Studies on the Motion of Viscous Flows— III 



that this deviation need not necessarily he considered small in any sense. The 

 subdomain Mj, may be a null domain for certain ranges of flow parameters, but 

 for other ranges it may not be so and then the deviation would be small in it. 

 This is to be considered incidental. However, as a hypothesis which is later 

 supported on the basis of the principle of minimum dissipation, this deviation 

 for a given Reynolds number will be considered to be a minimum consistent 

 with tiie governing equations and the actual boundary and flow coyiditions. The 

 potential flow then assumes the position of a base flow from which the deviations 

 take place. This holds for all flow conditions and, in particular, for all Reyn- 

 olds numbers. , 



In the immediately following pages we present an examination and critique 

 of significant experiments and observations made by distinguished investigators 

 which accord with and support the above hypothesis. We shall consider the 

 beautiful experiments carried out in 1899 by Professor Hele-Shaw [27,28]. It is 

 helpful to quote here the following passages from his paper of 1899, 



If we take two sheets of glass, and bring them nearly close to- 

 gether, leaving only a space the thickness of a thin card or piece 

 of paper, and then by suitable means cause liquid to flow under 

 pressure between them, the very property of viscosity, which as 

 before noted, is the cause of the eddying motion in large bodies 

 of water, in the present case greatly limits the freedom of mo- 

 tion of the fluid between the two sheets of glass, and thus pre- 

 vents not only eddying or whirling motion, but also counteracts 

 the effects of inertia. Every particle is then compelled by the 

 pressure behind and around it to more onwards without whirling 

 motion, following the path which corresponds exactly with the 

 stream-lines in a perfect liquid. 



But at this stage you may reasonably enquire how it is that we 

 are able to state, with so much certainty, that the artificial con- 

 ditions of flow with a viscous liquid are really giving us the 

 stream-line motion of a perfect one; and this brings me to the 

 results which mathematicians have obtained. 



The view now shown represents a body of circular cross-section 

 past which a fluid of infinite extent is moving, and the lines are 

 plotted from mathematical investigation and represent the flow of 

 particles. This particular case gives us the means of most elab- 

 orate comparison; although we cannot employ a fluid of infinite 

 extent, we can prepare the border of the channel to correspond 

 with any of the particular stream-lines, and measure the exact 

 positions of the lines inside. 



By means of a second lantern, the real flow of a viscous liquid 

 for this case is shown upon the second screen, and you will see 

 that it agrees with the calculated flow around a similar obstacle 

 of a perfect liquid. The diagram shown on the wall is the actual 



523 



