Explicit equations for leak rates through narrow cracks

Explicit equations to describe the leak rate of a single phase fluid through a narrow crack under a low pressure gradient have been developed and are presented. Four distinct flow regimes, which change with crack opening displacement, have been previously identified and are the basis of this model. The fluid flow is governed by the pressure gradient and the tortuosity of the crack, which is particularly important when the opening displacement is small. The equations have been developed by considering the pressure forces created when the fluid flows down an idealized zig-zag channel. The nature of the flow, and hence the governing equations, change as the crack aperture increases. The power of this approach is clearly seen when the flow rates predicted using this model are compared both to the flow rates obtained from computational fluid dynamics analysis and those found by experimentation. The agreement between these sets of data is good, showing that the major effects governing the flow rate have been identified and then accounted for.