42 
BUIJLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 
In a like manner, j^lotting values of the exponent of D as ordinates 
against tlieir respective depths of flow as abscissae, the equation for 
the exponent of D for any depth of flow was found to be (see text- 
fig. 2) 
a = 0.6284(^2)) (43) 
Then writing the equation to cover every depth of flow in clay tile, 
we have 
0.6284 
F = 
55.57 
m 
D 
ar 
(44) 
/.o 
.5 
.6 .7 .8 
.9 
1.0 
V 
I 
r 
2 
.6 
N 
\ 
\i 
V^ 
^\ 
^ 
^^ 
Cl 
.AY T 
ILE 
= N 
"V 
N 
/cl\-639 
Ejuafion of Line ex. =. f2S4(-^j 
Fig. 2.— Relation of exponent of D to depth of flow in formulse 35-40. 
d 
When y. equals 1 — in other words when the tile is flowing full- 
and assuming the exponent of s to be 0.5 for all depths oi flovv, 
F= 55.57 D""-^-' 
(45) 
A study of figures 3 to 8, Plate X, shows that the 4-inch concrete 
tile appears to have a greater coefficient of roughness than do the 
larger sizes. This is also indicated in Table 4. Therefore it was 
decided to eliminate the 4-inch tile and consider only the remaining 
sizes in deriving a new formula. The formulae for the concrete tile 
for the 5, 6, 8, 10, and 12 inch sizes for all depths of flow then become: 
For tile flowing full, F=51.15 D"-^'''' s"-^^^ (46) 
for tile flowing 0.9 depth, F=50.80 D°-^«^ s^-^^^ (47) 
for tile flowing 0.8 depth, F=51.49 D^--^^^ 5O.496 (4g) 
for tile flowing 0.7 depth, F=51. 93 i>o«25s0.5oi (49) 
for tile flowing 0.6 depth, F-51.37 D^-^^a ^o-sm (50) 
for tile flowing 0.5 depth, F=49.22 D^-'^^^ sO-«io (51) 
