Question

The main uptake air duct of a forced air gas heater is 0.300 m in diameter. what is the average speed of air in the duct if it carries a volume equal to that of the house's interior every 15 min? the inside volume of the house is equivalent to a rectangular solid 13.0 m wide by 20.0 m long by 2.75 m high.

Answer 1

The average speed of air in the duct is 675.76 m/min.

Step-by-step explanation:

To find the average speed of air in the duct, we need to calculate the volume flow rate of the air. The volume of the house's interior can be found by multiplying its length, width, and height. In this case, the volume is 13.0 m x 20.0 m x 2.75 m = 715 m³. Since the air carries a volume equal to that of the house's interior every 15 minutes, the volume flow rate is 715 m³ / 15 min = 47.67 m³/min (1st keyword: volume flow rate).

The area of the duct can be found using the formula for the area of a circle: A = πr², where r is the radius of the duct. In this case, the diameter of the duct is 0.300 m, so the radius is 0.300 m / 2 = 0.150 m. The area of the duct is then A = π(0.150 m)² = 0.0706 m² (2nd keyword: area of duct).

The average speed of air in the duct can be found using the formula for volume flow rate: Q = A * v, where Q is the volume flow rate, A is the area of the duct, and v is the average speed of air. Rearranging the formula, we get v = Q / A. Plugging in the values, we have v = 47.67 m³/min / 0.0706 m² = 675.76 m/min (3rd keyword: average speed of air).

Answer 2

Total volume of the house is given by

`V = L * W * H`

`V = 13*20 * 2.75`

`V = 715 m^3`

now we will say that this volume of air is carried out in 15 minutes

so volume flow rate will be

`(dV)/(dt) = (715)/(15*60) = 0.794 m^3/s`

now we will have same flow rate for the duct

flow rate for duct is given by