ON THE FLOW OF WATER THROUGH ORIFICES. 



249 



cable to many of the most ordinary and most useful cases iu practical 

 hydraulics, in reference to the flow of water through orifices in thin plates, 

 or from the wetted internal surface of vessels terminating abruptly in 

 orifices. In devising and arranging these investigations I have aimed at 

 putting them in such form as that they may be intelligible and completely 

 demonstrative to students even in the early stages of their progress in 

 d3'namical studies. 



Definition. — The free level for any particle of water in a mass of statical 

 or of flowing water is the level of the atmosphei-ic end of a column, or 

 of any bar straight or curved, of particles of statical water, having one end 

 situated at the level of tlie particle, and having at that end the same pres- 

 sure as the particle has, and having the other end consisting of a level 

 siirface of water freely exposed to the atmosphere, or else having other- 

 wise atmospheric pressure there ; or briefly we may say that the free level 

 for any particle of water is the level of the atmospheric end of its pressure- 

 column, or of an equivalent ideal pressure-column. 



Theorem I. — In the case of steady flow from approximate rest of water 

 or any liquid considered as frictionless and incompressible, the velocity of any 

 particle in the stream is equal to the velocity which a body would receive in 

 falling freely from rest through a vertical space equal to the fall of free level 

 tvhich is incurred by the pirticle in the stream dunng its flow from rest to its 

 existing p)Osition. 



Or, in briefer words sufficiently suggestive, it may be said that, in respect 

 to water or any liquid flowing so as to admit of its being regarded as truly 

 enough frictionless and incompressible. In steady jhw, the velocity generated 

 from, rest is that due by gravity to the fall of fre.' level. 



Or if 'Q be the fall of free-level sustained by any particle in passing from 

 a statical region of the mass of water to a point in the region of flow, and 

 if V be the velocity of the particle when at that point, then 



In fig. 5, let W L be the still-water surface-level, and let B'BB" be a 



Fig. 5. 



