90 



NA TURE 



\_May 



1884 



jhfNow one of the most noticeable facts in experimental hydro- 

 dynamics is the difference in the way in which water flows along 

 contracting and expanding channels. Such channels are now 

 projected on the screen, surrounded and filled with clean, still 

 water. The mouth of the tube at which the water enters is 

 wide ; the tube then contracts for some way, then expands ag tin 

 gradually until it is as wide as at the mouth. At present nothing 

 is to be seen of what is going on. On colouring one of the ele- 

 mentary streams, however, outside the mouth, a colour-band is 

 formed. This colour-band is drawn in with the surrounding 

 water, and shows what is going on. It enters quite steadily, 

 preserving its clear streak-like character until it has reached the 

 neck, where convergence 1 eases ; then on entering the expanding 

 channel it is altogether broken tip into eddies. Thus the motion 

 is direct and steady in the contracting tube, sinuous in the 

 expanding. 



The theory of hydrodynamics affords no clue to the cause of 

 this difference, and even as seen by the method of colour-bands 

 the reason for the sinuous motion is not obvious. If the current 

 be started suddenly at the first instant, the motion is the same in 

 both parts of the channel. Its changing in the expanding pipe 

 seemed to imply that there the motion is unstable. If this were 

 so, it ought to appear from the theory. I am ashamed to think 

 of the time spent in trying to make this out from the theory 

 without any result. I then had recourse to the method of colour 

 again, and found that there is an intermediate stage. 



When the tap is first opened, the immediately ensuing motion 

 is nearly the same in both parts ; but, while that in the con- 

 tracting tube maintains its character, that in the expanding 

 changes its character: a vortex ring is formed which, moving 

 forwards, leaves the motion behind that of a parallel stream 

 through the surrounding water. When the motion is sufficiently 

 slow, the stream is stable, as already explained; there is then 

 direct motion in both the contracting and expanding portions of 

 the tube, but these are not similar, the first being a faggot of 

 similar elementary contracting streams, the latter being that of 

 one parallel stream through surrounding fluid. The first is a 

 stable form, the second an unstable, and on increasing the 

 velocity the first remains, while the second breaks down, and, as 

 before, the expanding tube is filled with eddies. This experi- 

 ment is typical ofa large class of motions. Whenever fluid flows 

 through a narrow neck, as it approaches the neck it is steady, 

 after passing the neck it is sinuous. The same is produced by 

 an obstacle in the mid. lie of a stream, and virtually the same 

 by the motion of a solid through the water. 



The objei 1 proji 1 ted on the screen is not unlike a ship. Here 

 the ship is fixed and the water (lowing past it, but the effect 

 would lie the same Here the ship moving through the water. In 

 the front of the ship the stream is steady, sm long as ii contrai ts, 

 until it has passed the middle ; you then see the eddies formed 

 as the streams expand again round the stern. It is thi 

 which account for the difference between the actual and theo- 

 retical i hips. 



It appears then that the motion in the expanding channel is 

 sinuous, because the only steady motion is that ofa stream 

 through still water. Numerous cases in which the motion is 

 sinuous may be explained in the same way, but not all. If we 

 have a parallel channel, neither contracting or expanding, the 

 steady moving streams will lie a faggot of steady parallel 1 Ii 

 streams all in motion hut having different velocities, those 111 the 

 middle moving the fastest. Here we have a stream but not through 

 standing water. When this invesl rot known 



whethei itch a stn tm was evei steady; but there was a well- 

 known anonialym the resistance encountered in parallel channels. 

 In rivers and all pipes of sensible sj ze experience had shown that 

 I as the square ol the \< lot ity, whereas in 

 very small pipes, such as represent the smaller \eins in animal-, 

 Poiseuille had provi d that the resistance increase.! a- tl 

 Thus since the resistance would be as the square of the velocity 

 with sinuous motion, and as the velocity in the case of direct 

 motion, it appeared that the discrepancy would be accounted foi 

 if it could be shown that the motion becomes unstable at suffi- 

 ciently large velocities according to the size of the pipe. This 

 has been done. You see on the screen a pipe with its end open. 

 It is surrounded by water, and by opening a tap I can draw the 

 water through it. This makes no difference to the appearance 

 until I colour one of the elementary streams, when you see a 

 beautiful streak of colour extend all along the pipe. So lai il. 

 stream has been running steadily, and il appears quite stable. 

 As the speed increases the colour-band naturally becomes finer, 

 but on reaching a certain speed the colour-band becomes unsteady 



and mixes with the surrounding fluid filling the pipe. fhi- 

 sinuous motion conies on at a definite velocity; diminish the 

 velocity ever so little, the band becomes straight and clear, in- 

 crease it again and it breaks up. This critical speed depends 

 on the size of the tube in the exact inverse ratio, the smaller the 

 tube the greater the velocity. Also the more viscous the fluid 

 the greater the velocity. 



We have here then not only a complete explanation of the 

 difference in the laws of resistance generally experienced and that 

 found by Poiseuille, but also we have complete evidence of the 

 instability of steady streams flowing between solid surfaces. The 

 cause of this instability is not yet completely ascertained, but this 

 much is certain, that while lateral stiffness in the walls of the 

 tube is unimportant, incxtensibility or tangential rigidity is essen- 

 tial to the creation of eddies. I cannot show you this, because 

 the only way in which we can produce the necessary condition is 

 by wind blowing over the surface of water. When the wind 

 blows over water it imparts motion to the surface of the water 

 jusl as a moving solid surface. Moving in this way the water 

 is not susceptible of eddies, it is unstable, but the result is 

 waves. This is proved by a very old experiment, which has 

 recently attracted considerable notice. If oil be put on the 

 surface it spreads out into an indefinitely thin sheet with only 

 one of the characteristics of a solid surface, it offers resistance, 

 very slight, but still resistance to extension or contraction. 

 rice, slight as it is, is sufficient to entirely alter the 

 character of the motion. It renders the motion of the water 

 unstable internally, and instead of waves what the wind does is 

 to produce eddies beneath the surface. To those who have 

 ■lie phenomenon of oil preventing waves there is 

 probably nothing more striking throughout the region of 

 mechanics. A film of oil so thin that we have no means of 

 illustrating its thickness, and which cannot be perceived except 

 by its effects — which possesses no mechanical properties that 

 can be made apparent to our senses — is yet able to prevent an 

 action involving forces the strongest that we can conceive, able 

 to upset our ships and destroy our coasts. This, however, 

 becomes intelligible when we perceive that the action of the oil 

 aim the sea by sheer force, but merely, .is by its moral 

 her the manner of motion produced by the action of 

 the wind from that of the terrible waves on the surface into the 

 harmless eddies below. '1 he wind brings the water int.. a highly 

 ondition, into what morally we should call a condition 

 of great excitement ; the oil by an influence we cannot perceive 

 directs this excitement. This influence, although insensibly 

 small, is however now proved to be of a mechanical kind, and 

 to me 11 -c ir.s that this instance of one of the most powerful 

 mechanical actions of which the forces of Nature are capable 

 being entirely controlled by a mechanical force so slight as to be 

 imperceptible does away with every argument against strictly 

 mechanical sources for what we may call mental and moral forces. 



But to return to the instability in parallel channels. This 

 has been the most complete as well as the most definite result 

 of the methoel of colour-bands. The circumstances are such as 

 render definite experiments possible ; these have been made and 

 reveal a definite law of instability, which law has been tested by 

 reference to all the numerous and important experiments that 

 have been recorded with reference to the law of resistance in 

 pipes, whence it appears that the change in the variation of the 

 from the velocity to the square of the velocity agrees 

 as regards the velocity at which it occurs with the change from 

 stability instability. Ii is thus shown that water behaves in 

 exactly the same manner, whether the channel i~, as in I'ois- 

 euille's experiments, ol the size of a hair, or whether it be the 

 size of .' water main or of the Mississippi. The only difference 

 being that in order that the motions may be compared the 

 velocities must be inversely as the size of the channels. This 

 is not the only point explained. 



If we consider other fluids than water, some fluids like oil 

 or treacle apparently How more slowly and steadily than 

 water ; this however is only in smaller channels. The velocity 

 at which sinuous motion commences increases with the viscosity. 

 Thus while water in ordinary streams is always above its 

 critical velocity and the motion sinuous, the motion of treacle in 

 such streams as we see is below its critical velocity and the 

 motion is steady. But if Nature had produced rivers of treacle 

 the size of the '1 flames the treacle would have flowed as easily as 

 water. Thus in the lava streams from a volcano, although 

 looked at closely the lava has the consistency of a pudding, in 

 the large and rapid streams down the mountain side the lava 

 Hows with eddies like water. 



