A Galilean invariant weak-equilibrium turbulence hypothesis that is sensitive to streamline curvature is proposed. The hypothesis leads to a fully explicit algebraic expression for Reynolds stress in terms of the mean velocity field and kinetic energy and dissipation of turbulence. The model is tested in curved homogeneous shear flow which is a homogeneous idealization of the circular streamline flow. The agreement is excellent with Reynolds stress closure model and adequate with available experimental data.