Answer:
The minimum required flow rate of fresh air that needs to be supplied to the lounge is 390L/s.
The diameter of the duct mus be of 24.9cm at least if thte air velocity is not to exceed 8m/s.
Step-by-step explanation:
First, in order to find the minimum required flow rate of fresh air, we need to take the ASHRAE standard and multiply it by the number of heavy smokers, so we get:

This value can be converted to


Once we got this value we use the volumetric flow formula, which tells us that:

where A is the area of the duct and v is the velocity of the air flow.
We also know that:

so we can substitute that into our equation, so we get:

which can be solved for the diameter, which yields:

and we can next substitute the values the problem provides us with:

so the duct must have a diameter of at least 24.9cm for the velocity not to exceed 8m/s.