Predicting the head leakage behaviour of cracks in pipe elbows

In this study, finite element analysis (SAP2000 program) was used to investigate the relationship between the pressure and leakage area in 90° pipe elbows with longitudinal, spiral, and circumferential cracks. The results show that leakage areas expand linearly as the internal pressure increases and its inclination is called the pressure–area slope (m). A sensitivity study was conducted to recognize the influence of different parameters (inside diameter, wall thickness, modulus of elasticity, longitudinal stress, Poisson’s ratio, and finally crack orientation) on both m and leakage exponent (N). The results reveal that the elasticity modulus has the dominant impact on m, followed by elbow wall thickness, and then elbow inside-diameter. The Poisson’s ratio and the longitudinal stress have an insignificant influence on m. Moreover, the slope m varies more in the longitudinal and spiral cracks than the circumferential cracks. The amount of leakage through the different cracks is a function of the internal pressure raised to an exponent ranging from 0.5 to 1.01. An attempt was made to find empirical equations to express the pressure–area slope as a function of elbow properties and crack orientation. The study’s findings were checked against numerical and experimental results and good correlations were obtained.