the Flow of Gases. 



189 



Since the stream is steady, equal weights of the fluid 

 must pass each section in the same time ; or, if u be the 

 velocity, p the density, and A the area of the stream, the 

 joint product upA is constant all along the stream, so that 



W 



gpit 



where — is the mass of fluid which passes any section per 



second. 



In the case of a liquid p is constant, so that the area of the 

 section of the stream is inversely proportional to the velocity, 

 and therefore the stream will continuously contract in sec- 

 tion in the direction in which the velocity increases, and the 

 pressure falls, as in fig. 1, also fig. 2 A. 



In the case of a gas, however, p diminishes as the velocity 

 increases and the pressure falls ; so that the area of the sec- 

 tion will not be inversely proportional to u, but to uxp, and 

 will contract or increase according to whether u increases 

 faster or slower than p diminishes. 



As already described, the value of pu may be expressed in 

 terms of the .pressure. Making this substitution, it appears 

 that pu increases from zero as p diminishes from a definite 

 value pi until p = '527p 1 ; after this pu diminishes to zero as 

 p diminishes to zero. A varies inversely as pu, and there- 

 fore diminishes from infinity as p diminishes from p x till 

 p~'527p i ; then A has a minimum value and increases to 

 infinity as p diminishes to zero, as in fig. 2. 



The equations contain the definite law of this variation, 

 which, for a particular fall of pressure, is shown in fig. 2 a. 



