6 BULLETIN 724, U. S. DEPARTMENT OF AGRICULTURE. 
100 per cent of the total precipitation may be drained from the 
watershed during a storm. The extreme rate occurs principally, in 
paved cities in the closely built up business sections, but 80 per cent 
run-off may occur in very steep, impervious or compactly shaped 
watersheds. Under the worst conditions, therefore, it may be neces- 
sary to design surface drains and culverts with capacity sufficient 
to remove about 6 inches of water from a watershed in 24 hours 
and to take care of an extreme precipitation of about 1 inch in 1 
hour. Under other circumstances, the maximum rate of rainfall 
may be considerably less than that mentioned above, and the maxi- 
mum run-off during storms may be only about 15 or 20 per cent of 
the total precipitation on the watershed, though this low run-off 
does not apply often to road drainage. 
CAPACITY OF DRAINS. 
The amount of water required to cover an acre of land to a depth 
of 1 inch is. 3,630 cubic feet. If the maximum rainfall and run-off 
and the area to be drained can be determined, therefore, the total 
volume of water which a given drain should be designed to accommo- 
date can be computed readily. From what has been said, it is ap- 
parent that any estimate of the run-off necessarily will be a- rather 
rough approximation, and due allowance on the safe side always 
should be made as a safeguard against possible inaccuracies in such 
estimates. 
The size of drain necessary to carry a given volume of water in a 
given time may be estimated from the formula 'i)=c\/rs z in which v= 
mean velocity of water; ^hydraulic mean radius of the drain; s= 
the slope of the drain ; and e=a coefficient, the value of which depends 
on the character of the surface of the drain, the slope, and the hy- 
draulic mean radius. Kutter's formula is the one generally consid- 
ered most reliable for determining the value of the coefficient, c. Ac- 
cording to this formula when English units are used, 
,00281 mi 
s n 
c=- 
( 41 . 6 + ^0281\ 
1 + 1 
in which s=slope ratio of drain; ^hydraulic mean radius in feet, 
and n=a constant which depends on the character of the surface of 
the drain. Under average conditions the value of n may be assumed 
as follows : for open ditches, 0.025 to 0.040 ; for cobble gutters, 0.020 
to 0.035 ; for concrete gutters, 0.015 to 0.020; for tile pipe. 0.015. The 
following tables have been computed by means of the above formula? 
especially for use in planning drainage systems. 
