THE FLOW OF WATER IN DRAIIT TILE. 45 
the tile during the experiments indicated that there is additional 
resistance to the flow caused by the action of the air on the water sur- 
face in tile flowing partly full, to which may be due the decided decrease 
in the velocity at the partial depths. Therefore it was decided to vary 
the formula for concrete tile, 
by substituting 7p for D, thus, 
(A \0.56 
-^) s'" (60) 
and to determine the proper values of /for the various depths of flow. 
In the formula 60, the values of V, s, A, and P from the experiments 
(Ffrom Plate IX, the others from Table 4) were used, and the values 
of/ were found to be as follows: 
Tile flo\ving full 1. 00 
Tile flowing 0.9 depth , L 15 
Tile flomng 0.8 depth L 20 
Tile flowing 0.7 depth L 25 
Tile flowing 0.6 depth L 35 
Tile flowing 0.5 depth 1. 50 
The above discussion is given merely as a method of making allow- 
ance for air resistance to flow. Further experiments are considered 
necessary to establish the necessity of making such allowance. 
A comparison of the various formulae which have here been derived 
may be made from Table 7. The formulae have been arranged sys- 
tematically, so that variations may be noted at a glance. They have 
been so classified that all involving the hydraulic radius are in one 
column, while those involving the diameter are in another column. 
The number opposite each formula refers to the corresponding equa- 
tion in the text. 
