Irrotational flow (of a magnetic field or incompressible fluid) around a screen with a slot

Problems concerning irrotational flows past obstacles may have physical applications in magneto- and electrostatics, as well as in the description of hydrodynamical flows of incompressible fluids. It is shown that for a magnetic field flow (or a flow of incompressible fluid in the hydrodynamical case) around an ideally conducting (impermeable) screen of width D with a narrow slot of width Delta a substantial flux passes trough the slot, so that, for example, a magnetic field (the velocity in the hydrodynamical problem) averaged over a slot with the width Delta = 0.01D will be 26 times greater than its far upstream value. The hydrodynamical problem is also formulated for an axisymmetric case for a circular screen and orifice. In this case, if the orifice is small enough, the flux of fluid proves to be proportional to the orifice diameter Delta, whereas fluid speed in the orifice increases as 1/Delta if Delta is decreased, i.e., even faster than in plane geometry.