364, 
FLUID MOTIONS.} 
Le is apparent that in dealing with a large and 
interesting class of fluid motions we cannot go 
far without including fluid friction, or viscosity as it 
is generally called, in order to distinguish it from the 
very different sort of friction encountered by solids, 
unless well lubricated. In order to define it, we may 
consider the simplest case where fiuid is included be- 
tween two parallel walls, at unit distance apart, which 
move steadily, each in its own plane, with velocities 
which differ by unity. On the supposition that the’ 
the viscosity is 
fluid also moves in plane strata, 
measured by the tangential force per unit of area 
exercised by each stratum upon its neighbours. When 
we are concerned with internal motions only, we have 
to do rather with the so-called ‘‘ kinematic viscosity,”’ 
found by dividing the quantity above defined by the 
density of the fluid. On this system the viscosity 
of water is much less than that of air. 
Viscosity varies with temperature; and it is well to 
remember that the viscosity of air increases while 
that of water decreases as the temperature rises. Also 
that the viscosity of water may be greatly increased 
by admixture with alcohol. I used these methods in 
1879 during investigations respecting the influence of 
viscosity upon the behaviour of such fluid jets as are 
sensitive to sound and vibration. 
Experimentally the simplest case of motion in which 
viscosity is paramount is the flow of fluid through 
capillary tubes. The laws of such motion are simple, 
and were well investigated by Poiseuille. This is the 
method employed in practice co determine viscosities. 
The apparatus before you is arranged to show the 
diminution of viscosity with rising temperature. In 
the cold the flow of water through the capillary tube 
is slow, and it requires sixty seconds to fill a smati 
measuring vessel. When, however, the tube is heated 
by passing steam through the jacket surrounding it, 
the flow under the same head is much increased, and. 
the measure is filled in twenty-six seconds. Another 
case of great practical importance, where viscosity 
is the leading consideration, relates to lubrication. 
In admirably conducted experiments Tower showed 
that the solid surfaces moving over one another should 
be separated by a complete film of oil, and that when. 
this is attended to there is no wear. On this basis a 
fairly complete theory of lubrication has been de- 
veloped, mainly by O. Reynolds. But the capillary 
nature of the fluid also enters to some extent, and 
it is not yet certain that the whole character of 
a lubricant can be expressed even in terms of both 
surface tension and viscosity. 
It appears that in the extreme cases, when viscosity 
can be neglected and again when it is paramount, we 
are able to give a pretty good account of what passes. 
It is in the intermediate region, where both inertia 
and viscosity are of influence, that the difficulty is 
greatest. But even here we are not wholly without 
guidance. There is a general law, called the law of 
dynamical similarity, which is often of great service. 
In the past this law has been unaccountably neglected, 
and not only in the present field. It allows us to infer 
what will happen upon one scale of operations from 
what has been observed at another. On the present 
oceasion I must limit myself to viscous fluids, for 
which the law of similarity was laid down in all its 
completeness by Stokes so long ago as 1850. It 
appears that similar motions may take place provided 
a certain condition be satisfied, viz., that the product 
of the linear dimension and the velocity, divided by 
the kinematic viscosity cf the fluid, remain unchanged. 
1 From a_ discourse delivered at the Royal Institution on March 20 by 
the Right Hon. Lord Rayleigh, O.M., F.8.S. 
NO: (2327, VOL. 03) 
NATURE 
| 
[JUNE 4, 1914 
Geometrical similarity is presupposed. An example 
will make this clearer. If we are dealing with a 
single fluid, say air under given conditions, the kine- 
matic viscosity remains of course the same. When 
a solid sphere moves uniformly through air, the char- 
acter of the motion of the fluid round it may depend 
upon the size of the sphere and upon the velocity 
with which it travels. But we may infer that the 
motions remain similar, if only the product of diameter 
and velocity be given. Thus, if we know the motion 
for a particular diameter and velocity of the sphere, we 
can infer what it will be when the velocity is halved 
and the diameter doubled. The fluid velocities also 
will everywhere be halved at the corresponding places. 
M. Eiffel found that for any sphere there is a velocity 
which may be regarded as critical, 7.e. a velocity at 
which the law of resistance changes its character 
somewhat suddenly. It follows from the rule that. 
these critical velocities should be inversely proportional 
to the diameters of the spheres, a conclusion in pretty 
good agreement with M. Eiffel’s observations.* But 
the principle is at least equally important in effecting 
a comparison between different fluids. If we know 
what happens on a certain scale and at a certain 
velocity in water, we can infer what will happen in air 
on any other scale, provided the velocity is chosen 
suitably. It is assumed here that the compressibility’ 
of the air does not come into account, an assumption, 
which is admissible so long as the velocities are small 
in comparison with that of sound. 
But although -the principle of similarity is well 
established on the theoretical side and has met with 
some confirmation in experiment, there has been much 
hesitation in applying it, due perhaps to certain dis- 
crepancies with observation which stand recorded. 
And there is another reason. It is rather difficult to 
understand how viscosity can play so large a part as 
it seems to do, especially when we introduce numbers, 
which make it appear that the viscosity of air, or 
water, is very small in relation to the other data 
occurring in practice. In order to remove these doubts 
it is very desirable to experiment with different vis- 
cosities, but this is not easy to do on a moderately 
large scale, as in the wind channels used for aero- 
nautical purposes. I am therefore desirous of bring- 
ing before you some observations that I have recently 
made with very simple apparatus. 
When liquid flows from one reservoir to another 
through a channel in which there is a contracted 
place, we can compare what we may call the head 
or driving pressure, i.e. the difference of the pressures 
in the two reservoirs, with the suction, i.e. the differ- 
ence between the pressure in the recipient vessel and. 
that lesser pressure to be found at the narrow place. 
The ratio of head to suction is a purely numerical 
quantity, and according to the principle of similarity 
it should for a given channel remain unchanged, pro- 
vided the velocity be taken proportional to the kine- 
matic viscosity of the fluid. The use of the same 
material channel throughout has the advantage that 
no question can arise as to geometrical similarity, 
which in principle should extend to any roughness 
upon the surface, while the necessary changes of 
velocity are easily attained by altering the head and 
those of viscosity by altering the temperature. 
The apparatus consisted of two aspirator bottles 
(Fig. 1) containing water and connected below by a 
passage bored in a cylinder of lead, 7 cm. long, fitted 
water-tight with rubber corks. The form of channel 
actually employed is shown in Fig. 2. On the up- 
stream side it contracts pretty suddenly from full 
bore (8 mm.) to the narrowest place, where the 
diameter is 2:75 mm. On the down-stream side the 
2 Comptes rendus, December 30, 1912, January 13, 1913. 
