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<br />i Estimating the Muskingum X parameter in an ungaged situation can be <br />very difficult. X varies between 0.0 and 0.5, with 0.0 providing the maximum amount <br />of hydrograph attenuation and 0.5 no attenuation. Experience has shown that for, <br />channels with mild slopes and flows that goout of bank, X will be closer to 0.0. for <br />steeper streams, with well defined channels that do not have flows going out of bank, <br />X will be closer to 0.5. Most natural channels lie somewhere in between these two <br />limits. leaving a lot of room for "engineering judgement." One equation that can be <br />used to estimate the Muskingum X coefficient in ungaged areas has been developed <br />by Cunge. The equation is taken from the Muskingum-Cunge channel routing <br />methods, which is written as follows: <br /> <br />X=l (1- Q 0 ) <br />2 BS oC 6X <br /> <br />(15) <br /> <br />Where: <br /> <br />Q = reference flow from the inflow hydrograph <br />o <br />c = flood wave speed <br />S = friction slope or bed slope <br />B 0 = top width of the flow area <br />6X = length of the routing sub reach <br /> <br />The choice of which flow rate to use in this equation is not completely clear. <br />Experience has shown that a reference flow based on average values (midway <br />between the base flow and the peak flow) is in general the most suitable choice. <br />Reference flows based on peak flow values tend to accelerate the wave much more <br />than it would in nature, while the converse is true if base flow reference values are <br />used. <br /> <br />3.3. SELECTING THE NUMBER OF SUBREACHES. The Muskingum <br />equation has a constraint related to the relationship between the parameter K and the <br />computation interval 6t. Ideally, the two should be equal, but 6t should not be less <br />than 2KY to avoid negative coefficients and instabilities in the routing procedure. <br /> <br />2KY < 6t s K <br /> <br />(16) <br /> <br />A long routing reach should be subdivided into subreaches to that the travel time <br />through each sub reach is approximately equal to the routing interval 6t. That is: <br /> <br />Number of subreaches = K <br />6t <br /> <br />(17) <br /> <br />This assumes that factors such as channel geometry and roughness have been taken <br />into consideration in determining the length of the routing reach and the travel time <br />K. <br /> <br />7-45 <br />