The objective of the study is to use a 3D Acoustic Doppler Velocimeter (ADV) to gauge the typical flow and turbulence characteristics within a non-uniform open channel. The findings of experimental examinations of the subcritical flow along the channel are presented in this work. The behavior of sand grains in turbulent open channel flow across porous and rough bed surfaces was examined in laboratory research, and the results were obtained. The properties of turbulent flow, i.e., turbulence intensity, turbulent kinetic energy, and Reynolds shear stresses, are determined from ADV data. The continuity equation and the Reynolds equation of open-channel flow have been used to build theoretical formulations for the velocity distribution and Reynolds stress distribution in the vertical direction. Measured profiles of vertical velocity and Reynolds stress are compared to the derived expressions. The impact of the size of particles on the distribution of mean flow characteristics is discussed. This work provides a novel origin for the profile and analyzes the behavior of the vertical velocity distribution in the region where fully formed turbulence is dominating in open channels using the Navier–Stokes equations. In comparison to other sand roughness, Chopan sand bed (with greater density) exhibits the strongest turbulence intensities in both vertical and streamwise direction just next to the bed when away from the channel boundary. In contrast to flow across a rough surface, the variance ranges between 150 and 250% concerning the channel bed’s roughness type, impacting the velocity triple products that signifies transfer of turbulent kinetic energy.