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

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

$\frac{dV}{dt} = \frac{715}{15*60} = 0.794 m^3/s$

now we will have same flow rate for the duct

flow rate for duct is given by

$\frac{dV}{dt} = area * speed{/tex]

[tex]\frac{dV}{dt} = \pi r^2 * v{/tex]

[tex]0.794 = \pi * (0.15)^2 * v{/tex]

[tex]v = 11.24 m/s$