EXPLANATION OF THE RIBS OR FLUTINGS IN THE SPLASH OF A SMOOTH SPHERE.
The fact thus established experimentally, that the surface of a smooth sphere must be rigid if the film is to envelop it closely, suggests also a satisfactory explanation of the flutings. For we know from other researches on the motion of liquids,[J] that a layer of liquid actually in contact with a solid can have no motion relative to the solid, but must move with it. Thus in the film or sheath which rises over and envelops the sphere, the layer of liquid next to the solid must be moving downwards with it, while the outermost layers at least are moving upwards; thus there must be a strong viscous shear in the film impeding its rise. If by any fortuitous oscillation a radial rib arises, this will be a channel in which the liquid, being farther from the surface, will be less affected by the viscous drag; it will therefore be a channel of more rapid flow and diminished pressure, into which, therefore, the neighbouring liquid will be forced from either side. Thus a rib once formed is in stable equilibrium, and will correspond to a jet at the edge of the rim. This explains the persistence of the ribs when once established, and we may attribute their regular distribution to the fact that they first originate in the spontaneous segmentation of the annular rim at the edge of the advancing sheath. This explanation quite accords with the appearance of such figures as Fig. 6 of page 91 and Figs. 1 and 2 of page 113, in which, firstly, we see that the flutings are absent from that part of the sheath which has left the sphere, and, secondly, we see how much higher in every case the continuous film has risen in that part which has left the sphere than in the part which has clung to it, and has been hindered by the viscous drag. Especially is this the case in Fig. 2, Series XIV (p. 105), where the liquid was pure glycerine. The effect of the viscous drag is, in fact, most marked in the most viscous liquid, and it is also in the viscous liquid that the ribs are most strongly marked.
INFLUENCE OF THE NATURE OF THE LIQUID EXPLAINED.
Finally, in confirmation of our explanation, we have the fact that with a liquid of small density and surface-tension, such as paraffin oil, a much smaller velocity of impact with a highly polished sphere suffices to give a "rough" splash than with water, a liquid of greater density and surface-tension, the reason being without doubt that the tangential velocity given by the impact is greater with the lighter liquid, as, indeed, is proved to be the case by the greater height to which the surrounding sheath is thrown up. The surface-tension also being smaller, the less is the abatement of velocity on account of work done in extending the surface.
FOOTNOTES:
[I] See _Nature_, vol. xxix., January 31, 1884.
[J] See Whetham on "The Alleged Slipping at the Boundary of a Liquid in Motion." _Phil. Trans. Roy. Soc._, Vol. 181 (1890).
CHAPTER X
CONCLUSION
We have now reached the end of the story, as far at least as I am able to tell it. But there is certainly more to be found out. No one has yet examined what happens when a rough sphere enters a liquid with a very high velocity. That the motion set up must differ from that at a low velocity is apparent to any one who has thrown stones from a low bridge into deep water below. The stone that is thrown with a great velocity makes neither quite the same sound nor the same kind of splash as a slow-falling stone, and though in the light of our present knowledge we may conjecture the kind of difference to be expected, yet experience has taught me that the subject is so full of unexpected turns that it is better to wait for the photographic record than to speculate without it.
It would be an immense convenience, as was suggested in the first chapter, if we could use a kinematograph and watch such a splash in broad daylight, without the troublesome necessity of providing darkness and an electric spark. But the difficulties of contriving an exposure of the whole lens short enough to prevent blurring, either from the motion of the object, or from that of the rapidly-shifting sensitive film, are very great, and any one who may be able to overcome them satisfactorily, will find a mult.i.tude of applications awaiting his invention.
But even were the photographic record complete, what does it amount to?
All that we have done has been merely to follow the rapid changes of form that take place in the bounding surface of the liquid. The interior particles of the liquid itself have remained invisible to us. But it is precisely the motion of these particles that the student of hydrodynamics desires to be able to trace. His study is so difficult that even in the apparently simple case of the gently-undulating surface of deep water, the reasoning necessary to discover the real path of any particle can at present only be followed by the highly-trained mathematician. In other and more complicated cases such as are exemplified by the sudden disturbances that we have studied, any definite information that can be obtained, even as to the motion of the surface, may afford a clue to the solution of important questions; and I have been encouraged to hope that the observations here recorded may serve as a useful basis of experimental fact in a confessedly difficult subject.
To take a single ill.u.s.tration of a possible application in an unexpected quarter, I would invite the attention of the reader to the two photographs in the frontispiece, which exhibit the splash of a projectile on striking the steel armour-plate of a battleship. These are ordinary photographs taken after the plate had been used as a target.
They represent the side on which the projectile has entered. In one picture the projectile is still seen embedded in the plate.
No one looking at these photographs can fail to be struck with the close resemblance to some of the splashes that we have studied. There is the same _slight_ upheaval of the neighbouring surface, the same crater, with the same curled lip, leading to the inference that under the immense and suddenly applied pressure, the steel has behaved like a liquid.
Such flow of metals under great pressure is familiar enough to mechanical engineers, but what I desire to suggest is, that from a study of the motions set up in a liquid in an a.n.a.logous case, it may be possible to deduce information about the distribution of internal stress, which may apply also to a solid, and may thus lead to improvements in the construction of a plate that is intended to resist penetration.
CHAPTER XI
(SUPPLEMENTARY)
A NEW PHENOMENON THAT APPEARS WITH AN INCREASE IN THE VELOCITY OF ENTRY OF A ROUGH SPHERE
A slight delay in the pa.s.sage of this book through the press has enabled me to obtain some of the missing information referred to in the opening paragraph of the last chapter.
If any reader who may have been persuaded to try for himself the simple experiment mentioned at the beginning of Chapter VII, will extend his observations by increasing the height of fall of the roughened marble to 4 or 5 feet (say to 140 centim.), he will find that while, as before, much air is still carried down, there is nevertheless, now, no rebounding jet projected high into the air, such as is invariably seen with the lower fall of 2 feet (60 centim.), and he will notice a curious "seething" appearance at the surface.[K] Thinking that this appearance which the naked eye detects must be due to an entanglement of the rising jet with the bubble, which entanglement was likely to produce confused motions that could not be profitably studied, I had not till now been sufficiently curious to examine what really happened. But certain recent observations of the persistence with which the seething motion again and again recurred when a stone was dropped or thrown into a river, led me to suspect that something required investigation. I was, however, quite unprepared to find the remarkable change of procedure that is revealed by the following series of photographs (Series XVII), in the taking of which I owe much to the kind and skilful a.s.sistance of Dr. Bryan. The earlier figures show the very rapid rise of the crater and its closing as a bubble much before the entrapped column of air divides. Before the division takes place, the liquid now flowing in from all sides closes over the upper end of the long air-tube, separates it from the air outside, and _forms a downward jet which shoots down the middle of the air-tube in pursuit of the sphere_. The first formation of this jet is not easy to observe, because the view is obscured by much splashing and turbulent vortical motion resulting apparently from the collision of the streams that converge from all sides on the axis of the air-tube at its upper end. Thus in Fig. 5 the jet is not yet well established, or at least not easily discerned; but in Fig. 6 the turbulence has cleared away from the upper part, and from this stage onwards the jet is well seen in all the figures, and it persists long after the segmentation of the air column has taken place. The reader must not suppose that this jet is a mere _falling_ of the water under the action of gravity, for the rapidity with which it advances is far greater than could be accounted for in this way; indeed, as the "times" show, the effect of gravity during the establishment of the jet is insignificant.
[Ill.u.s.tration: SERIES XVII
Rough sphere falling 140 cm. into water. Scale 2/3.
1 0006 sec.
2 0008 sec.
3 0015 sec.
4 0021 sec.
5 0038 sec.]
The segmentation of the air column appears to be independent of the jet; but some photographs, such as Fig. 7, show the jet striking the side and breaking into the surrounding liquid with a great accompaniment of "air-dust."
[Ill.u.s.tration: SERIES XVII--(_continued_)
6 0043 sec.
7 0052 sec.]
N.B.--Each of these figures is made up from two photographs; one of the upper and one of the lower portion taken from different splashes, but with the same "timing."
The reader will observe that after division of the air-tube has taken place, say from Fig. 9 onwards, the water entering the jet at the top and coming out again at the bottom must circulate as in a vortex ring, part of the core of which is filled with the air surrounding the jet.
It is also to be observed that after the establishment of the jet, there is a steady increase in the size of the heap above the surface; but it is not easy in any given photograph to say how much of this protuberance is air and how much is water. An examination of Figs. 7, 8, and 9 shows that the place of origin of the jet is gradually lifted above the level of the free surface.
That the jet we now see should be directed downwards rather than upwards may, I think, be explained in a general way as follows:--The great initial momentum of the sphere causes it to continue in rapid motion after the bubble has closed, thus the sphere acts as a sort of piston, which by increasing the length of the air-tube diminishes the pressure in it and so sucks in the bubble, which is driven down by the greater atmospheric pressure above. The converging horizontal inflow near the mouth of the air-tube cannot, of course, produce the downward-directed jet without an equal and opposite generation of momentum upwards; but this is now expended, not in producing a similar upward jet, but in balancing the excess of atmospheric pressure. The reaction, in fact, to the projection of the jet downwards, is the force which holds up and slowly raises the roof of the long air-shaft.
[Ill.u.s.tration: SERIES XVII--(_continued_)
8 0057 sec.
9 0063 sec.
10 0073 sec.
11 0089 sec.]
When, as in the last figure of Series VI, p. 85, we saw the upward-directed jet, then also there must have been an equal and opposite generation of downward momentum distributed in some way through the liquid below the basin, of which, however, there could be no visible sign. Hence we see that the present downward jet is, in a sense, not a new phenomenon, but one which, having existed unnoticed before, is now rendered visible to us by reason of its being produced in air instead of in water.
By means of a hole bored through the ceiling of the dark room, the fall was then increased to 281 centim. (just over 9 feet). The very beautiful earlier stages of the splash at this height are shown in Series XVIII.
Fig. 4 shows very well the internal splashing at the top of the air-column which accompanies the initiation of the jet. Some later photographs taken at this height (not yet quite presentable) show the jet pa.s.sing right down the narrow neck of air-tube and probably striking the top of the sphere, the descent of which must thus be liable to a curious irregularity.
A further increase of the height of fall to 686 centim. (22-1/2 feet) was found to produce but little change in the phenomena.
[Ill.u.s.tration: SERIES XVIII
Early stages of the splash of a rough sphere (diam. 15 centim.) falling 281 centim. (about 9 feet) into water.
1 T = 0 2 0003 sec.
3 0005 sec.
4]
FOOTNOTES: