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<br />~ <br /> <br />and 7 into equation 4 and assuming the <br />is V, <br /> <br />Substitution of equations 5 <br />approach velocity to each plant <br />YC. V21:Ai <br />YALS - _ ~v2 <br />2g <br /> <br />(~) 2 (~) <br />1. 49 A <br /> <br />PL = 0 <br /> <br />(8) <br /> <br />1/3 <br /> <br />Simplifying equation 8 and solving for V2, <br /> <br />V2 <br /> <br />S <br /> <br />(9) <br /> <br />C.LAi <br />+ <br />2gAL <br /> <br />(~) 4/3 <br /> <br />2 <br />C ~~9 ) <br /> <br />By expressing the average velocity according to the conventional <br />Manning's formula and equating to equation 9, one obtains: <br /> <br />V2 ( \49) 2 S (~ ) 4/3 <br />= <br /> S (10) <br /> C.LAi C~~9) 2 (~) 4/3 ' <br /> 2gAL + <br /> <br />in which n is the total roughness coefficient, including boundary and <br />vegetation effects. Solving for n in equation 10 and substituting R for <br />(A/P) the following equation results: <br /> <br />n <br /> <br />where: <br /> <br />no <br /> <br />c. <br /> <br />g <br />A <br />R <br />LAi <br /> <br />L <br /> <br />= no ~ 1 = l-2:~Li) C~~9) 2 R4/3 <br /> <br />(11) <br /> <br />Manning's boundary roughness coefficient, excluding the <br />effect of the vegetation; <br />effective drag coefficient for the vegetation in <br /> <br />the direction of flow; <br />gravitational constant, in feet per second squared; <br />cross-sectional area of flow, in square feet; <br />hydraulic radius, in feet; <br />total frontal area of vegetation blocking the <br />flow in the reach, in square feet: and <br />length of channel reach being considered, in feet. <br /> <br />Equation 11 gives the n value in terms of the boundary roughness, no: <br />the hydraulic radius, R; the effective drag coefficient, c.; and the <br /> <br />vegetation characteristics, LAi/AL. The vegetation density, Vegd' in the <br />cross section is represented by the expression <br />LAi <br />AL <br /> <br />Vegd <br /> <br />(12) <br /> <br />5 <br />