Friction Slope Averaging in Backwater Calculations

In calculating water surface profiles, the average friction slope is estimated from conditions at the ends of a reach. Methods used to approximate the average slope include use of the arithmetic, geometric, and harmonic means of reach‐end friction slopes, and the arithmetic mean of the reach‐end conveyances. Systematic variations exist in the slopes, and consequently the water levels, calculated by the various methods. Previous known investigations of the methods are limited, in their application, to prismatic channels. For irregular channels, the true friction slope line can be approximated by a third degree polynomial. Differences between the various approximations and the true average slope of such a curve show that the arithmetic mean of the reach‐end friction slopes has the lowest maximum error but does not always give the smallest error. Its use is suggested, coupled with systematic selection of cross section locations and occasional use of the geometric mean of reach‐end slopes.