Development and verification of methods for predicting flow rates through leaks in valves and couplings

This is the final report of a research effort which addresses the title problem. The report discusses two broad models of flows, which represent the following extreme cases: (1) inertia-dominated flow, where friction is relatively insignificant; and (2) friction-dominated flow where inertia is insignificant. In class (2), the leak channel might consist of the gap between a scratch in a plastic seal and a polished metal plate against which the seal is pressed. Here, the cross section of the leak channel is modeled as a flat bottomed crescent. A publication generated under the present grant period presents an exact solution of the equations of fully-developed laminar pipe flow of a liquid in the case of a crescent beneath a hyperbolic arc. A Master's thesis project supported by the present grant presents the corresponding solution beneath a circular arc. A second publication reviews the flow of a gas through the same channel, which may be analyzed by a standard one-dimensional model (Fanno flow) for an engineering approximation. Finally, the report discusses the design and progress in the fabrication of a leak-test cell, in which one may measure the flow of fluid through a controlled flaw in a seal. The aim of such measurements is to furnish data for comparison with the predictions of the theory.