Problem 1.49[Difficulty: 4]Given:Dimensions of soda can: D = 66 mm, H = 110 mm Find:Measurement precision needed to allow volume to be estimated with an uncertainty of ± 0.5 percent or less. Solution: Use the methods of Appendix F: Computing equations: 12222HDDH4uuuπ∀∀=⎡⎤∂∀∂∀⎛⎞=±+⎢⎥⎜⎟∀∂⎝⎠⎣⎦Since 24, then 2DH4∂∀∂=and DHD2∂∀∂=. Letting DDuxδ= ±and HHux= ±, and substituting, 11222224HD4DDH2uDH 4 HDH 2DHDxxxxπδππ∀⎛⎞⎛⎞++⎜⎟⎜⎟⎝⎠⎝⎠Solving, 22212u()HDxδδ∀⎡⎤⎛⎞⎛⎞⎛⎞⎛⎞=+=+⎢⎥⎜⎟⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠⎝⎠⎢⎥⎣⎦()112212110mm66mmu0.0050.158 mm() ()x∀⎡⎤++Check: 3H3D0.158 mm
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.