THE FLOW OF WATER IN" DRAIN" TILE. ^ 
NOMENCLATURE. 
The following symbols are used throughout this report: 
(/=mean depth of flow in the drain, in feet. 
Z)=mean inside diameter of the tile, in feet. 
r=mean inside radius of the tile, in feet=^ B. 
Q=mean discharge of the tile during the test, in second-feet. 
J.=mean area of the tile bore, in square feet=7rr2. 
«=average area of flow in the tile, in square feet. 
F=mean velocitv of the water during the test in feet per second=— • 
P=wetted perimeter in the tile, in feet. 
a D 
i?=mean hydraulic radius=p; in a tile drain running fulli?=^- 
s=hydraulic grade or slope. 
n=coefRcient of roughness in Kutter's formula. 
C=coefficient in Chezy's velocity formula. 
Cy;=coeflicient in the Williams-Hazen velocity formula. 
A=total difference in elevation between ends of a main drain, in feet. 
Z=length of the drain tested, in feet. 
6=summation of the amounts of excess head in the submains, in feet. 
T= number of submains. 
t^=depth of the soil over the main drain at its head, in feet; used only when 
main drains are 1,000 feet or more in length. 
s==mvz is the general equation for the flow of water in drain tile, in which z 
is always constant and m varies only with the size of tile. 
m—eD^ is the equation for the variation of m for a series of drain tile of various 
sizes but of the same material; e and x are constants. 
?7i^=the special values of m found for each series of tile. 
Whenever a test is numbered, the reference is to the correspond- 
ing numbers in Tables 3 and 4 and to Plates X and XI. 
Throughout this discussion the term '^ concrete tile" is used 
instead of '^cement tile." The American Society for Testing Mate- 
rials, in its standard specifications for drain tile, defines concrete 
tile as tile made of '^a suitable mixture of Portland cement, mineral 
aggregates, and water, hardened by hydraulic chemical reaction." 
FORMULA FOR FLOW OF WATER IN DRAIN TILE. 
It is common knowledge that the water enters drains at the joints 
and not through the walls of the tile. Since there is a joint either 
every foot or every 2 feet in the length of the drain, water enters the 
tile drain throughout its entire length. In tile of small sizes, this 
leads to an appreciable variation in the amount of water carried 
at different points in the tile; but in the larger sizes the amoimt 
entering is so small a proportion of the amount carried as to be 
unimportant in considering carrying capacity. 
The water in any tile drain is caused to flow and velocity is set 
up by two forces, one due to the grade of the tile line, and the other 
created when there is a variation in areas of water cross-section. 
