In open channel flows, sometimes it is necessary to determine the best possible hydraulic cross-section (i.e. minimum area) for a given flow rate , slope and roughness coefficient . The flow rate can be written as,
                                                (6)
which can be rearranged as,
                                                (7)

For a channel with given flow rate the quantity in the parentheses is constant which means the channel with minimum is also with minimum .