Analytical Investigation of Longitudinal Velocity Theories in Flow Vertical Direction

Computation of longitudinal velocity in the vertical direction and extracting the applied theories have been conventional manner from past years among the hydraulic engineers. In many previous investigations, the researchers have tried to extract some applied equations, separately, by dividing the flow depth namely from bed to water surface to various regions. As it is accepted by all of the researchers, the laminar sublayer zone has a linear velocity profile while out of this zone, the velocity simulation follows a logarithmic law which its accuracy in estimation of the velocity decreases by increasing the distance from the bottom of the channel. Also, it is not applicable for dip phenomenon which occurs bellow the free surface. In the current study, 12 experimental data series, operated under different experimental conditions, were collected from previous researches. Also, three common theories of log law, log- wake law, and modified log- wake law have been applied to simulate longitudinal velocity profile in the vertical direction. Finally, it is seen that the modified log- wake law has a better agreement with the experimental data, and also it can be operated for predicting the dip phenomenon bellow the free surface. For solving the equation of the mentioned theory, the factors of von Karman, wake strength, and shear velocity are assumed unknown. Then, the mentioned parameters have been extracted using a non-linear optimization technique of the least square curve fitting.