A common belief is that a hole in a jet plane can suck a person out. On an episo

Question

A common belief is that a hole in a jet plane can suck a person out. On an episode of the popular TV series Myth Busters, hosts Adam and Jaime attempted to determine whether this is possible. According to the hosts' experiment, such an event cannot happen (that is, they "busted" the myth). But did they need to perform the experiment? As a science advisor to the show, Adam and Jaime ask you to perform a crude calculation to test the myth. A typical jet plane travels at 542 mph at a cruising altitude of 32500 ft. The windows on a jet plane measure 14.0 in × 14.0 in. Calculate the force exerted on such a window as the plane flies at 32500 ft. above the sea level. (Assume the density and pressure of air at 32500 feet is 0.410 kg/m3 and 259 mbar but the interior of the plane remains pressurized to atmospheric pressure, that is, 1 atm.)

Explanation / Answer

velocity of the plane(v) = 542 mph = 242 m/s
sides of the window = 14 in = 0.356 m
pressure at 32500ft(P_o) = 259 mbar = 25900 Pa
pressure in airplane(P_a) = 1 atm = 101325 Pa
density of the air outside the plane() = 0.410 kg/m^3


now,
P = 1/2 v^2+(P_a+P_o)

P = 1/2*(0.42 kg/m^3)*(242 m/s)^2+(101325 Pa - 25900 Pa)

P = 87723.44 Pa

We can now get the net force on the window by applying the equation:

P = F/A where, F = net force and A = area of the window

F = P*A = 87723.44 Pa * (0.356 m)^2

F = 11117.717 N

F = 2499.14 lb

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