Dynamic equations for steady spatially varied flow in uniform channels are derived separately based on momentum and energy principles. It is shown that the momentum equation is inherently different from the energy equation. In general, six different gradients are involved in steady spatially varied flow: the friction slope in the momentum equation, the dissipated energy gradient in the energy equation, the total head gradient, the gradient of the piezometric head, the free surface slope, and the channel slope. Conventional practice of using the Manning, Chezy, or Weisbach formulas to evaluate the friction slope or the dissipated energy gradient is only an approximation.
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Yen et al. (1970) studied this question.