Leakage Through a Channel Formed by a Gasket, a Sealing Surface, and a Filament Trapped Between Them

Plumbing for the transport of liquid Hydrogen or liquid Oxygen at the Kennedy Space Center (KSC) is very critical. Every piece of hardware for handling such a hazardous cryogen is subject to testing prior to installation and use. Safe, realistic testing of all such hardware is prohibitively expensive, which leads, perforce, to expidients such as: (1) lead testing with non-flammable tracer fluids (e.g, liquid nitrogen) and (2) leak testing with room temperature tracer fluids (e.g. liquid helium). Such expedients undermine the realism of the tests. If however, one could apply rational fluid dynamics methods to derive a general analytical expression with which one could relate the throughput of gaseous Helium through a given leak channel to the throughput of liquid Hydrogen through the same channel, then one could recover much of the information that one would otherwise forfeit through these expedients. These facts lead to the following questions: (1) What would be an example of a generic flaw in a gasket?; and (2) How can one calculate the flow of fluid in it? The report addresses these questions. It considers a particular leak geometry, namely one formed by a gasket, a sealing surface, and a filament trapped between them (so that the cross section of the leak channel is a flat bottomed curvilinear triangle, two sides of which are circular arcs and which has cusps on all three corners).