(6) The efficiency of a culvert may be materially increased by so arranging the upper end that the water may enter it without retarded. The discharging capacity of a culvert can also be increased by increasing the inclination of its bed, provided the channel below will allow the water to flow away freely after having passed the culvert.
(7) The discharging capacity of a culvert can be greatly in creased by allowing the water to dam up above it. A culvert will discharge twice as much under a head of four feet as under a head of one foot. This can be done safely only with a well-constructed culvert.
The determination of the values of the different factors entering into the problem is almost wholly a matter of judgment. An estimate for any one of the above factors is liable to be in error from 100 to 200 per cent, or even more, and of course any result deduced from such data must be very uncertain. Fortunately, mathematical exactness is not required by the problem nor warranted by the data. The question is not one of 10 or 20 per cent of increase; for if a 2-foot pipe is insufficient, a 3-foot pipe will probably be the next size, an increase of 225 per cent; and if a 6-foot arch culvert is too small, an 8-foot will be used, an increase of 180 per cent. The real question is whether
a 2-foot pipe or an 8-foot arch culvert is needed.
Calculating Area of Waterway. Numerous empirical for mulas have been proposed for this and similar problems; but at best they are all only approximate, since no formula can give accurate results with inaccurate data.
The size of waterway may be determined approximately by the following formula: in which Q = the number of cubic feet per acre per second reaching the mouth of the culvert or drain.
C = a coefficient ranging from .31 to .75, depending upon the nature of the surface; .62 is recommended for general use.
r = average intensity of rainfall in cubic feet per acre per second.
S = the general grade of the area per thousand feet.
A = the area drained, in acres.