Dayside and nightside merging rates usually differ; first one dominates and then the other to maintain long-term flux balance. The polar cap, defined as the area in the ionosphere penetrated by open field lines, expands when closed field lines open during dayside merging and contracts when open field lines close during tail merging. The patterns of convection, electric field and current for polar cap inflation and deflation differ from those of steady state convection. This report models the flow and electrical parameters of polar cap inflation and deflation. We treat the idealized case of uniform conductivity, a planar ionosphere, and ''pure Bz'' merging (i.e., no By effect, although we note how the approach used here is readily modified to account for the By effect). For this idealized case, the potential associated with polar cap inflation and deflation is seen to be described by the same equations that govern the two-dimensional hydrodynamic flow into and out of an expanding and contracting cylinder with a gap in its side. The gap corresponds to the breach in the polar cap boundary through which magnetic flux passes as a result of merging. The calculated potential pattern displays the usual two cell convection configuration, but the foci of the two cells are the edges of the flux gaps. Thus the cells are displaced sunward during dayside merging and tailward during tail merging.