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21. O 'I rl {)9 '".I , l~ f..) .,', q various ranges of discharge were experienced. Table 2 is an example of the information so prepared. This table shows flow-duration data for the gaging station on Vermillion Creek near Wamego, Kansas, for each complete water year of record, 1937-45, 1955, 1956. Daily discharges were separated into the 20 ranges or class limits of flow listed in the first column. The class limits were spaced uniformly by logarithmic scale to inClude the range in daily discharge dur ing the period of record from the minimum to just over the maximum. The number of days when the daily discharges fell within each class limit is shown for each year. The second from the last column shows a summary of the days in each class. These days are accumulated in the next to last column to show the total number of days duration that the dis- charge was equal to or greater than the discharge in the first column. The last column is a convers ion of the accumulated days duration to percent of time duration, where the total days of record is equal to 100 percent. It should be observed that these results define the variations of flow without regard to chronological sequence. Flow distribution relations may be expressed in a number of graphical forms. A plot of the data in the second from last column of table 2 with num- ber of days by ordinate scale and discharge by logarithmic abscissa scale would define a bell shaped graph skewed to the right and familiar;to statisti- cians as a frequency distribution curve. Such a graph would illustrate the variation of flow, .but not in a conveniently usable form because of its curva- ture. Of g.reater versatility is a cumulative graph of the same data plotted from percent duration of flow in the last column of table 2. Graphs so de- fined are termed .flow-duration curves. They approach a straight line in shape if appropriate scales are selected. The ordinate scale of discharge should be logarithmic and the abscissa scale a probability scale ofp-e:reen:t of time as introduced by Hazen4 and mathematically developed by Foster. 5 A plot of the flow-duration data of table 2 is shown by open circles on figure 61. Discharges are expressed as cubic f<jet per second per square mile of drainag.e basin so the values may be compared with those of other stations. A curve through these circles would depict the actually observed duration of flow for the period of record en<iing September 30, 1956. Similar values are shown for 122 stations in the section of this report entitled, I'Flow.Dura'tion Data. " Lo.n g - T e r m Com par a b Ie ReI a t ion s For statewide, long-range water-planning purposes, flow-duration curves should incorporate the three following characteristics: (1) The period of rec- 4 Hazen, Allen, 1916, Journal Boston Soc.. Civ. Engr., pp. 77, 209c303" 324-328. 5 Foster, H, A. 1950, Stream 'flow variability, Trans. Amer. Soc. Civ. Eng";, vol. 115, pp. 1101-1108.