Numerical calculations are conducted for liquid-metal magnetohydrodynamic flows through a circular pipe with an electrically conducting wall in both the magnetic field inlet region and the outlet region. Conservation equations of fluid mass and of fluid momentum and the Poisson equation for electrical potential are solved numerically. The calculations are performed by a cylindrical coordinate system using a staggered grid in order to obtain numerically stable solutions, covering Hartmann numbers up to the order of 10 000. As to the loss coefficient ζ for the pressure drop, the value of ζ/(Ha2/Re) does not depend on the Ha number, the Re number, and the wall conductance ratio very much for both the magnetic field inlet section and the outlet section. The value of ζ/(Ha2/Re) changes mainly with the gradient of the applied magnetic field for both the magnetic field inlet section and the outlet section.