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A simplified equation for computing the backwater curve of steady flows in a wide rectangular channel is derived by using a perturbation method. The obtained formula is expressed in such a manner that water depth is given as a function of the distance from the downstream end, while most of the formulae previously proposed express the distance as a function of water depth. The results computed by the obtained formula are compared with those by the finite difference method, and it is proved that the formula has the satisfactorily high accuracy for practical computation of backwater curves. If neglecting the inertia term, or gradient of velocity head in the fundamental equation, the formula could be further simplified. But the omission of that term yields the large error of computation for such hydraulic condition that the ratio of normal water depth to critical water depth is less than about 2.

A SIMPLE FORMULA FOR COMPUTING THE BACKWATER CURVE OF STEADY FLOW IN WIDE RECTANGULAR CHANNEL