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Determination of the velocity profile in open channels (particularly in narrow channels) with turbulent flows has always been the subject of attention and studies of researchers. This is due to the fact that knowing the velocity distribution it is possible to calculate the distributions of shear stress and the discharge in the channels. However, due to the complexity of conditions governing the flow, which are the consequences of the non-isotropic state of turbulence and the existence of Prandtl type 2 secondary flows; it is difficult to introduce a model that would be capable of properly defining the velocity distribution in narrow open channels. Many researchers have tried to modify the famous logarithmic law, which responds well in the case of wide open channels, to suit the narrow channels as well, thereby allowing the modified model to describe the negative gradient of velocity beneath the free surface of water (known as dip phenomenon). However, in this context, they have been forced to set limitations on their models, which have in turn limited their applications. For this reason by using the laws of mathematics and simplifying the Navier-Stokes equations, some researchers have presented models that are capable of calculating the velocity profile in narrow channels in a satisfactory manner with the least constraint for application. Two models that are derived from Navier-Stokes are introduced in this study and their results are compared with experimental data.

Review of Models Introduced to Estimate the Distribution of Longitudinal Velocity in Open Channels based on Navier-stokes Equations