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<br />2.3 <br /> <br />2.2 Constitutive Eauations <br />The MUDFLOW model has incorporated the DHM numerical algorithm for solving <br />the momentum and continuity equation usi ng a fi n i te di fference numeri ca I scheme. <br />The DHM model is derived from the complete dynamic momentum and mass,continuity <br />equat ions for shallow water, open'channel fl ow in two d[imens'i ons. The reader <br />is referred to Hromadka and Yen (1987) for additional discussion, The fully <br />dynamic tWD,dimensional, unsteady, shallow water equations consists of the <br />continuity equation <br /> <br />aqx + 8qy + aH = 0 <br />ax 8y at <br /> <br />(2.1 ) <br /> <br />$' <br /> <br />and two equations of motion. In the x,direction (flow direction) <br /> <br /> aqx a q 2 a (M..ID') I (I' aH) 0 <br /> ;9t' + ax (T) + ay h + g 1 .) fx + at = <br />and in the hori zonta I direction perpendicular to the flow <br /> 8q a q 2 +L ~ . aH <br /> a?' + ay (T) ( h ) + gh (Sf/ at) = 0 <br /> ay <br /> <br />(2.2) <br /> <br />(2.3) <br /> <br />where qx and qy are discharges per unit width in the x' and y,directions and <br />Sfx and Sfy represent friction slopes in the x and .Y directions, H is the <br />water'surface elevation, h is the flow depth, and g is the gravitational <br />acce I erat ion. The vari abl es x, y, and t are the spat i a I and temporal <br />coordi nates. These equat ions represent i ncompressi bIll fl ui d flow with the <br />assumption of a hydrostatic pressure distribution, To derive the diffusive <br />equation, it is simpler to present a one,dimensional fDrm of Equation 2,2. <br /> <br />Sf = So ' ~ ' ~ ~~ <br /> <br />Kinematic wave equation ="-J <br />(steady uniform flow) <br /> <br />Diffusive wave equation <br />(steady nonuniform flow) <br /> <br />Quasidynamic equation <br />(steady nonuniform flow) <br /> <br />Full dynamic equation <br />(unsteady, nonuniform flow) <br /> <br />1 av <br />g at <br /> <br />(2.4) <br />