The Empire State Building in New York City is approximately 306 meters tall. Assume that the air density from the bottom to the top of the building is a constant all of the way up and is equal to 1 kilogram per cubic meter. Then, using hydrostatic balance, compute what the pressure change is from the bottom to the top of the skyscraper. (Hints: insert 1 for the air density in the hydrostatic balance equation, and then insert 306 for the distance; solve for the pressure difference, and divide by 100 to get your answer in millibars.) Your answer is an approximation because density actually decreases in the vertical. Even so, it explains why your ears “pop” when riding the high-speed elevators up to the observation deck of the Empire State Building.
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