Monday, December 11, 2017

Cabin Pressurization of an Airplane

The end of the semester is drawing near, and I am counting down the days until I can board my flight back home. Some people don't really like the idea of traveling via a giant aluminum cylinder shooting through the sky, but I absolutely enjoy flying. But then I start to think: how am I still able to breathe while at a cruising altitude of 36,000 feet? I mean, obviously the cabin is pressurized for our comfort and survival, but I've never really thought about how it all works. So I did what any fellow millennial would do and consulted the internet.

According to an article by George C. Larson from Air & Space Smithsonian, if you've ever been worried about there being a hole in the plane, then don't worry because there already is one and it's supposed to be there. Larson describes the pressurization system as an inflated balloon with a small hole. The balloon is being constantly inflated with air, while at the same time, air leaves the balloon through the hole. In an airplane's pressurization system, air from the engines becomes heated to a high temperature and simultaneously pressurized. This hot, pressurized air is then systematically cooled and circulated throughout the cabin. The circulated air then leaves the outflow valve (hole in the plane) in a controlled manner monitored by a pressure sensor. At ground level, the outflow valve is always open, but as the plane begins its ascent, it closes to pressurize the cabin and opens periodically.

At altitudes of 36,000 feet, the outside air pressure can drop to as low as 3.3 psi, or 0.225 atm (22753 Pa). In a week, I'll be traveling on a Boeing 717-200, which has a fuselage length of 34.3 m (112'8"), a diameter of 3.4 m (11'), and a cabin temperature of 75 degrees F.

In order to keep passengers safe, the air pressure inside the cabin should be equivalent to the air pressure at an altitude of 7,000 feet, or 11.3 psi (0.769 atm or 77911 Pa). This means there should be 9813 moles of air inside the cabin at a given time.
n = (77911 Pa)(311 m^3) / (8.314 J/mol K)(297 K)
n = 9813 mol air

If the plane suffered rapid decompression (and ignoring the change in air temperature), using PV=nRT, there would only be 2895 moles of air inside the airplane at the most.

n = (22753 Pa)(311 m^3) / (8.314 J/mol K)(297 K)
n = 2895 mol gas

According to FAA regulations, there should be 0.55 lbs/min of fresh air per person while flying, or 250 g/min of air per person. With air having a molecular mass of 28.97 g/mol, that means the cabin should have 8.63 mol/min of air for one person to comfortably breathe. If a Boeing 717-200 has a capacity of 134 passengers and 5 crew members, that is 1200 mol/min of air for the whole plane.

In order to keep the cabin pressurized at a safe and comfortable level, 9813 moles air need to be inside the cabin at all times. Furthermore, in order to allow all passengers and crew the total required rate of air of 1200 mol/min, the pressurization of the cabin must have a system that has a constant intake and release of air. And don't worry: just in case of times of rapid decompression, oxygen masks will drop down for a supply of air while the highly capable, trained pilots land the plane. Happy flying!


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