Laserfiche WebLink
<br />2.4 <br /> <br />where Vis the mean fl ow velocity in the x,di rect i on and S" is the channel <br />bed slope. The full dynami c equation for unsteady, lion un i form fl ow represents <br />a nonlinear, second-order hyperbolic partial differential equation. In this <br />form, it is difficult to apply a computer model to simulate flow over variable <br />topography that is cost effect i ve and computer time effi ci ent. Fortunately, <br />severa 1 reasonabl e assumptions permit the development of a more simple, yet <br />applicable equation. For example, several terms can be considered negligible <br />when compared with the bed slope and resistance or friction slope. This is <br />particularly true for the steep slopes of alluvial fans and their contributing <br /> <br />watersheds. First, the assumption of steady flow eliminates the i ~~ term, <br /> <br />Assuming that the nonuniform flow term Y. aav is a'lso negligible, eliminates both <br />g x <br />the inertial terms and leaves only the diffusive equation terms <br /> <br />4i" , <br /> <br />~' S Qy <br />"0' f = ax <br /> <br />(2.5) <br /> <br />Simply stated, the variation in velocity over one time step and one grid spac' <br />ing in the numerical scheme is small compared tD the Dther terms. For flow <br />regimes with Froude number less than 4 or a velocity 'less than 25 fps, the <br />diffusion can be considered an adequate representation of the full momentum <br />equation. It should be noted that the two,dimensional, quasi'dynamic equation <br />with the convective acceleration term requires about 50 percent more computa' <br />tiona1 effort than the diffusive model. For steep slopes, the variation of the <br />water surface in the flow direction is comparatively small and only the kinematic <br />wave approximation to the momentum equation remains <br /> <br />Sf = So <br /> <br />(2.6) <br /> <br />Equat ions 2.5 and 2.6 are used in the MU[)FLOI~ model. The fri ct ion slope term <br />is represented by the Sf value in Manni ng" s equat i on for fully developed, <br />turbulent flow. <br /> <br />v = 1.~86 h2/3Sfl/2 <br /> <br />(2,7) <br />