(SUPPLEMENTARY)
A NEW PHENOMENON THAT APPEARS WITH AN INCREASE IN THE VELOCITY
OF ENTRY OF A ROUGH SPHERE
A slight delay in the passage 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 assistance 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.
[Illustration: SERIES XVII
Rough sphere falling 140 cm. into water. Scale 2/3.
1 0.006 sec.
2 0.008 sec.
3 0.015 sec.
4 0.021 sec.
5 0.038 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."
[Illustration: SERIES XVII--(_continued_)
6 0.043 sec.
7 0.052 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.
[Illustration: SERIES XVII--(_continued_)
8 0.057 sec.
9 0.063 sec.
10 0.073 sec.
11 0.089 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 passing 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.
[Illustration: SERIES XVIII
Early stages of the splash of a rough sphere (diam. 1.5 centim.) falling
281 centim. (about 9 feet) into water.
1 T = 0
2 0.003 sec.
3 0.005 sec.
4]
FOOTNOTES:
[K] I can recommend any reader who is not afraid of being late for
breakfast to keep a bag of marbles in his bath-room.
PRINTED BY
WILLIAM BRENDON AND SON, LTD
PLYMOUTH
[Transcriber's Note: The following changes have been made to the
original text.
Page 10: "the same in 1, 3 and 4" changed to
"the same in 1, 2 and 4"
Page 66: ".04 of a gram" changed to "0.4 of a gram"
Page 77: Added full stop to image caption 9 "0.042 sec."
End of Project Gutenberg's A Study of Splashes, by Arthur Mason Worthington