In the theory of flow in open channels two stages of flow with principally different characteristics have to be considered, streaming flow and shooting flow. The velocity of flow in the first case is smaller than the velocity of propagation of translatory waves, in the latter case it is larger. The phenomena occurring in streaming flow are well known and theoretically solved, if we neglect the influence of friction. This latter simplification means that the velocity has a constant value for each point of the cross-section. For this assumption also the theory of the hydraulic jump has been successfully attacked, where the stage of flow changes from the shooting to the streaming condition. The present paper, however, deals with problems of flow of the shooting stage only and extends the theory of hydraulics to all cases of supercritical flow, where the variation of depths and velocities due to changes in the direction of flow is desired.
An outstanding example of such a type of flow is the case of curved sections in a rectangular open channel. This case has been investigated in the following analytically by the principles developed, and its solution was then compared to an extensive experimental investigation. It is shown that an adequate solution of the case of high velocity flow in curved sections of open channels has been found.
