Equations describing the magnetospheric flow in regions of equipotential convection are developed for the case of uniform ionospheric conductivtiy and zero cross-field current inside the regions. The approach is equivalent to that of Vasyliunas, since the assumptions are those of equipotential convection. Flux tubes are regarded as fluid elements, and terms appear in the equations corresponding to the stress due to the interaction of a flux tube with its neighbors and to stresses transmitted through the ends. The convective velocity is found to be expressible as the gradient of a two-dimensional potential that obeys either Laplace's or Poisson's equation. The equations are applied to flow in the polar caps to determine what type of applied outer magnetospheric force produced the observed flows. It is required that flux tubes anchored near the outer boundary of the polar cap be subject to a shear force relative to other polar cap flux tubes to produce the narrow latitude-limited flows often observed.