To find the steady flow water surface profile, it is possible to use Bernoulli’s equation, which is
a discrete form of the differential energy equation. Such an approach requires the average energy
slope between cross-sections to be estimated. In the literature, many methods are proposed
for estimating the average energy slope in this case, such as the arithmetic mean, resulting in the
standard step method, the harmonic mean and the geometric mean. Also hydraulic averaging
by means of conveyance is commonly used. In this study, water surface profiles numerically
computed using different formulas for expressing the average slope were compared with exact
analytical solutions of the differential energy equation. Maximum relative and mean square
errors between numerical and analytical solutions were used as measures of the quality of
numerical models. Experiments showed that all methods gave solutions useful for practical
engineering purposes. For every method, the numerical solution was very close to the analytical
one. However, from the numerical viewpoint, the differences between the methods were
significant, as the errors differed up to two orders of magnitude.
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