362 HYDRAULICS 



with the loss due to friction and is therefore neglected. The 



formula used for long pipes, is v = \ I 



\ fl 



The value of / depends not only on the roughness of the pipe, 

 but also on its diameter and the velocity of flow. Its values 

 for a smooth pipe are given in the preceding table. For 

 rough pipes, these values should be multiplied by 2. 



COEFFICIENTS FOR ANGULAR BENDS 



(a = angle of bend in degrees) 



When the pipe is shorter than 1,000 diameters and the first 

 of the preceding formulas is used, the component 

 parts forming the value of c must be ascertained 

 and the results added and substituted in the 

 formula. The coefficient k s for angular bends can 

 be taken from the accompanying table giving its 

 value for different angles. The coefficient for 



a 

 circular bends is c e = k c , in which a is the angle 



of the bend and k c is a constant depending on the 

 ratio of the radius of the pipe to that of the bend and is given 

 in the following table for circular bends. 



COEFFICIENTS FOR CIRCULAR BENDS 



(r = radius of pipe. R = radius of bend) 



Valves. With reference to the accompanying illustration, 

 the coefficients of resistance j for different ratios of b to d are as 

 follows: 



