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<br />,. <br /> <br />i ' <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 <br />of weighted discharge. When X = 0.0, the equation reduces to S = KO, indicating that <br />storage is only a function of outflow, which is equivalent to level-pool reservoir routing <br />with storage as a linear function of outflow. When X =0.5, equal weight is given to <br />inflow and outflow, and the condition is equivalent to a uniformly progressive wave <br />that does not attenuate. Thus, "0.0" and "0.5" are limits on the value of X, and <br />within this range the value of X determines the degree of attenuation of the flood <br />wave as it passes through the routing reach. A value of "0.0" produces maximum <br />attenuation, and "0.5" produces pure translation with no attenuation. <br /> <br />The Muskingum routing equation is obtained by combing equation 9.15 <br />with the continuity equation (9.11). and solving for 0 2' <br /> <br />o 2 = C 11 2 + C 21 1 + C 30 1 <br /> <br />(9) <br /> <br />The subscripts 1 and 2 in this equation indicate the beginning and end, <br />respectively, of a time interval ,At. The routing coefficients C l' C 2' and C 3 are defined <br />in terms of At, K, and X. <br /> <br />c = lot-2KX <br />1 - <br />2K(1-X)+At <br /> <br />(10) <br /> <br />c =....t + 2KX <br />2 <br />2K(1-X) + At <br /> <br />(11 ) <br /> <br />C 3 = 2Kll-XI-,t <br />2K(1-X) + At. <br /> <br />(12) <br /> <br />Given an inflow hydrograph, a selected computation interval At, and estimates for the <br />parameters K and X, the outflow hydrograph can be calculated. <br /> <br />3.2. DETERMINATION OF MUSKINGUM K AND X. In a gaged situation <br />the Muskingum K and X parameters can be calculated from observed inflow and <br />outflow hydrographs. The travel time, K, can be estimated as the interval between <br />similar points on the, inflow and outflow hydrographs. The travel time of the routing <br />reach can be calculated as the elapsed time between centroid of areas of the two <br /> <br />7-43 <br />