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 508 mph at a cruising altitude of 29500 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 29500 ft. above the sea level. (Assume the density and pressure of air at 29500 feet is 0.470 kg/m3 and 308 mbar but the interior of the plane remains pressurized to atmospheric pressure, that is, 1 atm.)

Explanation / Answer

First thing to do is convert all given info into common units throughout and list the known values. I will convert to SI but come back to lbs for the answer.

velocity of the plane(v) = 508 mph = 227 m/s
sides of the window = 14 in = 0.356 m
pressure at 29500ft (P_o) = 308 mbar = 30800 Pa
pressure in airplane(P_a) = 1 atm = 101325 Pa
density of the air outside the plane() = 0.47 kg/m^3

Now we need to calculate the pressure difference between the inside and outside of the plane using the following formula:

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

P = 1/2*(0.47 kg/m^3)*(227 m/s)^2+(101325 Pa - 30800 Pa)

P = 82634 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 = 82634 Pa * (0.356 m)^2

F = 10472 N

Convert Newtons to pound force:

10561 N = 2354 lbs of force on the window

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