Methods of Determining Waterway

METHODS OF DETERMINING WATERWAY. There are two methods of determining the area of the waterway required: (1) by the use of an empirical formula, and (2) by direct observation. The first method is the only one that can be employed in a new country or where there are no other structures over the stream; while the second method is applicable on a line already open or in a territory well settled up.

The determination of the values of the different factors entering into the problem is almost wholly a matter of judgment. An esti mate for any one of the factors mentioned in the preceding section may 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 21-foot pipe will probably be the next size—an increase of 50 per cent,—and if a 6-foot arch culvert is too small, an 8-foot will be used—an increase of 80 per cent. The real question is whether a 2-foot pipe or an 8-foot arch culvert is needed.

Empirical Formulas.

Numerous empirical formulas have been proposed; but at best they are all only approximate, since no formula can give accurate results with inaccurate data. The several formulas for area of waterway, when applied to the same problem, give very discordant results, owing (1) to unavoidable errors in estimating the various factors mentioned in ?l 1117 and (2)• to the formulas' having been deduced for localities differing widely in the essential characteristics upon which the results depend. For ex ample, a formula deduced for a dry climate, as India, is wholly inapplicable to a humid and swampy region, as Florida; and a formula deduced from an agricultural region is inapplicable in a city.

However, an approximate formula, if simple and easily applied, may be valuable as a nucleus about which to group the results of personal experience. Such a formula is to be employed more as a guide to the judgment than as a working rule; and its form, and also the value of the constants in it, should be changed as subsequent experience seems to indicate.

There are two classes of these formulas, one of which purports to give the quantity of water to be discharged per unit of drainage area, and the other the area of the waterway in terms of the area of the territory to be drained. The former, often called run-off formulas, give the amount of water supposed to reaoh the culvert; and the area, slope, form, etc., of the culvert must be ad justed to allow this amount of water to pass. There are no reliable data by which to determine the discharging capacity of a culvert of any given form, and hence the use of the formulas of the first class adds complication without securing any compensating reliability. Such formulas will not be considered here.* Of the formulas giving directly the area of the waterway in terms of the territory to be drained, Myers's and Talbot'a are the only ones in common use.

Myers's Formula.

This formula was proposed by E. T. D. Myers in 1887, and is said to be the one most used by engineers in the New England and Atlantic States. It is: in which C is a variable coefficient to be assigned. For slightly rolling prairie, C is usually taken at 1; for hilly ground at 1.5; and for mountainous and rocky ground at 4. For most localities, at least, this formula gives too large results for small drainage areas. For example, according to the formula, a culvert having a waterway of one square foot will carry the water from only a single acre. Further, if the preponderance of the testimony of the formulas for the quantity of water reaching the culvert from a given area can be relied upon, the area of waterway increases more rapidly than the square root of the drainage area as required by this formula. Hence, it appears that neither the constants nor the form of this formula were correctly chosen; and, consequently, for small drainage areas it gives the area of waterway too great, and for large drainage areas too small.