The critical Reynolds number at which the flow downstream of an orifice or nozzle in a pipe becomes turbulent is an important parameter as it is the demarcating point between purely laminar flow and relaminarising flow. The value of the critical Reynolds number is estimated for sharp-edged orifices, quadrant-edged orifices and long radius nozzles from indirect evidences using mean flow measurements. Different criteria are considered such as the variations of coefficient of discharge, loss coefficient, loss as percentage of piezometric head differential across the meter, and pressure recovery length downstream of the orifice. These criteria identify a range of transition Reynolds number for different orifices and nozzles. The critical orifice Reynolds number is seen to approach a constant value for low values of orifice or nozzle diameter to pipe diameter ratio. The critical Reynolds number increases gradually with increase in edge radius with the nozzle having the highest value.