LOSSES AT BENDS 



253 



out on bends of small radius, so that not much reliance is to be placed 

 in the results. 

 For sharp bends or elbows (Fig. 113), Weisbach deduced the formula 



o 



Loss = F-^ feet 

 %9 



where F = '946 sin 2 f- + 2'05 sin 4 |, 



A A 



being the angle of deviation of the elbow. 



With a tee branch pipe (Fig. 114) the loss is rather greater than in a 

 right-angled elbow (see p. 256). 

 Recent experiments by the author on elbows of rectangular section, 



1 in. X 1 in., showed the loss to be proportional to r' 2 for all velocities 

 up to 22 feet per second, and gave the following values for F: 



These correspond to the relationship F = '0000676 6> 2 ' 17 where is in 

 degrees. The values are considerably greater than those given by 

 Weisbach's formula, and while the difference may be due to some extent 

 to the difference in the shapes and sizes of the passages, recent experi- 

 ments on elbows of circular cross section, see p. 254, tend rather to 

 confirm the author's value when 6 90. 



Experiments by Alexander, 1 by Williams? and by Brightmore, 3 the 

 former using varnished wooden pipes of 1J inches diameter, Williams 

 using asphalted pipes of 12, 16, and 30 inches diameter, and Brightmore 

 using cast-iron pipes of 3 and 4 inches diameter, indicate that the 

 additional loss due to the curvature of a pipe does not, as might be 

 expected, diminish uniformly as the radius of curvature increases, but, 

 after attaining a minimum value for a value of R = 5 r (Williams and 

 Alexander), R = 7'5 r (Brightmore), increases slightly to a point where 



1 " Proceedings Institute Civil Engineers," vol. 159, p. 341. 



2 (i Proceedings American Society Civil Engineers," 1901, p. 314. 



3 " Proceedings Institute Civil Engineers," 1906-7, vol. 169, p. 315. 



