Method and apparatus for abrasively machining a channel port with an abrasive fluid

In a process to cut a fine aperture for e.g. an automotive fuel injection jet, the hole is cut using an abrasive fluid directed at pre-defined high pressure. The volume of fluid passing through the hole is monitored, and on reaching a predetermined value a constant volumetric flow is maintained and the pressure monitored until reaching a steady target value. Also claimed is a suitable assembly.