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 19 m/s ; the size of the window in your room is 1.4 m × 2.6 m .

1. 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.

2. What is the magnitude of the net force that the air exerts on the window?

3. What is the direction of the net force that the air exerts on the window? (inward or outword)

Explanation / Answer

speed is 19 m/s

density of air is 1.30 kg/m3

size of the window in your room is 1.4 m × 2.6 m

1) From Inside the room you have the following pressures on the window:
Ps - static pressure (rho * g * h)

( 1.30 kg/m3*9.81*.1.4)= 17.85

So Total Pressure = Ps = 17.85pa

From outside the room at the window you have the following pressures:
Ps - static pressure (rho * g * h) =17.85
Pdyn = 1/2 * rho * v^2 =( 1/2*1.30*19) = 12.35
So Total Pressure = Ps + Pdyn =17.85+12.35 = 30.2pa

2) Now the question is for v^2. Weather reports 19 m/s at essentially ground height. Since it is inviscid flow assumption, the wind speed at 48th floor can also be assumed to be 19 m/s

Net force on the window is Total Pressure Difference (Outside - Inside):
delta Pt = Ptout - Ptin
=(Ps + Pdyn) - Ps
= Pdyn
= 1/2 * rho * v^2

Net Force = Pressure * Area
= 1/2 * rho * v^2 * (1.4 * 2.6)

=30.2*(1.4*2.6) =110N

3) the direction of the net force that the air exerts on the window is inward

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