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<br /> <br />F,:M 1110-Z-1601 <br />1 July 70 <br /> <br />Y.. <br /> <br />C:"the interaction of the local boundary shear and the size and gradation of the <br />riprap material. <br />(Z) Average boundary shear. The average boundary shear over the <br />wetted perimeter of a channel cross section (from ref 3) is given by <br /> <br />. <br /> <br />i' = yRS <br />o <br /> <br />(30) <br /> <br />where <br /> <br />i' = average boundary shear, psf <br />.0 . <br />y = unit weight of water, pcf <br />R = hydraulic radius, ft <br />S = slope of energy gradient <br />By utilizing equations 1 and 6, equation 30 becomes <br /> <br />i' = <br />o <br /> <br />yyZ <br />( 1Z.ZR)Z <br />3Z.6 log10 k <br /> <br />(31) <br /> <br />where <br /> <br />f <br /> <br />"- <br /> <br />y = average cross-sectional velocity, fps <br />k = equivalent channel boundary surface roughness, ft <br /> <br />(3) Local boundary shear. In a straight trapezoidal channel with equal <br />bottom and side roughness, the boundary shear varies over the wetted perim- <br />eter as shown in plate 31. By substituting in equation 31 the depth Y (in <br />feet) for R, the. average local velocity in the vertical v (in feet per second) <br />for Y, and the average stone theoretical diameter D50 (in feet) for k, the <br />local boundary shear at any point on the wetted perimeter can be determined <br />- <br />by the equation <br /> <br />, <br />1 <br />, <br />j <br /> <br />T = <br />o <br /> <br />y';;Z <br /> <br />( )z <br />1Z.Zy <br />3Z.6 log10 D50 <br /> <br />(32) <br /> <br />, <br /> <br />14g(3) <br /> <br />40 <br /> <br />! <br />\--,- <br /> <br />