290 Dr. Rankine on the Acceleration and Retardation of Streams. 



At the end of the process the stream, on arriving at the second 

 place where the pressure is ^^ will now no longer return to the 

 same velocity, but its energy of flow will be 



f = | -U, + U - ( P \'dp = f + ("'(s-^dp, . (6) 



and there will have been on the whole a change of energy of 

 flow to the following amount, 



-%-! = ] {ss')d P ; (7) 



which is a gain or a loss, corresponding to an acceleration or a 

 retardation, according as it is positive or negative, its sign being 

 the same with that of the product (/?i— J» )(^ ""$')■ 



4. Circulating Stream. — Let the place at which the stream 

 arrives and where the pressure is p Y be the same with that from 

 which it sets out ; and on the return of each particle to that 

 place let a quantity of heat be abstracted or added, as the case 

 may be, so as to restore the thermodynamic function to its ori- 

 ginal value (j>. .That quantity of heat is expressed by 





(8) 



Then in the course of each complete circuit made by a unit of 

 mass of the fluid in that stream there is a change in the 

 energy of flow to the amount expressed by equation (7) ; and ac- 

 cordingly as that change is a gain or a loss, there is on the whole 

 a disappearance or a production of heat to an equivalent amount, 

 expressed by 



f* (Ti-T 9 )#= PW)* ( 9 ) 



•V JPO 



5. Examples. — Amongst particular cases of the thermody- 

 namic acceleration and retardation of streams the following may 

 be specified. 



Acceleration by the addition of heat at and near a place of 

 maximum pressure : — the draught of a furnace ; and the produc- 

 tion of disturbances in the atmosphere in regions where the 

 ground is hotter than the air. 



Retardation by the abstraction of heat at and near a place of 

 maximum pressure: — the dying away of atmospheric disturbances 

 in regions where the ground is colder than the air. 



Acceleration by the abstraction of heat at and near a place of 

 minimum pressure: — the injector for feeding boilers, in which a 

 jet of steam,. being liquefied by the abstraction of heat, is enabled 

 not only to force its way back into the boiler, but to sweep a 



