Hot flue gas is flowing through a furnace, flue and chimney as a result of draft created by the chimney. Calculate the mass flow rate $(m^{})$ of the flue gas through the chimney. Assume that frictional losses in the furnace and flue are negligible.

Given

Density of air outside $({}_{\text{a}\text{i}\text{r}})=1\mathrm{.}1kg{m}^{-3}$

Density of hot flue gas $({}_{\text{h}\text{o}\text{x}})=0\mathrm{.}8kg{m}^{-3}$

Viscosity of hot flue gas $()=2\mathrm{.}5{10}^{-5}kg{m}^{-1}{s}^{-1}$

Height of the chimney $(z_1-z_2)=50m$

Chimney is of square cross$-$section with edge length of $1m.$

Assume the chimney wall to have $\frac{e}{d}=0\mathrm{.}004$