  This study derived the vertical distribution of streamwise velocity in wide
open channels by maximizing Tsallis entropy, in accordance with the maximum
entropy principle, subject to the total probability rule and the conservation
of mass, momentum, and energy. Entropy maximizing leads to a highly nonlinear
differential equation for velocity which was transformed into a relatively
weaker nonlinear equation and then solved analytically using a non-perturbation
approach that yielded a series solution. The convergence of the series solution
was proved using both theoretical and numerical procedures. For the assessment
of velocity profile, the Lagrange multipliers and the entropy index were
obtained by solving a system of nonlinear equations by Gauss-Newton method
after approximating the constraint integrals using Gauss-Legendre quadrature
rule. The derived velocity profile was validated for some selected sets of
experimental and field data and also compared with the existing velocity
profile based on Tsallis entropy. The incorporation of the above constraints
and the effect of entropy index were found to improve the velocity profile for
experimental as well as field data. The methodology reported in this study can
also be employed for addressing other open channel flow problems, such as
sediment concentration and shear stress distribution.
