12 BULLETIN 193, U. S. DEPARTMENT OF AGRICULTURE. 



may overflow and the pumps be flooded, for short periods, but it 

 seems economically impracticable to provide against such unusual 

 conditions. 



RUN-OFF FORMULA. 



Many attempts have been i^iade to devise a mathematical expres- 

 sion involving various of the factors that modify the maximum 

 run-off rate, for use in estimating run-off when there are not actual 

 gagings that will serve as a fairly reliable guide. A formula has been 

 suggested by S. W. Frescoln for computing the run-off depth to be 

 expected from any simple drainage area. It is as follows: 



^ BL 



in which 



Z) = maximum rate of run-off, m inches per 24 hours, to be 



expected from the ramfall P. 

 C=Si coefficient depending solely upon the physical character 



of the soil, and determined by experiment. 

 21= the ratio of total rim-off to total rainfall, for the precipita- 

 tion P, varying with evaporation, deep percolation, lateral 

 seepage from the drainage channels, and duration of flood. 

 P = the depth of rainfall in inches in 24 hours (4 inches for 



Jefferson County). 

 F=the average slope of the ground surface of the drainage 



area, in feet per mile. 

 L = the mean length of the drainage area in miles. 

 B = one-half the mean width of the drainage area in miles. 

 For drainage areas that contain storage reservoirs, a special cal- 

 culation must be made to eliminate the effect of the reservoirs. 

 Where the main watercourse is formed by the junction of two or more 

 large tributaries, the formula is to be applied to each tributary 

 separately, and the proper value of the run-off depth for the entire 

 area will be the weighted mean of the values for the parts. 



APPLICATION or THE FORMULA. 



The values of L, B, and F are determined from the drainage sur- 

 vey, P from rainfall data as already explained, M and C by com- 

 parison with other drainage basins where gagings and other flood 

 data have been secured. 



The value of -yfF is determined for each simple drainage basin by 

 first dividing the area into units wherever there is a marked change 

 in the surface relief, as where a flat area joins a rolling or hilly section, 

 each unit wholly on one side of the main stream. The mean -yfF is 

 found for the course which the water will take from each corner of 

 the unit to the outlet of the whole basin and the average of these 



