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<br />2,8 <br /> <br />the mud and debris flows being simulated are laminar floNs. This assumption is <br />not particularly favorable as all mud floods and most mud flows are primarily <br />turbulent over the steep watershed and rough alluvial fan slopes on which they <br />flow and have velocities from 10 to 25 fps. Further, most mud flows have been <br />shown to be highly turbulent for concentrations less than 35 to 40 percent by <br />vol ume (O'Brien, 1986). <br />To continue with the derivation of the equations for hyperconcentrated <br />sediment flows, the fri ct ion slope of tht! channel is represented by <br /> <br />1 8T <br />Sf = 1m 8y <br /> <br />(2.14 ) <br /> <br />4i ' <br /> <br />Neglecting the inertial terms and substituting Equation 2.14 into Equation 2.5, <br />the momentum equation is written as <br /> <br />8h <br />ax <br /> <br />S + L !L [T + 11 du + C' <br />o 1m 8y y dy <br /> <br />2 <br />(dl!) ] <br />dy <br /> <br />o <br /> <br />(2.15 ) <br /> <br />using h as the mean flow depth in place of the depth variable y. By further <br />neglecting the dispersive stress and representing the last term as turbulent <br />shear stress by Manning's equations, the fonow'ing equation would result: <br /> <br />iJh S + L 8T v + !L 82u + <br />ax 0 1m 8y 1m 8y2 Sft <br /> <br />() <br /> <br />(2.16) <br /> <br />where Sft is given by <br /> <br />Sft <br /> <br />2 2 <br />(1.486) Y-- <br />n h 4/3 <br /> <br />(2.17) <br /> <br />where V is the mean velocity, and n is the average Manning's roughness value <br />for the channel reach. I f the flow is controlled pri mari 1 y by the vi scous <br />stress, it will result in lower velocities and, therefore, the turbulent stress <br />term will make a smaller contribution to the momentum equation. Conversely, if <br />the viscosity and yield stress are small, the turbulent stress will dominate and <br />the velocities will be higher. This effect was shown in O'Brien (1986). If the <br />flow is approaching laminar flow, the contribution by the turbulent term in <br />Equation 2.16 is small, yet there may still be some momentum transferred out of <br />the flow as a result of channel constrictions, bends, and obstructions, <br />