Petroleum pumped from underground reservoirs leaves unfilled voids. If those cav

Question

Petroleum pumped from underground reservoirs leaves unfilled voids. If those cavities were to collapse, earth's surface would move inward causing a decrease in earth's physical size similar to partially deflating a balloon. Model earth as a sphere and determine the average change in its radial size resulting from such a collapse due to petroleum consumption from 1 January 2009 to 31 December 2009 (one decade). Dr. Hastly read in Scientific American that similar causes may be responsible for the subsidence of New Orleans, LA. Clearly explain the logic underlying the problem.

Explanation / Answer

One decade would be from Jan 1999 to Dec 2008! Since the rate of consumption is not given 80,000,000 bbl/day might be a reasonable guess. 1 bbl = 5.61 ft^3 (oil not other liquids) Ve = 4/3 * pi * R^3 volume of earth R = 3960 mi = 2.1 * 10E7 ft mean radius of earth dVe = 4 * pi R^2 dR change in volume due to change in radius dR = = dVe / (4 * pi * R^2) dVe = volume of oil = 10 * 365 * 8 * 10E7 * 5.6 = 1.6 * 10E12 ft^3 dR = 1.6 * 10E12 / (4 * pi * 4.4 * 10E14) = 1.6 * 10E12 / 5.5 * 10E15 dR = .00029 ft = .0035 in

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