Problem 1.49

# Problem 1.49 - Problem 1.49[Difficulty 4 Given Dimensions...

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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: 1 2 2 22 HD DH 4 uu u π ∀= ⎡⎤ ∂∀ ∂∀ ⎛⎞ + ⎢⎥ ⎜⎟ ∀∂ ⎝⎠ ⎣⎦ Since 2 4 , then 2 D H4 ∂∀ = and DH D2 ∂∀ = . Letting D D u x δ = ± and H H u x = ± , and substituting, 1 1 2 2 2 2 2 4H D 4D DH 2 u DH 4 H DH 2 D H D xx x x πδ ππ + + Solving, 2 2 21 2 u( ) H D x δδ ⎛⎞⎛ ⎞⎛ =+ = + ⎜⎟⎜ ⎟⎜ ⎝⎠⎝ ⎠⎝ () 11 2 2 12 110mm 66mm u 0.005 0.158 mm () () x + + Check: 3 H 3 D 0.158 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.

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