﻿70 Royal Society, 



If no change of total bulkiness arises from the mixture of the com- 

 ponent streams, the volume occupied by a given mass of the mixture 

 is simply the sum of the volumes of its ingredients ; so that we have 



AVS^ow 



S, 



and the expression for the loss ol energy becomes 



m^AV^AyfSrfp (30) 



•2s 2S B.Jfb 

 When the fluids are all liquids, whose compressibility may be neg- 



• f P 

 lected, we have \ °Sc?P = S {P — p ); and substituting for the 



f JPo 



difference of pressures its value according to equation (2), the fol- 

 lowing expression is found for the loss of energy at the junction, 



a fg; ,(»- Y n ; (3D) 



that is to say, in the case of liquids all the energy due to the several 

 velocities (v— V) of the component streams relatively to the resultant 

 stream is lost. 



"When the expression (3 D) is reduced to a single term, it becomes 

 the well-known value of the loss of energy of a single stream of 

 liquid at a sudden enlargement in a tube. 



6. Efficiency of Combined Streams. — The efficiency of a set of com- 

 bined streams may be defined as the fraction expressing the ratio 

 borne by the total energy of the resultant stream after the combina- 

 tion to the aggregate energy of the component streams before the 

 combination. It is expressed as follows : — 



AV 



(4) 





7. General Problem of Combined Streams. — In most cases the pro- 

 blem of combined streams takes one or the other of the two following 

 forms. In each of the two forms the areas of the nozzles a lt a 2 , &c. 

 are given, and also the area of the throat, A. 



First Form. — The quantities given, besides the before-mentioned 

 areas, are the pressure at the nozzles, p , and the velocities of the 

 component streams, v v &c. The functional values given are those of 



s 0> lt s 0> 2 , &c, in terms of p oi and of S in terms of P 



°' s, 



0> 1 "0, 2 



&c. Those functional values are to be substituted in the equations 

 (1) and (2) ; and the solution of these equations will give the nume- 

 rical values of Y and of P . In the case of liquids of sensibly con- 

 stant bulkiness, * 0> , &c, and S are quantities sensibly independent 



