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 25 m/s ; the size of the window in your room is 1.1 m × 2.8 m .

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?

Outward or Inward

Explanation / Answer

A)
use Bernoulli principle,
Inside room = outside room
Pi + 0.5*rho*Vi^2 = Pf + 0.5*rho*Vf^2
Pi + 0.5*rho*0 = Pf + 0.5*1.3*(25)^2
Pi = Pf + 0.5*1.3*(25)^2
Pi - Pf = 0.5*1.3*(25)^2
= 406.25 Pa
Answer : 406.25 Pa

B)
Net force = P*A
= 406.25 * (1.1*2.8)
= 1251.25 N
Answer: 1251.25 N

C)
Since Pi is greater than Pf
Net force will be outward

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