152 



TRANSACTIONS OF THE CANADIAN INSTITUTE. 



[Vol. II. 



without increased head and when you consider that the system of 

 sewers forms a net work you will see that this head cannot be obtained, 

 as the sewage will make its escape throus^h other connections, and the 

 sedimentation goes on till the pipe is completely choked. This may be 

 seen again and again in Queen street sewer and other sewers throughout 

 the city. 



TijNM 



r{^,JI. 



A formula for calculating the coefficient of friction in pipes running 

 partly full is as follows :— Coef. of F=v7^^5^ ; regarding the coef as unity 

 when the pipe is running full or half full, as you will thus see, the whole 

 F. Sur. -i- whole vol. = i. or yi ¥. Sur. -=r]4 vol = i . 



Fig. VII, shows the circle divided into two segments by the side of 

 an inscribed equilateral triangle, figures VIII. and IX. are similarly 

 divided by the side of an inscribed square and hexagon respective!}-. 

 In Fig. VII., consider the sewer filled to the line a. a., the frictional 

 surface would be represented by ^, while the Vol. of Sew. = |-. Then 

 by applying the formula f^=: -833, = Coef. of F. While the small Seg. 

 would give |75=r6=Coef. of F. The latter being double of the former. 



Similarly, if Fig. VIII. were filled to the line a. a., the Y. Sur. would 



be ^, while the Vol. of Sew. would be \^ ; then by applying the formula 



we get j^ = -825, = Coef F. While the smaller Seg. shown by b. b. 



would be rri = 275==Coef. of F. The latter more than three times the 

 former. 



Fig. IX. gives a more marked contrast still. In the large Seg. cut off 

 by a. a. the F. Sur. is represented by f while the Vol. of Sew. is i|-, then 

 if^='882,=Coef. of F While the small Seg. cut off by b. b. would give 

 a result of j^g= 3.00. Coef of F., nearly four times as great as in the 

 larger segment. You will observe that figures VII. VIII. and IX. give 

 Coef respectively, of -833. '825 and -882, thus Fig. VIII. having the 

 lowest Coef would give the best maximum of velocity. And thus we 

 obtain the paradoxical result that a pipe flowing partly full will have a 

 better Coef. of discharge than when flowing full. 



