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mws_mec_dif_discrete_examples

# mws_mec_dif_discrete_examples - Chapter 02.03...

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Chapter 02.03 Differentiation of Discrete Functions-More Examples Mechanical Engineering Example 1 To find the contraction of a steel cylinder immersed in a bath of liquid nitrogen, one needs to know the thermal expansion coefficient data as a function of temperature. This data is given for steel in Table 1. Table 1 Coefficient of thermal expansion as a function of temperature. Temperature, T ( ) F Coefficient of thermal expansion, (in/in/ ) F 80 6 10 47 . 6 40 6 10 24 . 6 40 6 10 72 . 5 120 6 10 09 . 5 200 6 10 30 . 4 280 6 10 33 . 3 340 6 10 45 . 2 (a) Is the rate of change of the coefficient of thermal expansion with respect to temperature more at F 80 T than at F 340 T ? (b) The data given in Table 1 can be regressed to 2 2 to get 2 11 . Compare the results with part (a) if you used the regression curve to find the rate of change of the coefficient of thermal expansion with respect to temperature at F 80 1 0 T a T a a 10 T 9 6 1.2215 10 6.2790 10 6.0216 T T and at F 340 . T Solution (a) Using the forward divided difference approximation method at F 80 T , T T T dT T d i i i 1 ) ( 80 i T 40 T T T T i i 1 40 40 80 02.03.1

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