The need to improve the methods used when designing emergency, pressure-relief systems on polymerisation reactors, has made the flow of highly viscous fluids in pipeline fittings highly topical. This paper investigates the flow processes involved in single-phase, viscous flows in nozzles and orifice plates. These fittings were chosen because they would give an insight into the behaviour of highly viscous flows in other geometries, such as the flow upstream of the seat in a pressure relief valve. Experimental data are presented for a pipe, two conical nozzles and a sharp-edged orifice plate for laminar flows in the Reynolds number range 50-400 and for turbulent flows. The volume flow rate-pressure drop characteristics are presented for both nozzles and the orifice plate. The discharge momentum flow rate for the pipe, a nozzle and the orifice plate are also given. Analysis of the data shows that nozzles and orifice plates that are geometrically similar have a similar resistance to flow. It is also shown that the contraction coefficient for an orifice plate tends to unity at low Reynolds numbers.