Use of the steady-state orifice equation in the computation of transient flow through pipe leaks

The implementation of the unsteady leak rate simulation by the Method of Characteristics is discussed, and the respective numerical equations are derived. The use of the steady-state orifice equation for the computation of unsteady leak rates from pipe through-crack or rupture is discussed and evaluated. Five different shapes of artificially made pipe through-cracks were experimentally considered. These types of leak sources include a circumferential crack, a loose weldment crack, multiple small cracks, a longitudinal long crack and a loose union fitting. Different values of steady-state leak rates were run through each of these crack types and a leak opening dimensional coefficient analogous to that of the orifice was established. Severe transient flow through the same leak opening was then run, and the average steadystate value for this coefficient was used to establish a leak rate history throughout the transient course. A comparison between this leak rate history and the corresponding measured rate was considered, and it was found that the use of the steady-state orifice equation for the computation of leak rate from pipe through-crack (rupture) during transient flow conditions was accurate for normal-sized leaks.