the Flow of Gases. 



191 



that when p 2 was less than '527/?,, the narrowest portion of 

 the stream would be at N, for since the stream converges to 

 N the pressure above N can be nowhere less than 'b"21p l ; 

 and since emerging into the smaller surrounding pressure^ 

 the stream would expand laterally, N would be the minimum 

 breadth of the stream, and hence the pressure at N would be 

 *527/>!. In a broad view we may in the same way look on 

 an orifice in the wall of a vessel as the neck of a stream. 

 But if we begin to look into the argument, it is not so clear, 

 on account of the curvature of the paths in which some of 

 the particles approach the orifice. 



Since the motion with which the fluid approaches the 

 orifice is steady, the whole stream, which is bounded all round 

 by the wall, may be considered to consist of a number of 

 elementary streams, each conveying the same quantity of 

 fluid. Each of these elementary streams is bounded by the 

 neighbouring streams, but as the boundaries do not change 

 their position they may be considered as fixed. 



The figure (4) shows approximately the arrangement of 

 such stream. But for the mathematical difficulty of inte- 

 grating the equations of motion, the exact form of these 



