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order of dryness on these different bases will not place them in the same order. One year may be the dryest with reference to rainfall, another with reference to runoff, and still another with reference to the maximum storage required. In this discussion such differences are overlooked, and the 99 per cent dry year is considered as a type, and always refers to the year defined as above with reference to whatever matter may be under investigation at the time.

In the northeastern United States the 95 per cent dry year seems to be the best ordinary basis of rating. Using it, there is a probability that the full supply can be maintained for 95 of each 100 years. In the other 5 years there will be shortages, with deficiencies ranging from 1 to 10 per cent and possibly to somewhat more than 10 per cent at long intervals, and averaging about 6 per cent in all the years of shortage, these being 5 per cent of the whole number.

There is no fixed rule in regard to using the 95 per cent dry year, but, in general, the suffering of a community due to a moderate shortage of supply at long intervals will not be great enough to warrant large additional investments to prevent it. The matter is one of economics and is discussed in the literature to which references are made.

Ground storage The days to be deducted for ground water storage represent the difference between a normal storage curve for a catchment area impervious, or nearly so, and the actual area. Seventy-three days deduction in the first item in table 4, means that 73 times the daily maintainable flow at any given rate of draft may be deducted from the normal storage required to maintain that flow, as this amount of storage can be counted on from natural reservoirs. This is called ground storage, but the term is not quite accurate as it represents all the variations that there may be from whatever cause. The ground water storage is much the most important, but seasonal distribution of rainfall, snow conditions and other matters contribute to the result.

In cases where less than 50 per cent of the mean flow is to be utilized, figure 2 will be found convenient for estimating the storage required. The curves are based on data determined for the 95 per cent dry year from a large number of streams in the northeast states, north of the Potomac and east of the Alleghanies, having a coefficient of variation of 0.20 to 0.30. They should not be used elsewhere, unless records of flow indicate closely similar conditions. Statistics of flow

In table 4 are shown the mean annual flow, coefficient of variation and ground water storage, of representative streams that have been accurately gauged for a term of years.

Relations between mean flow and storage The relations between the percentages of the mean flow that can be delivered, and the required storage ratios for several representative cases are stated in table 5.

Tables in somewhat general form representing different parts of the country are to be found in the American Civil Engineers Pocket Book. A number of adjustments for evaporation and otherwise must be made and these should not be overlooked in using these figures. Tables cannot be safely reproduced without the accompanying full statement of limits to their use.

A short bibliography to aid in further study of this problem follows:

The selection of Sources of Water Supply. F. P. Stearns. Journ. Ass'n,

Engineering Societies, vol. 10, page 485, 1891. Rainfall, Flow of Streams, and Storage. Desmond FitzGerald. A. S. C. E.,

vol. 27, page 304, 1892. Yield of Croton Water Shed. John R. Freeman. Report on New York Water

Supply, City Document, page 120, 1900. Forest and Reservoirs in Their Relation to Stream Flow, with Particular

Reference to Navigable Rivers. H. M. Chittenden. A. S. C. E.

vol. 62, page 245, 1909. Report of Committee on Yield of Drainage Areas. F. P. Stearns, Chairman.

N. E. W. W. A., vol. 28, page 397, 1914. Storage to be Provided in Impounding Reservoirs. Allen Hazen. A.S. C. E.,

vol. 77, page 1539, 1914. Computing Runoff from Rainfall and Other Physical Data. Adolph F. Meyer.

A. S. C. E., vol. 79, page 1056, 1915. The Probable Variation in Yearly Runoff as Determined from a Study of

California Streams. L. Standish Hall. A. S. C E., vol. 84, page 191,

1921. Rainfall and Runoff Studies. C. E. Grunsky. A. S. C. E., vol. 85, page 66,

1922. The Operation of Reservoirs for Water Supply. Samuel A. Greeley. A. S. C.

E., vol. 85, page 496, 1922. Theoretical Frequency Curves and Their Application to Engineering Prob

lems. H. Alden Foster. A. S. C. E., vol. 87, page 142, 1924. Chapter on Yield and Storage. Allen Hazen. American Civil Engineers

Pocket Book, John Wiley & Sons, 4th edition, page 1192, 1920.

Elements of Statistics. Arthur L. Bowley. 3rd edition, Charles Scribner &

Son., 1907.
Introduction to Theory of Statistics. G. U. Yule. Charles Griffen & Co.,

Ltd., London, 1912.
Elements of Statistical Methods. W. I. King. Macmillan Co., 1912.

PROVISION FOR FLOOD DISCHARGE IN THE DESIGN OF SPILLWAYS

AND OTHER STRUCTURES

Nearly every year, in some part of the country, floods occur that cause serious loss of property and frequently of life. Merely because the floods for a number of years have not exceeded a certain size, the channels, through which great floods have in the past flowed, are frequently congested and reduced in carrying capacity. When the great flood comes these obstructions first prevent the water from flowing off as rapidly, thus backing up the water to higher levels than would have otherwise been the case, and then may be swept out, releasing the waters above with a resulting flood wave that causes great damage below.

That an unobstructed flood channel, sufficient in size to carry safely the largest flood that will probably come during a long period of years, should be maintained throughout the length of the stream is essential in all parts of the country where the adjacent land is to be utilized for building of homes and for manufacturing purposes. The lands within the channel of great floods may properly be used for other purposes which do not restrict the ability of the channel to carry water and which do not involve loss of life or property, when the stream claims its channel for flood discharge. Failure to maintain such flood channels must inevitably lead to disaster.

The determination of the size of this flood which may come sometime during a long period of years is difficult, but highly important for the design of many structures. It is essential to the determination of the capacity of spillways for dams, for bridge and culvert openings, for size of flood channels through cities, for the elevation and strength of foundations of structures built along the banks of streams, for flood protection works and for many other purposes.

Factors affecting floods

The factors which affect floods may be divided into two general classes, those which are dependent upon the conditions and characteristics of the stream in question and which tend to make the

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floods on that stream greater or less than on other streams and those which are largely independent of the particular stream itself, but are common to all streams, or at least to streams in the particular section of the country, and which make floods during some years greater or less than during others.

Under the first class of factors are the size of the drainage areas, the slope of the stream and its branches, the slope of the land draining into these streams, the number and distribution of the branches, the nature of the soil as to porosity and ability to absorb the water, the conditions as to general average intensity of rainfall, the average conditions as to the amount of snow which is held on the drainage area, the size of ponds, lakes and swamps on the area, and to many other conditions which are peculiar to the stream. These characteristics have much the same effect on the size of all floods which come during a period of years. They tend to make the average flood greater or less on some streams than upon others.

The second class of factors are those which are different from year to year and which are, in the main, dependent on chance or probability. Among these elements are the chance of occurrence of great storms, of such storms coming at times when the ground is saturated and when large quantities of snow are stored on the area, of such storms sweeping over the area in such a way as to concentrate the run off from different branches at some point simultaneously, and to- a great many other possible combinations of conditions. It is at least reasonable to suppose that these chances are somewhat similar on different streams, inasmuch as they are a function of probable combinations of circumstances. That the relation is a complex one is certain. In addition to these elements great floods may also result from failure of structures, such as dams or other artificial obstructions to waterways, which are constructed from time to time with more or less degree of safety, and from temporary obstructions, such as ice jams and jams of debris which may be subject again to artificial changes in the stream channel. These may vary from year to year and past records in such cases may be misleading

Formulas for flood flow Many different formulas have been proposed for estimating the maximum flow which may be expected. Table 6 gives some of these, together with the discharge for different sizes of drainage areas which result from their use. Where coefficients and variables are included in the formulas, values have been taken which correspond in a general way with conditions existing in this country for streams where large floods may be expected. Other values for these coefficients would, of course, change the amount of discharge.

For more extended discussion of these formulas, see American Sewerage Practice, Metcalf and Eddy, vol. i, page 249; Report on the New York State Barge Canal, 1901, by Emil Kuichling; Paper on Flood Flows, Transactions of the American Society of Civil Engineers, vol. lxxvii; Paper on Flood Flow Characteristics, Proceedings Amer. Soc. Civil Engineers, December, 1924, and discussion in proceedings for 1925.

The Fuller formula gives the flow in terms of a coefficient C, the drainage area A, and a factor of safety expressed in years. The coefficient C represents the characteristics of the particular stream, so that the expression

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represents the maximum rate of flow which may come on an average year.

The expression (1 + 0.8 log T") represents the ratio which the greatest flood in a period of years is to the average yearly flood. It is a factor of safety to provide for the chance of the extraordinary flood occurring.

As will be noted in table 6, the Fuller formula using C = 50, T = 50 gives results somewhat similar to the minimum obtained from the other formulas, while c = 200, T = 1000 gives results

C which correspond in a general way with the maximum obtained by the other formulas. Some streams in the country have coefficients at least as high as 200 and many have coefficients as low as and some lower than 50.

The use of T as 1000 is providing for but a moderate factor of safety for any important structure. It is like providing a factor of safety for steel sufficient so that only one in one thousand pieces will fail under the allowed stress. As a guide for obtaining the maximum flood for design, figure 3 is given which shows the results which are obtained by the Fuller formula for maximum flood discharge per square mile, where C = 100 and a factor of safety of five is provided to cover the floods which come at rare intervals. For other values of C or for other values of the factor of safety, the values obtained from this diagram may be increased or decreased in direct proportion.

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