The steady state of a quasi-neutral bulk of a cylindrical, current-carrying, fully ionized, collisional plasma confined by two coaxial metallic cylinders was analysed both analytically and numerically, using a magneto-hydrodynamic model. The plasma is magnetized by a uniform magnetic field, imposed parallel to the wall. The analysis did not assume Boltzmann equilibrium for the electrons, and the dependence of the mean electron-ion collision frequency on the varying plasma density was considered. The first integral of the model equations was found to be an algebraic relation between the self-consistent electric potential and the ion radial velocity. Radial distributions of characteristic plasma parameters (electric potential, density, velocities and currents) in the quasi-neutral region were calculated, and their dependences on the magnetic field strength, voltage and current were analysed. Trial and error was used in numerical calculations to choose the 'initial' ion radial velocity at the inner cylinder so that boundary conditions at the outer cylinder were satisfied. The results show that the variation in the radial ion velocity determined is mainly by competition between the Amperian force, which accelerates the ions, and the centrifugal force, which decelerates them. The competition may lead to non-monotonic variation in the ion velocity and density with the radial coordinate, depending on the electric current, while the electric potential in the plasma bulk is a monotonic function of the radial coordinate. The plasma rotates around the system axis with the frequency proportional to the electric current to the outer wall. The plasma azimuthal velocity calculated taking into account the ion viscosity is a non-linear function of the distance from the system axis. The calculated dependence of the current to the wall from the potential drop in the plasma bulk shows a monotonic transition from ion to electron current to the wall by increasing the voltage from negative to positive magnitudes. The current decreases with the increase in the magnetic field.