Velocity Distribution in Open Channel Flow

Velocity distribution equations for open channel flows are derived and compared. These equations are derived by a combined application of: (1) A probabilistic formulation of the velocity distribution problem; (2) the entropy concept in the selection of the probability distribution function of velocity; (3) a geometrical technique in modeling a curvilinear coordinate and the coordinate transformation between this and the Cartesian coordinates; and (4) the basic hydrodynamics concerning the rates of transport of mass, momentum, and kinetic energy by the flow through an open channel cross section. A technique to estimate the parameters of these velocity distribution equations is also developed. The equations are capable of modeling and simulating the velocity distribution from the channel bed to the water surface, which may have the maximum velocity occurring on or below the water surface.