A general form of the Hamiltonian for electrons confined to a curved one-dimensional (1D) channel with spin-orbit coupling (SOC) linear in momentum is rederived and is applied to a U-shaped channel. Discretizing the derived continuous 1D Hamiltonian to a tight-binding version, the Landauer-Keldysh formalism (LKF) for nonequilibrium transport can be applied. Spin transport through the U-channel based on the LKF is compared with previous quantum mechanical approaches. The role of a curvature-induced geometric potential which was previously neglected in the literature of the ring issue is also revisited. Transport regimes between nonadiabatic, corresponding to weak SOC or sharp turn, and adiabatic, corresponding to strong SOC or smooth turn, is discussed. Based on the LKF, interesting charge and spin transport properties are further revealed. For the charge transport, the interplay between the Rashba and the linear Dresselhaus (001) SOCs leads to an additional modulation to the local charge density in the half-ring part of the U-channel, which is shown to originate from the angle-dependent spin-orbit potential. For the spin transport, theoretically predicted eigenstates of the Rashba rings, Dresselhaus rings, and the persistent spin-helix state are numerically tested by the present quantum transport calculation.