Dec. 2, 1875J 



NATURE 



91 



As the pressure of the perfect fluid in the pipe at any point 

 depends upon the sectional area at that point, it follows that the 

 amounts of the pressures are independent of the distance, as 



Fig. 17. 



measnred along the pipe, in which the area of the pipe alters ; 

 so that if in the pipe shown in Fig. 18 the areas at aU the points 

 marked A are equal, if also the areas at all the points marked B 

 are equal, and so also with those at C and D, then the pressures 



at all the points A will be the same, the pressures at all the 

 points B will be the same, and so with those at C and D . 



Since, then, the pressure at each point depends on the sectional 

 area at the point and on that only, it is easy to see that the 

 variations in pressure due to the flow are not such as can cause 

 any total endways force on the pipe^ provided its sectional area 

 at each end is the same. 



Take the pipe shown in Fig. 19. The conical portion of pipe 

 A B presents the same area of surface effective for endways 

 pressure as does the conical portion H I, only in opposite 

 directions. They are both subject to the same pressure, being 

 that appropriate to their effective mean diameter J. Consequently 

 the endways pressxires on these portions are equal and opposite 

 and neutralise one another. Precisely in the same way it may 

 be seen that the endways pressures on B C, C D, D E, exactly 

 counteract those on G H, F G, E F ; and in precisely the same 

 way it may be shown that in any combination whatever of en- 

 largements and contractions, provided the sectional area and 

 direction of the pipe at the two ends are the same, the total end- 

 ways effect impressed on the pipe by the fluid flowing through 

 it must be nil. 



In the experiment I am about to show you, the several propo- 



sitions which I have been elucidating will be seen to be verified 

 step by step, if due allowance be made for the effect of friction. 



A cistern (see Fig. 20), in which a definite head of water is 

 maintained, discharges itself through a continuous series of pipes. 



which in the local changes of diameter exhibit the several cha- 

 racteristic features which have been under consideration. 



From a to ^ at the outlet end we have a contraction fjllowel 

 by an enlargement ; from <? to ^ the diameter is uniform, from 



Fia igb 



^ to / we have an enlargement followed by a contraction. 

 At the various critical features are fitted gauge-glasses such as 

 have been described, so that the level at which the water stands 

 in each indicates the pressure in the pipe at the point of attach- 

 ment 



The series of pipes is laid out on an [inclination which repre- 

 sents the mean resistance due to friction, or the "head" lost by 

 friction, between the cistern and the outlet, in other words, the 

 hydraulic mean gradient. 



The mean diameter of the ccmtracted part between a and b 



Fig. 20. 



has been so determined by well-known hydraulic rules, that when 

 it is compared with the adjoining parallel pipe, the hydraulic 

 gradient shall be the same in each. 



You observe that while the levels at which the water stands in 

 the several gauge-glasses corresponds from end to end with the 

 gradient from the head in the cistern to the head at the oatlet ; 



j when examined in detail, they verify throughout the propositions 

 1 I have been establishing. Broadly speaking, where the diameter 

 is smallest, the pressure falls most below the mean gradient ; at 

 ! the points where the diameters are equal, the pressures allowing 

 j for the gradient are equal, and what is a quantitative verifica- 

 ' tion, the gradient, or loss of head per foot between a and b. 



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