Hydrodynamics of vortex generation in flowing superfluid helium

The hydrodynamic energy for a system of vortices in a flowing superfluid is considered. We obtain the conditions in which the energy of vortices is reduced due to superfluid flow under a specified set of constraints, and the amount of this reduction. The deceleration of the superfluid (or the amount of extra pressure required to maintain constant superfluid flux) on vortex generation is calculated. The general theory is applied to two simple situations: superfluid flow in a smooth channel and superfluid flow through an orifice.