Predicting the Leakage Exponents of Elastically Deforming Cracks in Pipes

In this study, the relationship between the conventional power equation and the FAVAD (Fixed and Variable Discharges) equation for modelling leakage as a function of pressure is investigated. It is shown that different leakage exponent (or N1) values are obtained for the same leak when measured at different pressures. Analytical exploration of the two equations shows that N1 tends to 0.5 when the system pressure tends to zero and 1.5 when the system pressure tends to infinity. A new term called the dimensionless leakage number, NL, is defined as the ratio between the variable and fixed portions of a leak, and it is shown that a single function can be used to describe the relationship between NL and N1. This relationship is combined with previous work to predict the head-area slope for cracks in pipes to predict the leakage exponent for a range of crack widths and lengths in different pipe materials.