wrote:

No this is not a steam room it is a normal bathroom. Only partly tiled
aound the bath. A power shower is over the bath ie not an enclosed
unit. The fan is threre to simply extract steam and condensation when
the shower is on, in order to prevent the build up of condesation. The
room is heated with a radiator. the room is not airtight and air is
simply replenished from gaps around the door leading into an interior
hall.

Pick out the fan and see what the manufacturer recommends. Most
likely the 4" duct will be adequate.

R