You are on the 48th floor of the Windom Hotel. The day is stormy, and you wonder

Question

You are on the 48th floor of the Windom Hotel. The day is stormy, and you wonder whether the hotel is a safe place. According to the weather report, the air speed is 20 m/s ; the size of the window in your room is 0.50m 2.6m .

a) What is the difference in pressure between the inside and outside air? Assume the air flow to be laminar (non-turbulent) and non-viscous. The density of air is 1.30 kg/m3.

b)What is the magnitude of the net force that the air exerts on the window?

c)What is the direction of the net force that the air exerts on the window? (inward or outward)

Explanation / Answer

a) inside the room the pressure is

Ps - static pressure (rho * g * h)
So Total Pressure = Ps

outside the window

Ps - static pressure (rho * g * h)
Pdyn = 1/2 * rho * v^2
So Total Pressure = Ps + Pdyn

deltaP= Ps + Pdyn -Ps

deltaP=Pdyn

deltaP=1/2 * rho * v^2

air density of 1.30 kg/m3.

deltaP=1/2*1.30*20^2

deltaP=260 Pa

b)Net force =Pressure DIFFERENCE * Area

area of window =0.50*2.6

=1.3m^2

=260*1.3

Force=338N

c)since the force is positive so the direction of the net force that the air exerts on the window is inwards.

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