An upper-bound approach to Saint-Venant’s principle is presented for incompressible potential-flow fields. Upper bounds for the velocity and its potential are found for the flow in a rectangular channel and in an axially symmetric cylindrical channel. It is found that any deviation in velocity distribution at the entrance of the channel which does not change the net flow attenuates to a negligible quantity beyond a section which is at a distance of two channel widths from the entrance.

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