THE PLOW OF GASES, 169 



4. To understand this circumstance, it is necessary to 

 consider a steady narrow stream of fluid in which the 

 pressure falls and the velocity increases continuously in 

 one direction. 



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 upK is constant all along the stream, so that 



gpu 



W . 

 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 con- 

 tract in section in the direction in which the velocity 

 increases and the pressure falls, as in fig. i, 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 section will not be inversely proportional to u, but 

 to M X p, 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 j9i until /7= •527^1 ; after this pu diminishes 

 to zero as p diminishes to zero. A varies inversely as pu, 



