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.
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:
[tex]V'=30\frac{L}{s-persons}*13persons=390\frac{L}{s}[/tex]
This value can be converted to [tex]m^{3}/s[/tex]
[tex] 390\frac{L}{s}*\frac{1000cm^{3}}{1L}*\frac{1m^{3}}{(100cm)^{3}}=0.39m^{3}/s[/tex]
Once we got this value we use the volumetric flow formula, which tells us that:
[tex]V'=Av[/tex]
where A is the area of the duct and v is the velocity of the air flow.
We also know that:
[tex]A=\frac{\pi d^{2}}{4}[/tex]
so we can substitute that into our equation, so we get:
[tex]V'=\frac{\pi d^{2}}{4}v[/tex]
which can be solved for the diameter, which yields:
[tex]d=\sqrt{\frac{4V'}{\pi v}}[/tex]
and we can next substitute the values the problem provides us with:
[tex]d=\sqrt{\frac{4()0.39m^{3}/s}{\pi (8m/s)}}=0.249m[/tex]
so the duct must have a diameter of at least 24.9cm for the velocity not to exceed 8m/s.
