Final answer:
To find the average speed of air in the duct, we need to calculate the volume flow rate and divide it by the cross-sectional area of the duct. After the calculations, the average speed of air in the duct is approximately 2.10 m/s.
Step-by-step explanation:
To find the average speed of air in the duct, we need to calculate the volume flow rate. The volume flow rate is equal to the volume of air carried by the duct divided by the time it takes to carry that volume. The volume of the house's interior can be calculated by multiplying its dimensions: 13.0 m x 20.0 m x 2.75 m = 715 m³.
Since the duct is circular, we can use the formula for the volume of a cylinder to find the volume carried by the duct: V = πr²h, where r is the radius and h is the height. The radius is half the diameter, so r = 0.300 m / 2 = 0.150 m. The volume carried by the duct is therefore: V = π(0.150 m)²h.
Given that the duct carries a volume equal to that of the house's interior every 15 minutes, the volume flow rate is: Q = V / t.
Finally, to calculate the average speed of air in the duct, we divide the volume flow rate by the cross-sectional area of the duct: v = Q / A.
After these calculations, the average speed of air in the duct is approximately 2.10 m/s.