THE FLOW OF WATER IN DRAIN TILE. 



41 



However, for the 0.5 and 0.6 depths of flow the exponents of s were 

 found to be rather high; so for these two depths the centers of gravity 

 of the various sizes of tile were computed analytically, and the 

 exponents of s were found to be the same as the values determined 

 graphically. It should be noted that the diameter of the tile and 

 not the mean hydraulic radius was used in the formulae derived for 

 various depths of flow. In determining the equation of the line 

 showing the relation of m and the diameter D (equation 16), the 

 centers of gravity were computed lest appreciable error should be 

 introduced in attempting to draw these lines by eye. However, after 

 the lines were drawn through the computed centers of gravity, the 

 slopes of these lines were determined by scale.and the intercept was 

 read direct from the diagram. 



Depth off/or^ 

 .6 .7 .8 



1.0 



80 



^70 

 J? 



so 



/d\-3067 

 Equation of Une K-55.57\j}J 



Fig. 1.— Relation of coefficient K to depth of flow in formulae 35-40. 



The formulae for clay tile as derived from figures 3 to 8, Plate XI, 

 are as follows : 



^ N *'-»*^ 1>< ^ ) 



: 

















i 





F^**^"^ 











- 







j 



: ^""^ 



[L ) 



: 





CLAY TILE 













For tile flowing full, 7=57.8 Z> - 662 s - 512 



For tile flowing 0.9 depth, 7=57.5 Z>°- 678 s - 502 

 For tile flowing 0.8 depth, 7=57.1 D°- G82 s - 498 

 For tile flowing 0.7 depth, 7=60.5 Z> - 756 s - 507 

 For tile flowing 0.6 depth, 7=63.4 D - 881 s - 518 



s° 



(35) 

 (36) 

 (37) 

 (38) 

 (39) 

 (40) 



For tile flowing 0.5 depth, 7=72.2 D 1 - 01 s - 541 



These equations furnish sufficient basis for determining next a 

 general formula to cover every depth of flow. Since in this group of 

 formulae the exponent of s is about 0.5, each equation is of the form 



V=KD a s - 5 (41) 



Plotting the values of the coefficient K in formulae 35 to 40 as 



ordinates, against their respective depths of flow as abscissa?, an 



equation involving K and =, is determined (see text-fig. 1). This 

 equation is found to be 



/ /} \— 0.3067 



K= 55.57^ J (42) 



