How large must a heating duct be if air moving 3 m s⁻¹ along it can replenish the air in a room of 300 m³ volumes every 15 min? Assume the air's density remains constant. (Ans: 19 cm)



Data Given:


Velocity of air = v = 3 m s⁻¹

Volume of air = V = 300 m³

Tine = t = 15 min = 900 s


To Find:


Radius of the duct  = r = ?


Solution:


By using the formula for finding the volume of fluid flows in time interval t is

V = A v t

where A = π r²

V = π r² v t 

or

r =  `\sqrt frac {V}{π v t}`

by putting the corresponding values

r =  `\sqrt frac {300 m³}{3.1416 ｘ 3 m s⁻¹ ｘ 900 s}`

r =  `\sqrt frac {300 m³}{8482.32 m }`

r =  `\sqrt {0.0354 m²}`

r =  0.188 m

r =  0.19 m

or

r =  19 cm ----------------Ans.





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