IX. 



DISCONTINUOUS MOTIONS IN LIQUIDS.* 



By Prof. A.. Oherbeck. 



I. 



It is customary to designate by the term discontinuous fluid mo>- 

 tions, those phenomena of movement in which the velocity is not through- 

 out the whole space tilled with the fluid a continuous fuuctiou of the 

 location. Therefore iu such movements there occur surfaces within 

 the fluid that separate from each other regions within which the veloci- 

 ties differ from each other by finite quantities. The fundamental prin- 

 ciples of the theory of these motions were first given by Eelmholtz.t 



If we assume that a velocity potential (tp) does exist for so-called 

 steady fluid motions then the hydro-dynamic differential equations can 

 be summarized in the one equation, 



Now Helmholtz has shown that the pressure^ and consequently the 

 velocity can be discontinuous functions of the coordinates and that 

 there are a great number of phenomena of motion for which the assump- 

 tion of a discontinuous function is necessary. Especially has this theory 

 been applied by Helmholtz and by Kirchhoff to fluid jets,! an( l tue 

 boundaries of free jets can be given under the following assumptions: 



(a) That no accelerating force acts upon the fluid. 



(b) That the movement is steady. 



(c) That the movement depends only upon two variables, ./and y, and 

 is therefore everywhere parallel to a fixed plane. 



If in other cases, for instauce for jets that are symmetrical about an 

 axis or that are under the influence of the accelerating force of gravity, 



*Read at the session of the Physical Society iu Berlin, May 11, 1877. Translated 



from Wiedemann's Annalen der Physik unci Chemie, 1877, vol. n, p. 1-16. 



t See the Berlin Monalsberiehte, 1868, p. 215 [or No. II of this series of Translations.] 



t See Crelle's Journal vol. lxx, p. 289-299, [and Nos. Ill and VIII of this collection of 



Translations.] 



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