PART II. 



HYDROKINETICS. 



CHAPTER I. 



MOTION OF LIQUIDS. EFFLUX. RESISTANCE AND 

 WORK OF LIQUIDS. 



75. Velocity of a Liquid in Pipes.// a liquid 

 run through any pipe of variable diameter, which is 

 Icept continually full, and the velocity is the same in 

 every part of a transverse section, the velocities in the 

 different transverse sections vary inversely as the 

 areas of the sections. 



For as the tube is kept full, and the liquid is incom- 

 pressible (Art. 3), the same quantity of liquid which runs 

 through one section will, in the same time, run through 

 the next section, and so on through any other. Hence if 

 k, k' be the areas of any two sections, and v, v' the veloc- 

 ities of the particles at those sections, we have, since the 

 quantity of liquid which flows through any section in a 

 unit of time is the product of the area of the section by the 



velocity, 



kv = k'v' ; 



.'. v : v' : : k' : k. (1) 



Con. Hence, as the section of a mass of liquid decreases, 

 its velocity increases in the same proportion. For instance, 

 the velocity of a stream or river is greater at places where 

 its width is diminished. This demonstration is also 

 applicable to different sections of a liquid issuing through 

 the orifice of a vessel, whether the section be taken within 



