LEVEL-POOL ROUTING 135 



vals of time. Since the inflow is independent of the other variables, 

 the inflow hydrograph may be represented by the equation 



i=h{t) [1105] 



where i represents the rate of inflow and / represents the time. 



We are now reaay to establish the diff^erential equation, a modified 

 form of the law of continuity, the solution to which will be the desired 

 outflow hydrograph. In a brief interval of time a volume of water idt 

 will flow into the reservoir. During the same interval of time a volume 

 of odt will flow out of the reservoir. If idt is greater than odt the differ- 

 ence will be stored in the reservoir, so that we may write 



idt = odt-{-dS [1106] 



in which i = M), o = f\{E), and 5 = fz{E). If odt is greater than 

 idt, dS will be negative, indicating that the storage is decreasing. We 

 wish to obtain the relationship o = fsit). Even though the given 

 functional relationships are defined by simple equations it is impossible 

 to obtain a solution of the differential equation, except in certain special 

 cases. The only one of these having any practical value is when 



* = /4(0 = a constant 



or, in other words, when the inflow does not vary.^ If the inflow is 

 allowed to vary, solution of the differential equation is impossible 

 unless the other relationships have simple forms almost never found in 

 practice. 



Though this result may seem to preclude any chance of solving the 

 problem at hand it actually points the way towards an easy solution. 

 The computations must be made in steps, each step so short that during 

 its duration the inflow may be considered constant. Since values of the 

 inflow are ordinarily given at brief regular intervals — regular as a 

 matter of convenience, and brief in order to define clearly the shape of 

 flood peaks, a step-by-step solution is most convenient. The first step 

 methods to be used were awkward and laborious, requiring trial-and- 

 error solution of each step, but later methods introduced a direct pro- 

 cedure which greatly reduced the work of computation.^ The method 

 presented here is the result of further study, pointed toward reducing 



^ " Functional Design of Flood Control Reservoirs," C. J. Posey and Fu-Te I, 

 Trans. Am. Soc. Civil Engr., v. 105 (1940), p. 1638. 



^ " Hydraulics of the Miami Flood Control Project," S. M. Woodward, Technical 

 Reports of the Miami Conservancy District, PartVII, Chapter VII; " Flood Routing," 

 Edward J. Rutter, Quintin B. Graves, and Franklin F. Snyder, Trans. Am. Soc. 

 Civil Engr., v. 104 (1939), p. 275. 



