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Bernoulli's Equation: Airplane Load

CLMECH-KIARWB

A Cessna 172 airplane has a mass of $1100\:kg$ when empty. Each wing is roughly rectangular with horizontal dimensions of $4.9\:m \times 2.1\:m$. When the airplane is flying, air traveling over the wing flows a distance that is $1.3\:\text{times}$ farther than air flowing under the wing. At a typical cruise speed, the air flowing under the wing is moving at $45\:m/s$ relative to the wing.

Assuming the density of air is $1.2\:kg/m^3$ and the thickness of the wing is negligible, what is the load (e.g. of passengers, luggage, etc.) in kilograms that the airplane can carry (in addition to its empty mass)? Ignore any contributions to the lift from the tail or airplane body.

Airflow around the wing of an airplane. Suzanne Taylor. Created for Albert.io. Copyright 2016