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 adviser to the show, Adam and Jaime ask you to perform a crude calculation to test the myth. A typical jet plane travels at 552 mph at a cruising altitude of 29500 ft. The windows on a jet plane measure 14.0 in x 14.0 in. Calculate the force F 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 ft is 0.470 kg/m3 and 308 mbar but the interior of the plane remains pressurized to atmospheric pressure, that is, 1 atm. F= Calculate the fractional difference between this force and the weight Wman of a typical adult male (185 lb). FL wman How would you respond to Adam and Jaime? There is no need to perform the experiment; it is impossible for a person to be sucked out of a plane. O My calculation does not prove that such an event cannot happen; you will need to perform the experiment.

Answer 1

From Bernoulli’s theorem for horizontal flow:

$P_{1}+\frac{1}{2}\rho v_{1}^{2}=P_{2}+\frac{1}{2}\rho v_{2}^{2}$

If we consider the velocity inside the plane is zero and outside is v. Then the pressure difference will be

$P_{1}-P_{2}=\frac{1}{2}\rho v_{2}^{2}$

density of air at 29500 ft is 0.470 kg/m³. The velocity of air outside the plane is 552 mph or 246.77 m/s. Therefore,

$P_{1}-P_{2}=\frac{1}{2}\rho v_{2}^{2}=\frac{1}{2}\times 0.470\times 246.77^{2}=14310.43\ Pa=298.88\ lb-force/ft^{2}$

The force exerted on the window will be (area of window A = 14.0 inch x 14 inch = 1.361 ft².

$F=A\left (P_{1}-P_{2} \right )=1.361\times 298.88=406.78\ lb-force$

The fractional difference between this force and the weight

$\frac{F}{w_{man}}=\frac{406.78\ lb-force}{185\ lb}=2.199$

Second option: My calculation does noes not prove that such an event cannot happen.