(1) It is the maximum rate of rainfall during the severest storms which is required in this connection. This varies greatly in different sections of the country.
The maximum rainfall as shown by statistics is about one inch per hour (except during heavy storms), equal to 3,630 cubic feet per acre. Owing to various causes, not more than 50 to 75 per cent of this amount will reach the culvert within the same hour.
Inches of rainfall X 3,630 = cubic feet per acre.
Inches of rainfall X 2,323,200 = cubic feet per square mile.
(2) The amount of water to be drained off will depend upon the permeability of the surface of the ground, which will vary greatly with the kind of soil, the degree of saturation, the condition of the cultivation, the amount of vegetation, etc.
(3) The rapidity with which the water will reach the water course depends upon whether the surface is rough or smooth, steep or fiat, barren or covered with vegetation, etc.
(4) The rapidity with which the water will reach the culvert depends upon whether there is a well-defined and unobstructed channel, or whether the water finds its way in a broad thin sheet. It the water course is unobstructed and has a considerable inclination, the water may arrive at the culvert nearly as rapidly as it falls; but if the channel is obstructed, the water may he much longer in passing the culvert than in falling.
(5) The area of waterway depends upon the amount of the area to be drained; but in many eases the shape of this area and the posi tion of the branches of the stream are of more importance than the amount of the territory. For example, if the area is long and narrow, the water from the lower portion may pass through the culvert before that from the upper end arrives; or, on the other hand, if the upper end of the area is steeper than the lower, the water from the former may arrive simultaneously with that from the latter. Again, if the lower part of the area is better supplied with branches than the upper portion, the water from the former will be carried past the culvert before the arrival of that from the latter; or, on the other hand, if the upper part is better supplied with branch water courses than the lower, the water from the whole area may arrive at the culvert at nearly the same time. In large areas the shape of the area and
the position of the water courses are very important considerations.
(6) The efficiency of a culvert may be very materially increased by so arranging the upper end that the water may enter into it without being retarded. The discharging capacity of a culvert can be greatly 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 increased 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 exact ness 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 sufficient, 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 S-foot arch culvert is needed.
Valuable data on the proper size of any particular culvert may be obtained (1) by observing the existing openings on the same stream; (2) by measuring, preferably at time of high water, a cross section of the stream at some narrow place; and (3) determining the height of high water as indicated by drift and the evidence of the inhabitants of the neighborhood.