1914] on Fluid Motions 79 



Viscosity varies with temperature ; and it is well to rememljer 

 that the viscositv of air increases while that of water decreases as the 

 temperature rises. Also tliat the viscosity of water may be greatly 

 increased by admixture w^ith 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 to determine viscosities. 

 The apparatus before you is arranged to show the diminution of vis- 

 cosity with rising temperature. In the cold the flow of water through 

 the capillary tube is slow, and it requires sixty seconds to fill a small 

 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 lead- 

 ing 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 developed, mainly by 0. 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 

 difliculty 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 occasion I 

 must limit myself to viscous fluids, for which the law of similarity 

 was laid down in all its completeness by Stokes as 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 of the fluid, 

 remain unchanged. Geometrical similarity is pre-supposed. An 

 example will make this clearer. If we are dealing with a single 

 fluid, say air under given conditions, the kinematic viscosity remains 

 of course the same. When a solid sphere moves uniformly through 

 air, the character of the motion of the fluid round it may depend 

 tipon the size of the sphere and upon the velocity with which it 

 travels. But we may infer that the motions remain similar, if only 



