Liquid metal flow in a straight duct in a fringing magnetic field is considered. The magnetic field is uniform with two different levels upstream and downstream. In the region of a nonuniform magnetic field, the gradient of the field is aligned with the duct axis. The flow is assumed to be inertialess. It is analyzed using an asymptotic flow model at high values of the Hartmann number, Ha. A corresponding study of the flow is used as a starting point by Hua and Walker. The analysis leads to two two-dimensional partial differential equations for the core pressure and the electric potential of the duct wall. These equations are solved numerically using central differences on a transformed grid. It has been confirmed that for the flow in insulating circular ducts, the three-dimensional effects are very significant. For high values of Ha, the three-dimensional pressure drop is equivalent to the extension of the length of the duct with fully developed flow by 10 to 150 diameters. A parametric study of the flow has been performed for different values of the Hartmann number, field gradient, and field levels upstream and downstream. A solution for the benchmark problem has been obtained for Ha = 258 000, which is relevant to inlet/outlet pipes for ARIES. Finally, the effect of the finite length of the magnet in magnetohydrodynamic experiments has been evaluated.