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EM 1110-2.1416 15 Oct 93 n = Manning's n value R = hydraulic radius Chezy's Equation S · QIQI f A 2C2R in which C is the Chezy coefficient. Note the use of the absolute value of discharge; this keeps the sign of Sf proper for flow reversals. (5-6) (2) Equations 5-5 and 5-6 are semi-empirical equa- tions for steady flow, but they also produce acceptable results for unsteady flow. Other equations have been proposed for estimating the friction slope Einstein (1950), Simons and Sentiirk (1976), and ASCE (1975). Typi- cally, these equations are logarithmic and contain sedi- ment parameters. Most modelers have avoided these equations because they are computationally inconvenient, requiring an iterative solution to solve for the friction slope within each time step. c. Force exerted by structures. Bridge piers, embankments, dams, and other hydraulic structures exert a force on the flow which is not considered in the momentum equation presented above. To illustrate this force, consider submerged flow over a broad crested weir as shown in Figure 5-18. The unequal pressure distribu- tion on the upstream and downstream faces exerts a net force in the upstream direction on the flow. This force is not included in the friction term, nor is it included by the pressure force from the bank which is included in the water surface slope term. If the force is not included in the momentum equation, the computed swell head upstream of the structure will be too small. Moreover, the force is seldom quantified. The emphasis of research has been to quantify the energy loss through structures, which is useful for computing the swell head for steady flow. (1) Modelers Fread (1978), and Barkau (1985) have proposed augmenting the momentum equation with an additional slope term based on the energy loss: Figure 5.18. Exterior forces acting on a control volume of fluid flowing over a broad crested weir 5-24 Net Force on Fluid - - "- -I -