The characteristics of the longitudinal velocity in a $180^{circ}$ constant-radius, recirculating laboratory channel were investigated. Three-dimensional velocity fields were measured using a side-looking ADV. The shortcomings of existing equations for longitudinal velocity are discussed. An eddy viscosity model is adopted in the downstream momentum equation. A mathematical equation was developed to describe the vertical distribution of longitudinal velocity. The comparisons of the longitudinal velocity show generally good agreement. It is found that the curvature change in the curved channel affects the vertical location of maximum velocity and the vertical profile of longitudinal velocity.