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<br />Kinematic Wave Conservation of Momentum <br />Frictional forces = Gravitational forces <br /> <br />Sf = So <br /> <br />(3) <br /> <br />This equation states that the momentum of the flow can be approximated <br />with a uniform flow assumption as described by Manning's and Chezy's equations. <br />Manning's equation can be written in the following form: <br /> <br />Q = aAm <br /> <br />(4) <br /> <br />where a and m are related to surface roughness and flow geometry. Since the <br />momentum equation has been reduced to a simple functional relationship between area <br />and discharge, the movement of a flood wave is described solely by the continuity <br />equation. Therefore, the kinematic wave equations do no allow for hydro graph diffusion <br />(attenuation). Hydrographs routed with the kinematic wave method will be translated in <br />time but will not be attenuated. The kinematic wave equations are usually solved by <br />explicit or implicit finite difference techniques. Any attenuation of the peak flow that is <br />computed using the kinematic wave equations due to errors inherent in the finite <br />difference solution scheme. In spite of this limitation, the kinematic wave approximation <br />is very good for modeling overland flow at shallow depths or channel flow in moderately <br />steep channels. Application of the kinematic wave equations to a combination of overland <br />flow and channel flow elements is often used in urban watershed modeling. <br /> <br />3. BASIN REPRESENTATION WITH KINEMATIC WAVE ELEMENTS. <br /> <br />The contribution to the flood hydrograph from open and impervious areas <br />within a single subbasin is modeled in the kinematic wave method by using different types <br />of elements. The kinematic wave elements include an overland flow plane, collector and <br />main channel. In general, subbasin runoff is modeled with kinematic wave elements by <br />taking an idealized view of the basin. Rather than trying to represent every overland flow <br />plane, and every possible collector channel, subbasins are depicted with overland flow <br />planes and channels that represent the average conditions of the basin. Normally two <br />overland flow planes are used, one to represent the pervious areas and one to represent <br />the impervious areas. The lengths, slopes, and roughness of the overland flow planes <br />are based on the average of several measurements made within the basin. Likewise, <br />collector channels are normally based on the average parameters of several collector <br />channels in the subbasin. <br /> <br />Various levels of complexity can be obtained by combining different <br />elements together to represent a subbasin. The simplest combination of elements that <br />could be used to represent an urban subbasin are two overland flow planes and a main <br />channel. The overland flow planes are used to separately model the overland flow from <br /> <br />7-58 <br />