﻿68 Royal Society : — Dr. W. J. M. Rankine on the 



principal symbols used are as follows. For any one of the component 

 streams : — 



0, area of nozzle ; 

 v, velocity of flow at nozzle ; 

 * , bulkiness, or reciprocal of density, at nozzle. 

 The several component streams may be distinguished from each 

 other, when required, by suffixes, as 1, 2, 3, &c. 

 For the resultant stream : — 

 A, area of throat ; 

 V, velocity of flow at throat ; 

 S , bulkiness, or reciprocal of density, at throat. 

 Intensities of pressure, in absolute units on the unit of area : — 

 j) oi at the nozzle end of junction-chamber; 

 P , at the throat. 

 (These may be converted into units of weight on the unit of 

 area, by dividing by g.) 



The flow of each stream is supposed to be steady. The fluids 

 may be either liquid, vaporous, gaseous, or mixed. 



3. Equation of Continuity. — The mass of fluid that enters the 



av 

 junction-chamber through a given nozzle in a unit of time is — . 



AV 



The mass discharged in the same time at the throat is -=— . The 



flow being steady, the following equation must at every instant be 

 fulfilled: 



T-=2-T- « 



If S and the several values of s are given, that equation gives the 

 velocity of the resultant stream in terms of those of the component 

 streams ; viz. 



V=Jks.^ (1A) 



A s 



If all the fluids are liquids, each of sensibly invariable bulkiness, 

 we have also AV=S . av ; that is, the volume of flow of the resultant 

 stream is equal to the aggregate of the volumes of flow of the compo- 

 nent streams ; but if any or all of the streams are vaporous or ga- 

 seous, the values of s Q will depend upon that of p Q) and the value of 

 S upon that of P , and upon the changes of bulkiness of the fluids 

 which may take place in the junction-chamber, through change of 

 temperature, change of condition, or chemical action. 



In any case S may be regarded as a given function of P , and of 



av 

 the mutual proportions of the several values of — ; in other words, of 



the ingredients in the resultant stream. 



4. Dynamical Equation. — The aggregate momentum of the mass 



of fluid that enters the junction-chamber through the nozzles in a 



av 2 

 unit of time is S. — . The momentum of the equal mass which 



s n 



