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<br />3. MUSKINGUM METHOD. The Muskingum method was developed by the Corps of <br />Engineers in connection with studies of the Muskingum Conservancy District Flood Control <br />Project to directly accommodate the looped relationship between storage and outflow that <br />exists in rivers. With the Muskingum method, storage within a reach is visualized in two <br />parts: Prism Storage and Wedge Storage. Prism storage is essentially the storage under <br />the steady-flow water surface profile. Wedge storage is the additional storage under the <br />actual water surface profile. As shown in figure 1, during the rising stages of the flood <br />wave the wedge storage is positive and added to the prism storage. During the falling <br />stages of a flood wave the wedge storage is negative and subtracted rom the prism <br />storage. <br /> <br />FIGURE 1 <br />Muskln9um Prism and Wedge Storage Concept <br /> <br />3.1. Development of the Muskingum Routing Equation. prism storage is computed <br />as the outflow (0) times the travel time through the reach (I<). Wedge storage is computed <br />as the difference between Inflow and outflow (1-0) times a weighing coefficlent X and the <br />travel time K. The coefficient K corresponds to the travel time of the flood wave through <br />the reach. The parameter X Is a dimensionless value expressing a weighing of the relative <br />effects of inflow and outflow on the storage (S) within the reach. . Thus, the Muskingum <br />method defines the storage in the reach as a linear function of weighted inflow and outflow: <br /> <br />S = prism storage + wedge storage <br /> <br />(6) <br />(7) <br />(8) <br /> <br />S = KO + KX(I-o) <br />S = K [XI+(l-X)O] <br /> <br />WHERE: <br /> <br />S = Total storage in the routing reach <br />o = Rate of outflow from the routing reach <br />I = Rate of inflow to the routing reach <br />K = Travel time of the flood wave through the reach <br />X = Dimensionless weighing factor, ranging from 0.0 to 0.5 <br /> <br />The quantity in the brackets of equation (8) is considered an expression of <br /> <br />Colorado Flood <br />Hydrology Manual <br /> <br />76.5 <br /> <br />a:w=r <br />