When plasma in the near-Earth geomagnetic tail convect sunward, it passes the Earth at close distance. The highly conducting ionosphere exerts a drag on the plasma flow and yields a shear in the magnetic field. In the slow-flow approximation this shear must be balanced by pressure gradients in the equatorial plane, and observations indicate the presence of such, that is, azimuthal pressure gradients pointing toward local midnight in the inner magnetosphere. We investigate the role of parallel potential drops in the acceleration region in this context, using a steady one-dimensional convection model aligned with the azimuthal direction around the Earth. Parallel potential drops provide a means to decouple the magnetosphere from the ionosphere; thus they reduce ionospheric drag, and initiate a process whereby azimuthal pressure gradients in the equatorial plane are relaxed. By taking into account the reflection of Alfv¿n waves on the auroral acceleration region, we find that the decoupling becomes dependent on the transverse scale of the acceleration region. Being faster at small scales (~20 km), while at scales comparable to the width of the auroral oval, it is much slower, and the coupling becomes perfect. We find that it takes ~30 min to normalize the pressure at midnight after it had been doubled. The model also allows for estimates of the maximum pressure gradient present right before the decoupling process is initiated, and values up to 10 times higher than normal are found. Further more, a linear relationship between field-aligned currents/pressure gradient and the parallel potential drop is derived. At smaller scales (~20 km) the proportionality constant becomes similar to the Lyons-Evans-Lundin constant used in linear current voltage relations.