Wall and Bed Shear Force in Rectangular Open Channels
  This paper studies the effects of velocity gradients and secondary currents on the distribution of the shear force between the walls and bed of rectangular open channels. We show that neglecting the effect of secondary currents and assuming zero-shear division lines does not yield acceptable results. We, accordingly, introduce a method to determine the percentage of the total shear force acting on the walls and bed of rectangular open channels, which takes both the velocity gradients and secondary currents into account. Using the channel bisectors, along which there is no secondary flows effect, and orthogonal trajectories to isovels, along which there is no shear stress, we divide the channel cross section into three major subsections, namely bed area, walls area, and shared area. The geometry of each subsection is derived given the location of the maximum velocity. The share of the bed and wall shear forces from the shared area, are calculated afterward. The results for bed and walls shear forces agree well with the experimental data with an average relative error less than 5% for both regular flows and flows carrying suspended sediment. This method also provides a physics-driven range for the wall and bed shear forces which nicely covers the experimental data. 
Sasan Tavakkol and Amir Reza Zarrati
physics.flu-dyn