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6-96 <br />Appendix A <br />• SCS has adopted Manning's equation to estimate the rate of total energy <br />loss (Se); i.e., <br />Se = [(Q ne)/(1.486 ARz/~)]~ <br />where <br />ne a retardanee coefficient for total energy loss. <br />Furthermore, SCS has adopted the Manning-Strickler equation to estimate <br />the energy loss due to boundary roughness, (St); i. e., <br />~~ Report 108 of the National Cooperative Highway Research Program recom- <br />• mends using Km = 0.0395, with dm = dso expressed in feet. The Km value <br />is the same as the default value for Cn in Eq. 2 of TR-59, "Hydraulic <br />Design of Riprap Gradient Control Structures." <br />St = I(Q nt)/(1.486 ARz/~)]z <br />where <br />nt = Kmdm~/6 the Strickler equation -- retardance coefficient <br />due to boundary roughness only. <br />dm =_ a characteristic boundary particle size. <br />Km empirical coefficient relating dm to nt. <br />Units for Km must be consistent with units chosen for dm. <br />This leads to the following formula for actual average transverse stress <br />(tact.)' <br />Tact. = YR SL <br />where <br />Y 62.4 M/ft~ <br />R =_ hydraulic radius, ft. <br />St = (nt/ne)~ Se; Eq. 6-3, TR-25. <br />Shield's work establishes the critical relationship between the active <br />and passive forces; i.e., it relates the critical fluid tractive stress <br />(TC) for incipient motion to the gravitational resisting force. It was <br />verified for coarse grained materials (dm > 6 ~) by lane's study of <br />• prototype field canals and for discrete particle material (dm > .1 ~) <br />by Report 108. <br />