Total volume of the house is given by
[tex]V = L * W * H[/tex]
[tex]V = 13*20 * 2.75[/tex]
[tex]V = 715 m^3[/tex]
now we will say that this volume of air is carried out in 15 minutes
so volume flow rate will be
[tex]\frac{dV}{dt} = \frac{715}{15*60} = 0.794 m^3/s[/tex]
now we will have same flow rate for the duct
flow rate for duct is given by
[tex]\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[/tex]
