Estimation of Boundary Shear Stress in Smooth Rectangular Open Channel by Considering the Effect of Velocity Gradient

The estimation of hydraulic resistance of the flow in open channels has always faced a serious challenge because of presence of secondary currents and vortex viscosity. Determination of contribution of flow pipes in the bed and the wall is faced with error, due to effects of the walls on the maximum velocity position. In this study, the contribution of the flow pipes in the bed and the wall was approximated by using conformal mapping method and by plotting harmonic lines of current and potentials. Then, the shear stresses obtained from the weight of tube pipes in the bed and the walls were calculated by eliminating the effect of the velocity gradient factors in the simplified results of solving the conjugation and momentum equations. The rate of interaction of velocity gradient on shear stress results of the conformal mapping was determined by comparing the results of conformal mapping method with that of experimental results of direct shear stress measurement. Investigations have shown that the effect of the velocity gradient decreases with increasing aspect ratio, so that with increasing aspect ratio from 1 to 20, the effect of the velocity gradient on the shear stress of the bed has been reduced from 7 to 1 percent, and in the wall from 15 to 3 percent. Finally, measured values of shear stress in the bed and the wall were introduced by presenting some equations.