108 THE MOTION OF A PERFECT LIQUID. 



instcMid of liko the movement of a disorderly crowd, in whieli free 

 tights taking place at various points may be supposed to resemble the 

 local disturbances of whirlpools or vortices. 



The mod(d (fio-. 3) represents on a large scale a section of the chann(d 

 alread}' shown, in Avhich groups of particles of the water ar(> indicated 

 by round balls, lines in the direction of flow of these groups (which, for 

 convenience, we may call i)articles) being colored alternately. WhiMi I 

 move these so that the lines are maintained, Ave imitate "'stream-line"' 

 motion, and when, at any given point of the pipe, the succeeding par- 

 ticles always move at exactly the same velocity, we have what is undei-- 

 stood as ''steady motion." 



As long as all the particles mo\e in the straight portion of the chan- 

 nel their behavior is easy enough to understand. But as the chaniud 

 widens out it is clear that this model does not give us the proper dis- 

 tribution. In the model the wider portions are not tilled up, as they 

 would be with the natural fluid: for it must be clearh' understood that 

 the stream lines do not flow on as the balls along these wires, passing 

 througli a mass of dead water, but redistril)ute themselves so that 

 every particle of water takes part in the flow. Perhaps you may think 

 that if these wires were removed, and the wooden balls allowed to lind 

 th(Mr own positions, they would group themselves as with an actual 

 liijuid. This is not the case; and, for reasons that you will see pres 

 ently, no model of this kind would give us the real conditions of actual 

 flow. By means of a model, however, we may be able to understand 

 w'hy it is so absolutely essential we should realize the correct nature 

 of the grouping which occurs. 



First look at the two diagrams (figs. 4 and 5), whi<;h you will see 

 represent channels of similar form to the experimental one. The 

 same number of particles enter and leave in each under apparently the 

 same conditions, so that the idea may naturally arise in your minds 

 that if the particles ultimately flow with the same speed, whatever their 

 grouping in the larger portion of the channel, it can not nmch matter 

 in what particular kind of formation they actually pass through that 

 wider portion. To understand that is really Acry important, Lc^t us 

 consider a model (fig. 6) specially made for the purpose. You will see 

 that we have two lines of particles which we ma}' consider stream 

 lines, those on the left colored white and those on the right colored 

 red. The first and last are now exactly 18 inches apart, there ])eing 

 18 balls of 1 inch diameter in the row^ If I move the red ones upward, 

 1 cause them to enter a wider portion of the channel, where they will 

 have to arrange themselves so as to be three abreast (fig 7). It is quite 

 clear to you that as I do this their speed in the wider portion of the 

 channel is only one-third of that in the narrow portion, as you will see 

 from the relative positions of the marked particles. Now, directly the 

 first particle entered the wider channel, it commenced to move at a 



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