Realistic modeling of leakage and intrusion flows through leak openings in pipes

摘要

The hydraulics of leakage and intrusion flows through leak openings in pipes is complicated by variations in the leak areas owingudto changes in pressure. This paper argues that the pressure–area relationship can reasonably be assumed to be a linear function, and a modifiedudorifice equation is proposed for more realistic modeling of leakage and intrusion flows. The properties of the modified orifice equation areudexplored for different classes of leak openings. The implications for the current practice of using a power equation to model leakage andudintrusion flows are then investigated. A mathematical proof is proposed for an equation linking the parameters of the modified orifice andudpower equations using the concept of a dimensionless leakage number. The leakage exponent of a given leak opening is shown to generallyudnot be constant with variations in pressure and to approach infinity when the leakage number approaches a value of minus one. Significantudmodeling errors may result if the power equation is extrapolated beyond its calibration pressure range or at high exponent values. It isudconcluded that the modified orifice equation and leakage number provide a more realistic description of leakage and intrusion flows,udand it is recommended that this approach be adopted in modeling studies.