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 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 Τ from the other formulas, while C 200, T = 1000 gives results 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. TABLE 6 Comparison of various formulas for flood discharge in cubic feet per second Dun's Table A. T. & S. F. Culverts. . . . 1,000 6,790 21,200 64,000 T = length of drainage area width of drainage area discharge per square mile length of the period in years during which one such flood will probably occur on any one stream R = annual rainfall in inches Value of C C is the measure of the effect of all of the various factors previously noted under the first class, except size of the drainage area. The value of 100 used in figure 3 is higher than the average for streams in this country. The range of values for those streams in different parts of the country for which measurements have been made for a period long enough to enable a coefficient to be obtained is as follows: General range of coefficient C for streams Some streams within these districts will have greater and some much lower coefficients than the above. These coefficients are in the main for streams which have been measured by the United States Geological Survey over a period of some years. The method used in obtaining these values is, in general, to find the average of the single largest flood for each year on the basis of the flow during twenty-four hours. This average yearly flood is then divided by 40.8 (where A is the drainage area in square miles) to obtain the value of C. Figure 4 may be used for the purpose of finding the value of C where the average yearly flood is known. This diagram gives the average run off per square mile when C is 100. If the average flood, for the stream under consideration, is known, the amount per square mile may be found by dividing by the drainage area. The C for the stream is then the same proportion of 100 that this yearly flood |