4_Sources_of_Error(2).ppt

10 thermal expansion coefficient vs temperature t d d

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10 Thermal Expansion Coefficient vs Temperature T D D T( o F) α (μin/in/ o F) -340 2.45 -300 3.07 -220 4.08 -160 4.72 -80 5.43 0 6.00 40 6.24 80 6.47
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11 Regressing Data in Excel (general format) α = -1E-05T 2 + 0.0062T + 6.0234
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12 Observed and Predicted Values T( o F) α (μin/in/ o F) Given α (μin/in/ o F) Predicted -340 2.45 2.76 -300 3.07 3.26 -220 4.08 4.18 -160 4.72 4.78 -80 5.43 5.46 0 6.00 6.02 40 6.24 6.26 80 6.47 6.46 α = -1E-05T 2 + 0.0062T + 6.0234
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13 Regressing Data in Excel (scientific format) α = -1.2360E-05T 2 + 6.2714E-03T + 6.0234
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14 Observed and Predicted Values T( o F) α (μin/in/ o F) Given α (μin/in/ o F) Predicted -340 2.45 2.46 -300 3.07 3.03 -220 4.08 4.05 -160 4.72 4.70 -80 5.43 5.44 0 6.00 6.02 40 6.24 6.25 80 6.47 6.45 α = -1.2360E-05T 2 + 6.2714E-03T + 6.0234
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15 Observed and Predicted Values T( o F) α (μ in/in/ o F) Given α (μ in/in/ o F) Predicted α (μ in/in/ o F) Predicted -340 2.45 2.46 2.76 -300 3.07 3.03 3.26 -220 4.08 4.05 4.18 -160 4.72 4.70 4.78 -80 5.43 5.44 5.46 0 6.00 6.02 6.02 40 6.24 6.25 6.26 80 6.47 6.45 6.46 α = -1.2360E-05T 2 + 6.2714E-03T + 6.0234 α = -1E-05T 2 + 0.0062T + 6.0234
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16 Truncation Error
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17 Truncation error Error caused by truncating or approximating a mathematical procedure.
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18 Example of Truncation Error Taking only a few terms of a Maclaurin series to approximat e .......... .......... ! 3 ! 2 1 3 2 x x x e x x e If only 3 terms are used, ! 2 1 2 x x e Error Truncation x
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19 Another Example of Truncation Error Using a finite x to approximate ) ( x f x x f x x f x f ) ( ) ( ) ( P Q secant line tangent line Figure 1. Approximate derivative using finite Δx
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20 Another Example of Truncation Error Using finite rectangles to approximate an integral.
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