Assuming the height of the bathroom is 2.4m, that is a total area of 5.7m^3 - The fan will displace around 3.6m^3 a minute, so it will take about 2.5 minutes to clear 5.7m^3 (best case scenario). Although if you factor in ducting length, type, cowl, duct size then it'll affect throughput, usually negatively. So realistically, you are looking at 3.5-4.5 minutes.
I would personally go for at least 300m^3/hr but that's because I want any moist air to be removed quickly and don't want any condensation building up on the walls/ceiling.
The next question is do you have a vent/window that can allow the drawal of enough air? the last thing you want is an inline fan without a window/vent, unless you enjoy taking showers with the door open. Also, the direction of the air flow is also important if you want efficient removal of moist air.
Also, be careful of the soffits, some of the older types have asbestos in them.
Extraction-wise that's probably true. However, if one goes with something like dobby's suggested 300m³/h, I imagine that might have a marked effect on one's heating bills in Winter.
As above- that fan is shifting about 6 times what building regs require so 3m of rigid duct won't be a problem. Lots of good suggestions- v good idea to insulate the duct and have it sloping downhill. Hopefully you won't get too much backdraught through the thing when it isn't running.....
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