[en] This paper treats liquid-metal flow in rectangular ducts with thin conducting walls. A transverse magnetic field changes from a uniform strength upstream to a weaker uniform strength downstream. The Hartmann number and the interaction parameter are assumed to be large, while the magnetic Reynolds number is assumed to be small. If the magnetic field changes gradually over a long duct length, the velocity and pressure are nearly uniform in each cross section and the flow differs slightly from locally fully developed flow. If the magnetic field changes more abruptly over a shorter duct length, the velocity and pressure are much larger near the walls parallel to the magnetic field than in the central part of duct. Solutions for the pressure drops due to the magnetic field change are presented