What is a normal operating pressure of a fire hydrant at the nozzle when operational?

It varies. I have seen a range of between 50 psi to 225 psi. It is affected by distance, size of water lines and their configuration and elevation change from source to the hydrant, as well as the type of pressurization, gravity or pump. On average though 80 to 100 psi. Of course a larger nozzle would decrease the residual pressure while a smaller nozzle would tend to increase residual pressure. 125 psi is about the maximum pressure for a "hand line" in order to be manageable.