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.