Theoretical investigation and experimentation into the expansion of round holes and cracks within pressurised pipes

The derivation of the classical equation for flow through an orifice assumes a fixed orifice area. However, pipe materials exhibit expansion behaviour with increasing pressure, which alters the size of orifices and results in greater leakage rates. The purpose of this investigation was to study the behaviour of round holes and cracks in pipes through theoretical and experimental work. The results of the study include equations derived for increased flow through round holes in pressurized cylindrical shells and pipes. The theoretical models explain the increased flow experienced due to the leak area increasing. The models incorporate material properties, shell geometry and fluid properties for both uni-axially and bi-axially stressed pipe sections. Analytical results are compared with previous finite element investigations. In addition, an experimental study into the effects of pressure on a round hole in a class 6 uPVC pipe was conducted. Conclusions are made relating to the influence of material expansion to increased flow rate through openings in pressurised cylinders. The results compared positively with those of the theoretical equations. Conclusions are made relating to the influence of round hole or crack expansion to an increased flow rate through openings in pressurised pipes. Results include the effects of geometrical and material variables on the expansion of round holes. Better explanation of the increased flow through orifices, documented by practical observations, is presented. Results indicate that round hole area is linearly related to pressure. However, testing on longitudinal cracks resulted in a non-linear relationship between crack area and internal pipe pressure. Results indicate the expansion of round hole area is minimal. Leakage however is greatly affected over extended time periods by even the smallest increase in defect area. Critical pressures before brittle fracture obtained from testing on longitudinal cracks were compared to theoretical formulation. Results show a close relationship between current theory and experimentation.Prof. K. van Zy