92 



NATURE 



[Dec. 2, 1875 



as indicated by the gauge-glass levels a' and 6', is identical with 

 that indicated by e'/' g', the giuge-glass levels connected with 

 the parallel pipe. 



In dealing with pipes of varying sectional area I have hitherto 

 treated only of the modifications caused in the forward motion 

 of the particles of iliiid ; for I have limited the argument to cases 

 where the alteration in sectional area of the pipe is so gradual 

 that, practically, the only alteration in the motion of the particles 

 is that in their forward velocity ; but I have previously shown 

 that tortuosity in a pijie of uniform diameter does not introduce 

 endways pressure, provided the initial and terminal directions are 

 the same j and it is easy to see that an elongated system of such 

 gradually tapered pipes as we have been considering, may be also 

 tortuous without introducing endways pressure. Now tortuosity 

 of flow is but another word for sideways deviation of flow. 



This leads us up to the case of more sudden contractions or 

 enlargements in pipes, where the particles next the sides of the 

 pipes have to follow their surfaces and must therefore be moved 

 rapidly sideways in their course. 



We will, for simplicity, consider the case of a contraction (see 

 Fig. 21), and one in which the pipe resumes the same diameter 

 beyond the contraction. 



Fig. 21. 



The particles along the central line pursue a straight course, 

 and are subject only to the changes of pressure necessary to in- 

 duce the changes of velocity. 



To consider the behaviour of the other particles, let us assume 

 that we insert a number of perfectly thin partitions (see Fig. 22), 

 which we lay in such a manner that they exactly follow the paths 

 of the particles of flu d at each point, so as not in any way to 

 affect their motion ; these partitions are quite imaginary, and 

 merely assist us in looking upon the entire fluid in question as 

 divided into a number of small streams. These streams are 

 generally curvilinear, and vary in sectional area ; and at the 

 point beynd the contraction where the pipe resumes its former 

 sectional area, we shall naturally find these minor streams occu- 

 pying the same sectional area as before, and moving with the 

 same velocity as before. 



Now I ach of these small streams is exactly represented by a 

 stream of fluid flowing within a pipe, that pipe being curvilinear 

 and gradually varying in sectional area, ard its two ends being 

 of the same sectional area and in the same straight line. We 

 have seen that in the case of such a stream, the sum total of all 

 the forces due to its motion has no resultant longitudinally ; and 

 this will be equally the case, whether the envelope of the stream 



Fig. 22. 



be an actual pipe or the mutual pressure of adjacent streams ; 

 this envelope will not be moved endways by the flow of the fluid. 

 What is true of each stream is true of all put together ; and thus 

 it follows that the whole body of fluid which these separate 

 streams constitute does not exert any endways force ; or, in other 

 words, there will be equilibrium of fluid forces throughout the 

 passage of the fluid through a local contraction in a pipe such as 

 we have been considering. The same line of argument evidently 

 holds good in the case of an enlargement, where the pipe beyond 

 the enlargement regains the same diameter as before. 



In illusttation of the conclusions which have been thus far 

 established, if we had a perfect fluid with which to try the 

 experiment, we might exhibit a very instructive and striking 

 result. 



Assume a perfect stream of fluid flowing through a pipe of 

 very large diameter, ABC, with a contraction in it at B, as 

 shown in Fig. 23, and that the equal pressures at A and C on 

 either side of the contrattion are indicated by the head of fluid in 

 pressure-gauges A D, C E — the pressure at B, which will be less, 

 being represented by the height B F. Now, the condition of 

 the pipe at A will be just the same if we suppose the pipe 

 supplied from a large cistern G, as shown in Fig. 24 ; and the | 



appropriate pressure at A will be maintained, if the fluid stands 

 in the cistern G at a height 11, equal to the head A D in the 

 pressure-gauge. So, again, the condition of the pipe at C will 

 be the same if the pipe discharges into a cistern, I ; and the 

 appropriate pressure at C will be maintained, and can only be 



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Line 



Fig. 23. 



maintained, if the water in the cistern stands at a height J, equal 

 to the head C E in the pressure-gauge, which is, in fact, the 

 same level as H in the cistern G ; so that if we once establish 

 the motion through the pipe A B C, and maintain the supply of 

 fluid, we shall have the fluid running rapidly, and continuing to 

 run with unabated rapidity, from one cistern into another, though 

 both are at the same head. 



If we take such a condition of things that the pressure at B is 

 zero, or, in other words, if the velocity at B is that due to the 

 head A D, then we might cut the pipe at B and separate the 

 two cisterns as shown in Fig. 25, and we should find the fluid 

 issuing at B in a jet, and re-entering the pipe again at K, and 

 rising as before in the cistern I to the same level with a perpetual 

 flow. 



The experiment here suggested is, if rightly understood, only 

 a specialised instance of the properties of what in the previous 

 experiment was termed a contraction followed by an enlarge- 

 ment ; it is in fact as if in that experiment the diameter of the 

 contracted part had been so far reduced that the pressure within 

 it would have sunk apparently to zero, that is to say, in reality 

 to the pressure of the atmosphere ; in that case, of course, the 

 pipe which enclosed that portion of the stream would have 

 become simply an inert envelope, and might have been removed 

 without aff"ecting the dynamic properties of the stream. Theore- 

 tically indeed with the frictionless fluid the contraction of jet 

 might be carried so far as not merely to obliterate all positive 

 pressure, but to produce a negative pressure equal to that of the 



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atmosphere. For in fact the conditions thus brought info opera- 

 tion would be in effect identical with those which would exist 

 were the experiment performed in vacuo, and the head in cistern 

 and at the outlet were both increased by 34 feet ; but the theo- 

 retical possibility thus indicated is greatly curtailed by friction, 

 and the illustrative experiment I am about to exhibit deals only 

 with the case in which the pressure at the contraction is reduced 



