Example $2$

A large industrial building $(15m10m5m$ tall$)$ is initially at STP conditions. A large door $(5$ m wide by $4$ m tall$)$ is opened while loading supplies into the building for $2$ minutes during which a strong cold and dense $(1\mathrm{.}25k\frac{g}{m^3})$ wind blows into the door with a non$-$uniform velocity profile as shown. $V(y)$ models the flow in the atmospheric boundary layer, let $U=5\frac{m}{s}$ and $h=10m$ as the height of the boundary layer. The wind also impacts the building at an angle of $50$ degrees with respect to the door.

a$.$ What is the average velocity of the wind entering the open door $($door height is $4$ m $)?$

b$.$ While the door is open for $2$ minutes, windows are also open in the building and $3300$ kg of air exits the building. At the end of $2$ minutes the door and windows are shut, and the building is sealed. The HVAC system heats the building for $20$ minutes until it returns to the initial temperature of $300$ K $.$ An employee goes to leave for the night and opens a hinged door to the outside inward. Meanwhile the wind outside has died down to stagnant conditions and the pressure outside is standard atmospheric.

Do you expect that the employee will find it:

Hard to open the door, or

Will it open of its own volition upon released, based on the new pressure inside the building?

Find the new pressure in the building to back up your answer.

$V(y)=U[2\frac{y}{h}-\frac{y^2}{h^2}]$

side view of wind towards building

$49$