## Abstract

Logarithmic, power, and parabolic distribution laws were proven to be efficient for the prediction of vertical velocity distribution. Traditionally, the distribution formulas involve the friction velocity (u*) and the depth (y) of the measurement point. The low availability of friction velocity and limitation of real water depth data hindered the promotion and comparison of the available flow velocity formulas. In this paper, we proposed a new formula structure adopting a relative flow velocity based on mean vertical velocity (u/ū) and dimensionless relative water depth (y/H). The observations showed the following. (1) The substitution of u* and y with u/ū and y/H were reliable and applicable. Parabolic logarithmic and power fitting curves worked well, with an error of 7%, 10%, and 11%, respectively. (2) In water depth direction, the predicted results of the middle depth of the vertical profiles tend to be more reliable and precise. The highest estimated error appeared in the area near the water surface. (3) Higher catchment slope resulted in larger coefficients and constants in logarithmic and power fitting. (4) In the rivers with higher width-to-depth ratio, the maximum profile velocity occurred closer to the water surface, and mean profile velocity tended to happen more at the bottom.

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