Turbulent velocity distribution with dip phenomenon in conic open channels

Conic open-channel flow as occurs in sub-drains, sewers, and culverts is computed by Manning's or Darcy's resistance equations for the cross-sectional average velocity only. Yet, fish passage culvert design requires the cross-sectional velocity distribution, which is proposed in this paper based on two hypotheses: (i) centreline velocity distribution follows the conventional log-law with a cubic deduction near the water surface; (ii) cross-sectional velocity distribution is described by Guo and Julien's modified log-wake-law but neglecting the squared sine function. These hypotheses result in a novel and simple velocity distribution model without any fitting parameter. Its graphical interpretation for the elliptic, parabolic, and hyperbolic channels indicates reasonable velocity contours with dip phenomenon. Further, it agrees well with circular pipe data related to the average shear velocity, velocity-dip position, centreline and cross-sectional velocity distributions. A potential application includes fish passage culvert design by specifying a low velocity zone near the wall.