Abbreviations: H.S. = horseshoe shaped; B. & C = Brick and concrete; V.P. = vitrified pipe; G. = gravel; Q. = quicksand; S. C. = sand clay; C. = clay.
=28. The Rational Method.=—The water which falls during a storm must be removed rapidly in order to prevent the flooding of streets and basements, and other damages. The quantity of water to be cared for is dependent upon: the rate of rainfall, the character and slope of the surface, and the area to be drained. All methods for the determination of storm-water run-off, whether rational or empirical, depend upon these factors.
The so-called Rational Method can be expressed algebraically, as,
in which _Q_ = rate of run-off in cubic feet per second;
_A_ = area to be drained expressed in acres;
_I_ = percentage imperviousness of the area;
_R_ = maximum average rate of rainfall over the entire drainage area, expressed in inches per hour, which may occur during the time of concentration.
The area to be drained is determined by a survey. A discussion of _R_ and _I_ follows in the next two sections. An example of the use of the Rational Method is given on page 95.
=29. Rate of Rainfall.=—Rainfall observations have been made over a long period of time by United States Weather Bureau observers and others. Continuous records are available in a few places in this country showing rainfall observations covering more than a century. Such records have been the bases for a number of empirical formulas for expressing the probable maximum rate of rainfall in inches per hour, having given the duration of the storm. Table 13 is a collection of these formulas with a statement as to the conditions under which each formula is applicable. The formula most suitable to the problem in hand should be selected for its solution.[22]
────────────┬─────────────────────────┬──────────────────────────────── Name of │ Conditions for which │ Formula Originator │ Formula is Suitable │ ────────────┼─────────────────────────┼──────────────────────────────── E. S. Dorr │ │_i_ = 150⁄(_t_ + 30) A. N. Talbot│Maximum storms in Eastern│_i_ = 360⁄(_t_ + 30) │ United States │ A. N. Talbot│Ordinary storms in │_i_ = 105⁄(_t_ + 15) │ Eastern United States │ Emil │Heavy rainfall near New │_i_ = 120⁄(_t_ + 20), etc. Kuichling │ York City │ L. J. Le │For San Francisco. See T.│ Conte │ A. S. C. E. v. 54, p. │_i_ = 7⁄_t_^½ │ 198 │ Sherman │Maximum for Boston, Mass.│_i_ = 25.12⁄_t_^{ .687} Sherman │Extraordinary for Boston,│_i_ = 18⁄_t_ ^½ │ Mass. │ Webster │Ordinary for │_i_ = 12⁄_t_^{ 0.6} │ Philadelphia, Pa. │ │Ordinary storms for │ Hendrick │ Baltimore. Eng. & │_i_ = 105⁄(_t_ + 10) │ Cont., Aug. 9. 1911 │ J. de │Ordinary storms for │_i_ = 163⁄(_t_ + 27) Bruyn-Kops│ Savannah, Ga. │ C. D. Hill │For Chicago, Ill. │_i_ = 120⁄(_t_ + 15) Metcalf and │Louisville, Ky. Am. Sew. │_i_ = 14⁄_t_^½ Eddy │ Prac., Vol I. │ W. W. Horner│St. Louis, Mo. Eng. News,│_i_ = 56⁄(_t_ + 5)^{ .85} │ Sept. 29, 1910 │ R. A. │For Spokane, Wash. Eng. │_i_ = 23.92⁄(_t_ + 2.15) + 0.154 Brackenbuy│ Record, Aug. 10, 1912 │ Metcalf and │New Orleans │_i_ = 19⁄_t_^½ Eddy │ │ Metcalf and │For Denver, Colo. │_i_ = 84⁄(_t_ + 4) Eddy │ │ │Central Park, N. Y. │ Kenneth │ 51–Year Record. Eng. │_i_ = 400⁄(2_t_ + 40)[23] Allen │ News-Record, April 7, │ │ 1921, p. 588 │ ────────────┴─────────────────────────┴────────────────────────────────