Reply to the discussion in W.H. Hager on 'Explicit solutions of the Manning equation for partially filled circular pipes

摘要

The author thanks the discusser for bringing the equations proposed by Hager (1999) to his attention. Those equations which are relevant to this work are examined here. The author also appreciates the discusser's comments on stable flow in partially filled sewers and the limitations of the Manning equation. It was not within the intended scope of the paper, however, to outline the advantages and limitations of the Manning equation or those of any one of the alternative calculation methods. The paper simply presents explicit expressions that will facilitate calculations if one chooses to employ the Manning equation. Four types of problem that require iterative calculations are identified in the paper, whereas the discusser seems to consider only type I problems (eqs. [D1]-[D4] do not provide explicit solutions to the other three types of problem). The paper also introduces explicit equations that are based on Camp's curve for varying roughness coefficient. Although it is usually ignored, the effect of this variation can be significant (Fair and Geyer 1958). It should be noted that eq. [D4] and the other explicit equations based on the assumption of a constant roughness coefficient are not applicable if Camp's curve for the variation of n with h/D is accepted. It may also be remarked that Q = Q_f at h/D approx= 0.91 if varying n is assumed. This value is h/D =0.82 when n is assumed to be constant.