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<br />dS = Change in storage, storage within the reach during dt <br />dt = Time interval <br /> <br />One of the simplest routing applications is the analysis of a flood wave <br />that passes through an unregulated reservoir. The inflow hydrograph is known, and <br />it is desired to compute the outflow hydrograph from the reservoir. Assuming that all <br />gate and spillway openings are fixed, a unique relationship between storage and <br />outflow can be developed. <br />The equation defining storage routing, based on the principle of <br />conservation of mass, can be written in approximate form for a routing interval At. <br />Assuming the subscripts "1" and "2" denote the beginning and end of the routing <br />interval, the equation is written as follows: - <br /> <br />2 <br /> <br />2 <br /> <br />Q, + O2 = L,.:tL2-.5..2-S 1 <br />At <br /> <br />(2) <br /> <br />The known values in this equation are the inflow hydrograph, and the <br />storage and discharge at the end of the routing interval. With two unknowns (0 and, <br />S 2) remaining, another relationship is required to obtain a solution. The sto~age- <br />outflow relationship is normally used as the second equation. How that relationship <br />is derived is what distinguishes various storage routing methods. <br /> <br />In applying hydrologic routing methods to a channel, the' reach is <br />subdivided into a series of sub-reaches with each sub-reach routed through as if it was <br />an individual reservoir. Each sub-reach is selected such that the average travel time <br />through the sub-reach is equal to the computation time interval. <br /> <br />2. MODIFIED PULS ROUTING. Routing in natural rivers is complicated by the fact <br />that storage in a river reach is not a function of outflow alone. The water surface in <br />a channel, during the passing of a flood wave, is not uniform. The storage and water <br />surface slope within a river reach, for a given outflow, is greater during the rising <br />stages of a flood wave than during the falling. Therefore, the relationship between <br />storage and discharge at the outlet of a channel is not a unique relationship, rather it <br />is a looped relationship. . <br /> <br />In order to apply the Modified Puis method to a channel routing problem, <br />the storage within the river reach is approximated with a series of cascading <br />reservoirs. Each reservoir is assumed to have a level pool, and therefore a unique <br />storage-discharge relationship. The cascading reservoir approach is capable of <br />approximating the looped storage-outflow effect when evaluating the river reach as <br />a whole. The rising and falling flood wave is simulated with different storage levels <br />in the cascade of reservoirs, thus producing a looped storage-outflow function for the <br />total river reach. <br /> <br />7-39 <br />