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<br />simulated are assumed to be laminar. This assumption is not <br />particularly favorable as all mud floods and some mudflows are <br />turbulent over the steep watershed and rough alluvial fan slopes <br />where velocities reach 10 to 25 fps. Further, most mudflows have <br />been shown to be highly turbulent for solid concentrations less <br />than 35 to 40 percent by volume (O'Brien, 1986). If the flow is <br />controlled primarily by the viscous s;tress, it will result in lower <br />velocities and a smaller contribution by the turbulent stress term. <br />Conversely, if the viscosity and yield stresses are small, the <br />turbulent stress will dominate and the velocities will be higher. <br /> <br />By analogy with the work of MeY'3r-Pet.er and Muller (1948) and <br />Einstein (1950), the shear stress relationship (Eqn. 4) is written <br />in the following slope form: <br /> <br />Sf = Sy + Sv + Std <br /> <br />(7) <br /> <br />where the total friction slope Sf is the result of the components, <br />the yield slope Sy, the viscous slope Sv, and turbulent slope Std' <br />The viscous and turbulent slope 1:E!I'IlIS are rewritten in terms of <br />depth-averaged velocity V. The vi!wous slope can be written as: <br /> <br />S = ILn V <br />v 8 1m h2 <br /> <br />(8) <br /> <br />where 1m is the specific weight of .the sediment mixture. The <br />resistance parameter K for laminar flow equals 24 for smooth, wide <br />rectangular channels but increases with roughness and irregular <br />cross section geometry. <br /> <br />The flow resistance of the turbulent and dispersive components <br />of Eqn. 7 are combined into an equi.valent Manning's n value for the <br />flow in which Eqn. 8 can be reduc'ed for the metric form of the <br />turbulent-dispersive slope Std: <br /> <br />Std = <br /> <br />n2 V2 <br />h4/3 <br /> <br />(9) <br /> <br />Accordingly, the friction slope components can be wri ttcen as: <br /> <br />Sf <br /> <br />Ty <br /> <br />Kl) V <br /> <br />n2 V2 <br /> <br />= <br /> <br />+ <br /> <br />+ --- <br /> <br />1mh 81m h2 <br /> <br />h4/3 <br /> <br />(10) <br /> <br />Equations 2 and 3 are solved 1:0 determine the friction slope <br />Sf and the two velocity components V. and Vy. Reasonable values of <br />K and Manning's n can be assumed from 1:he roughness of the channel <br />and overland flow areas being modeled. The specific weight of the <br />fluid matrix 1m depends solely on the sediment concentration. The <br /> <br />21 <br />