Power-law numerical solution for post-die extrusion of plastic pipe

In a continuous plastic-pipe extrusion, melt emerges from an annular die and is then drawn freely into a sizing sleeve. Here, we investigate this extensional flow when a pressure difference is applied across the melt cone. A numerical solution to a power-law fluid is presented. Differential equations for the melt-cone shape are derived from a force balance on the melt cone. Design curves are then constructed from the solutions to these equations. These curves are helpful in predicting the pipe-extrusion operating conditions. The model is also used to predict an operating envelope for sizing-sleeve placement. Examples demonstrate how to use these results. We also compare it to an earlier analytical solution that excludes a pressure difference across the melt cone.