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XXXIII. On the Thermodynamic Acceleration and Retardation of 

 Streams. By W. J. Macquorn Rankine, C.E., LL.D. } 

 F.R.SS. Lond. and Edinb.* 



1. /GENERAL Principle stated. — The object of this paper 

 is to state in a more general and comprehensive form 

 than has hitherto been done to my knowledge, a thermodynamic 

 and hydrodynamic principle of which many particular cases are 

 well known and understood. That principle may be stated as 

 follows : — 



In a steady stream of any fluid, the abstraction of heat at and 

 near places of minimum pressure, and the addition of heat at and 

 near places of maximum pressure, tend to produce acceleration ; the 

 addition of heat at and near places of minimum pressure, and the 

 abstraction of heat at and near places of maximum pressure tend to 

 produce retardation ; and in a circulating stream the quantity of 

 energy of flow gained or lost in each complete circuit is equal to 

 the quantity of energy lost or gained in the form of heaf ; and in 

 the absence of friction, the ratios borne by that quantity to the heat 

 added and the heat abstracted [of which it is the difference) are 

 regulated by the absolute temperatures at which heat is added and 

 abstracted, agreeably to the second law of thermodynamics. 



2. Equation of the Flow of a steady Stream without Friction. 

 — Let a steady stream of "any fluid, whether liquid, vaporous, or 

 gaseous, flow in a suitable smooth passage or channel without 

 friction. At a given point in the stream let v be the velocity, 

 U the potential energy of attractive forces exerted on unity of 

 mass of the fluid, s the bulkiness, or volume of unity of mass, 

 and^? the pressure. Then by a well-known equation of hydro- 

 dynamics we have 



vdv + dU + sdp = 0, (1) 



or, in the integral form, 



~2 +U+ £sdp= constant; . . (1A) 



that is to say, what each unit of mass gains in energy of flow 



(denoted by — ) it loses in energy of head, as the quantity 



U+ $sdp may be called. When the attractive force considered is 

 gravitation near the earth's surface, we have V=gz, z being the 

 height above some fixed horizontal surface. 



3. Thermodynamic Acceleration and Retardation. — Let it be 

 supposed that a stream comes from a place where the pressure 

 isp„ and the potential energy of attraction Uj, flows through a 



* Communicated by the Author, having been read to the British Asso- 

 ciation at Liverpool (Section A), September 18/0. 



