(Requires a calculator that can compute fractional
Chapter 7, Problem 18(choose chapter or problem)
(Requires a calculator that can compute fractional powers.) Because wind speed increases with height, wind turbines are placed as high as possible, and certainly above the level of any existing structures or trees that may block the wind. In order to estimate typical wind speeds at various heights, wind engineers first measure the average wind speed S33 (in mph) at a height of 33 feet. Then they can estimate the wind speed Sh at height h using the formula Sh 5 S33(h/33)2/7 where h is in feet, and Sh and S33 are both in miles per hour. a. For an area likely to have hurricanes, wind engineers design for a wind speed of 90 mph at a height of 33 feet. Estimate the wind speed under hurricane conditions at the top of a building 120 feet tall. b. Rearrange the formula to express h in terms of Sh and S33. Using the hurricane conditions in part (a), at what height does the formula predict 156-mph winds?
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