial water, for 

 when water meets the bow of a solid, over the surface of which 

 it flows, no matter how slow and steady the current, the water 

 initially at any point near the surface will be drifted back 

 parallel to the surface with a velocity, if the motion is not 

 sinuous, diminishing to nothing at the surface. As, then, at 

 the bow, there is no water which has been initially adjacent to 

 the surface available to replace that which is swept back, the 



NO. 1507, VOL. 58] 



bow first becomes cleared of initial water. Then as the supply 

 of initially adjacent water swept back from the bow to replace 

 that swept back further along diminishes, the thickness of the 

 initial layer becomes taper from nothing at the bow to the 

 original thickness at the stern, and then, if the experiment 

 continues steadily, thins down till it becomes indefinitely thin. 



This is an experimental result which I have demonstrated 

 many times since first doing so before Section A at the Glasgow 

 meeting, 1876. All that is necessary is to surround a solid 

 object in a tank of clean water with coloured water, so that the 

 surface of the solid is coated with a sufficiently thin coat of 

 coloured water of the same density as the clear water, and thus 

 keeping the solid fixed, causes the water to flow uniformly 

 through the tank, when, if the velocity is below the critical 

 velocity, the gradual waste of the colour, commencing at the 

 bows, will at once be apparent, at rates proportional to the 

 velocity of flow, which may be such it takes seconds or many 

 minutes for the colour to disapjjear from the surface. 



In this experiment, if the velocity of flow be above the 

 critical velocity so that the motion is sinuous, the manner of 

 removal of the colour is very different, and the rate of removal 

 indefinitely enhanced, so that it seems as though it had been 

 removed with a rough brush. It is thus seen that the mainten- 

 ance of a layer of any finite thickness on the surface of a 

 discontinuous solid over which water is flowing is contrary to 

 well-established experience, and hence cannot account for the 

 clear bows observed in the photographs of the experiments 

 with air. 



While the manner of the removal of the colour from the 

 surface when the motion is sinuous proves that the sinuous 

 motion does extend up to the solid surface. 



(2) The use of air bubbles for the purpose of indicating the 

 lines of fluid motion is setting aside the most elementary pre- 

 cautions. Unless the indicating body, whether solid or liquid, 

 is of the same density as the fluid, the motion of which has to 

 be examined, although it will drift with the fluid, will besides 

 this motion of drift have a proper motion of its own through the 

 fluid, which may be simply that resulting from gravitation, as 

 in the case of a fluid in steady uniform motion, but which, in 

 the case of a fluid of more irregular motion, will also result from 

 the varying pressure in the fluid owing to its varying motion. 

 This varying motion impressed on the body by the drift of the 

 fluid causing it to move towards the higher pressure if denser 

 than the fluid, and if lighter towards the lower pressure. Now, 

 air bubbles form about the lightest bodies possible, and are thus 

 those best calculated, by their motion through the fluid across 

 the lines of motion, to seek out and indicate the positions at 

 which the pressure in the fluid are least. In this way they have 

 performed a very useful part in the study of fluid motion. It 

 was from the observation of the behaviour of air bubbles in the 

 wake of a vane moving obliquely through water that I was 

 enabled to study the action of the screws of steamships, and to 

 determine the cause of their racing. A most emphatic part 

 they have played is that of indicating the line of minimum 

 pressure in a vortex or vortex ring in water— a part which 

 was, I feel sure, emphasised in the demonstration I gave at the 

 College. 



It is thus seen, that while air bubbles are the most misleading 

 bodies that can be possibly chosen to indicate the lines of motion 

 in a fluid in sinuous motion, they are the very best to indicate 

 the lines and surfaces of mininum pressure, and by their absence 

 to indicate the positions in which pressure is greatest. Whence 

 it naturally follows that when the bubbles introduced in a 

 sinuous stream of fluid shun any specific positions in the fluid, 

 whatever may be the cause, the pressure in those parts are 

 greater than the pressures in the immediately surrounding 

 parts. 



Thus the conclusion to be drawn from the general existence 

 of light-bands adjacent to the solid surface over which the fluid 

 is flowing, as shown in the photographs, in sinuous motion 

 would, if there were no other proof of it, be that they afford 

 evidence that the pressure of water at the solid boundaries of 

 water in sinuous motion is a maximum, and diminishes rapidly 

 with the distance from the surface. As it is, however, it must 

 stand as an interesting verification of a well-established deduc- 

 tion from the laws of motion. For although probably but little 

 known, the existence of this maximum pressure at the boundaries 

 of fluid in sinuous motion, is one of the most direct conclusions 

 from the laws of motion, as I have shown in my paper on the 

 dynamical theory of a viscous fluid .(/%//. Trans. R.S., 1895, 

 p. 142). 



