THE FLOW OF WATER IN DEAIIT TILE. 
41 
However, for the 0.5 and 0.6 deptlis 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 foimd 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 formula 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. 
SO 
.5 
.6 .7 .8 
1.0 
70 
60 
^^, 
-^ 
Z\-K\ 
' TILE 
■ 
■ 
^^^ 
;^ > 
- 
^ 
SO 
/d\-3067 
Equation of Line K ~S5.57h 
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 : 
For tile flowing full, F=57.8 i)"-'''^^ 50.512 
For tile flowing 0.9 depth, F=57.5 i)^-'^^^ s^-^o^ 
For tile flowing 0.8 depth, F=57.1 D^-ss^ §0.498 
For tile flowing 0.7 depth, F=60.5 D^-^^e s^-sw 
For tile flowing 0.6 depth, F=63.4 D^-ssi s^-^is 
For tile flowing 0.5 depth, F=72.2 i)i-oi s^-^^i 
(35) 
(36) 
(37) 
(38) 
(39) 
(40) 
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 
F=Zi>«s«-5 (41) 
Plotting the values of the coefficient K in formulae 35 to 40 as 
ordinates, against their respective depths of flow as abscissae, an 
equation involving Z and -^ is determined (see text-fig. 1). This 
equation is found to be 
/ fl \— 0.3067 
Z=55.57(-^J (42) 
