On the potential of Whittington’s analytical approximation for computing within-element water surface profiles in SWMM

William James, Computational Hydraulics Int., Guelph, ON, Canada


In February 1960 R. B. Whittington published a 4-page note on the rapid computation of backwater curves without recourse to tabulated functions, and included estimates of error and a sample calculation. Eight months later the Journal of Irrigation and Power (JIP) re-published the short paper in their section entitled “Foreign Periodicals” but in their plagiarised version their typesetter made ten mathematical errors, some potentially serious. Regrettably it is the JIP version that is now readily available on the Internet.  

Whittington’s method is restricted to steady flow in prismatic conveyances (as is Manning’s equation, by the way). This current paper reviews Whittington’s original derivations in the light of modern North American numerical hydraulics procedures, summarises the JIP errors, and compares Whittington’s analytical solution with water surface profiles computed by both HEC-RAS and (PC)SWMM. Comparison with analytical solutions even for simplistic applications is instructive, and indicates the extent to which Whittington’s method might be useful for estimating WSEL profiles within the discretized sub-lengths of free surface flows.

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