PIPES. 20? 



where s is the length of the side of the section parallel to 

 the radius of curvature p. (See Weisbach's Mechs., p. 897.) 



Ilia. Pipe of Uniform Diameter Equivalent to 

 one of Varying Diameter. Pipes for the supply of 

 towns * often consist of a series of lengths, the diameter for 

 each length being the same, but differing from those of the 

 other lengths. In approximate calculations of the head 

 lost in such pipes, it is generally accurate enough to neglect 

 the smaller losses of head and to regard only the friction of 

 the pipe, and then the calculations may be facilitated by 

 reducing the pipe to one of uniform diameter, having the 

 same loss of head. Such a uniform pipe is called an equiv- 

 alent pipe. 



Let A be the pipe of varia- 

 ble diameter, and B the 

 equivalent pipe of uniform 



diameter. In A let l lf 1 Z) = 



etc., be the lengths, d lf d z , Fi s- 59a 



etc., the diameters, v lf v 2 , 



the velocities for the successive portions, and let I, d, r, be 

 the corresponding quantities for the equivalent uniform 

 pipe. Then the total loss of head in A due to friction is 



and in the uniform pipe B, 



If these pipes are equivalent, we have 



* Such pipes are called water mains. 



