254 



HYDRAULICS AND ITS APPLICATIONS 



li = about 13 /, and afterwards diminishes to zero with a curve of iniinite 

 radius. The experiments further show that the power of v, to which 

 the loss is proportional in a gradual bend, is the same for the bend as 

 for the straight pipe. Alexander, as the result of his own and of 

 Williams' experiments, concludes that the additional loss due to a bend 

 of radius R = 5 r, is equivalent to that offered by a length of straight 

 pipe equal to 3*38 I, where I is the length of the curved portion of the 

 pipe. Thus if the angle of the bend is 90 this makes the equivalent 

 length equal to 13'3 d, where d = pipe diameter in feet. This agrees 

 with the results of a number of experiments made at the Yorkshire 

 College, 1 from which it was concluded that the resistance of an easy right- 

 angled bend is equivalent to that in a straight pipe 10 to 15 diameters in 

 length, while for a sharp right-angled bend or elbow the equivalent length 

 is from 30 to 36 diameters. 



Brightmore's results point to the fact that for all curves of the best 

 radius, for all diameters of cast-iron pipes and for all velocities, the 

 additional loss of head due to the curvature in a right-angled bend is 



r 2 

 approximately equal to '3 ^- feet. 



* 9 

 The following values of F are deduced from Brightmore's results : 



Value of R -=- r. 



Value of R -r- r. 



Engineering, September 25, 189G, p. 390. 



