The modern Boeing 747 passenger jet airplane cruises at a speed up to 920 km/hr,

Question

The modern Boeing 747 passenger jet airplane cruises at a speed up to 920 km/hr, at an altitude of 11,000 m. The cabin pressure is maintained equivalent to the atmospheric pressure at an altitude of 2,000 m. This is called the "cabin altitude".
The pressure as a function of altitude is obtained via a simple formula that depends on the temperature and a variety of other physical parameters, as shown here.

http://en.wikipedia.org/wiki/Atmospheric_pressure#Altitude_atmospheric_pressure_variation

the area of the passenger windows in the 747 is about 0.08 m2.


Calculate the force on the window due to the rest pressure difference alone. In other words, if the airplane were stationary at its cruising altitude, what is the force on the window?

Explanation / Answer

Using the formula from the website: P = (101325)*(1 - (0.0065)(11000/288.15))^((9.8*0.029)/(8.314*0.0065)) = 22612.10 Pa At 2,000 m: P = (101325)*(1 - (0.0065)(2000/288.15))^((9.8*0.029)/(8.314*0.0065)) = 79483.86 Pressure diff = 79483.86 - 22612.10 = 56871.76 Pa F = PA = (56871.76)(0.08) = 4549.74 N

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