Question

1) A bush is cooled to pass it to the core. The diameter change (decrease) during the cooling of the bush is expressed in the following corelation. AD = DAAT D= original diameter (inch) a=thermal expansion coefficient at average temperature The bush cools from (80F) to (-108 F), with an average temperature (-14 °F). Thermal expansion coefficient-temperature relationship is given in the table below. table-Thermal expansion coefficient as a function of temperature Temperature T(F) 80 Thermal expansion coefficient ain/in/°F) 6.47x10 6.00x10* 5.58x10* 4.72x10* 3.58x10* 2.45-10 0 -60 - 160 -260 -340 I If the thermal expansion coefficient should be calculated at -14°F, which is the average temperature, calculate the coefficient of thermal expansion at T = -14 F with using the 2nd Degree Lagrange Polynomial. Find the approximate absolute relative error for 2nd degree polynomial interpolation.

Answer 1

December 2019 Week 49 8.00 am 07 SATURDAY (31.024) for second order Langrage polynomial 8.00 am interpolation the coefficient of thermal expansion 90 an 2002 - Eli (D) 20) 10.00 am - Lo (T) & (To) + L,G) *(T) + L (D) & (T2) - 0 9.00 am 10.00 am 1.00 pm 2.00 pm 11.00 am ince we want to find the ot at T--14°F - We need to choose data points that are closest to 12.00 noon T = -14°F . The To Three points are 1.00 pm To = 801 T, -0 Tortola at To=B0F (To) = 6.478106 To 2(1) - 6x106 300pm Tz 2-60 , 2(72) = 5.58810 gives LOCT) - T TITT-12 n jo To- To - To-T2 5.00pm LOL? 6.00pm 3.00 pm 4.00 pm JO 5.00 pm 6.00 pm EVENING 08 SUNDAY

2019 Week 50 December Put all values in eq"O al T2 -14 °F 4 MONDAY 09 d 14) = 0) (-lutbo) 6.47x10.9 +614-00) (-14760) Glogo am 40_9) (80560) *** Bobo 9.00 am +(-14-80) (014 (88) (0+60) 2 5.56x10f XO (-60-80) (-60-0) 10.00 am X +14) = 5.9072x10 b inlinlogo inlinor Any 11.00 am 12.00 noon The absolute relative approximate Error obtained between the results from the first and second order polynomial leal -15.9072x10 5.902x101x100 5.9072x106 ) (10) 1.00 pm 200 pm 3.00 pm 6.00 pm -0.08767 Am #According to rule ican solve only one question, but 4.00 pm for your comfort, Follow below steps for and aussion. samt similanily you can Bolue for 30 degree. 500 4 -D K(T) = Z Li (T) & (Ti) - Choose 4 temp. Cosest to 12-14°F and calculate LOG), L, (T) LG L T s. 26-14) = 5.9077x10 bin linler y TEL = 0.0063 867 f. a AUC S EP OCT NOV EVENING MEMORANDA DEC SEP