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Strupczewski W.

Przegląd Geofizyczny

1998

R.43, z.3-4

147-163

The Chezy formula for steady flow in a uniform symmetric channel with constant slope-friction factor is mathematically examined. First of all a wide rectangular channel and a semicircular channel are compared in respect to mean flow velocity using the Chezy formula with Manning. Chezy and logarithmic law of velocity. Then the inverse Chezy problems, i.e., the determination of the channel shape above the initial level for both a given rating curve of depth-flow discharge and flow area-flow discharge, are posed and the differential-integral equations for their solution are derived. It is shown that in general there is a double solution of the both problems. One solution gives a widening shape with depth and it may be unlimited in water depth, while the other is always upper bounded and it presents a narrowing shape with depth. The condition for the upper bound of the both solutions is given. The solution of the first inverse problem is demonstrated for a rating curve in the form of the product of flow discharge of trapezoid shape above an initial level and an exponential function. It is shown that an exponential reduction of channel flow capacity changes a linear channel sides into convex sides making a cross-section shape wider while an exponential increase of flow - into concave sides, i.e. reducing a section width, which is against the common sense. .The solution of the second inverse problem is presented for a rating curve with the constant slope/mean velocity ratio (m) above an initial level. In particular, it is shown that a solution for a negative value of m exists, which is evidently against the common sense.