Tema24 - 24.9 24.10 Time After Injection(sec Semilog Dye Concentration Constant Product 9 0.11 1 0.11 9.5 0.14 2 0.28 10 0.18 2 0.36 10.5 0.25 2

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Unformatted text preview: 24.9 24.10 Time After Injection (sec) Semilog Dye Concentration Constant Product 9 0.11 1 0.11 9.5 0.14 2 0.28 10 0.18 2 0.36 10.5 0.25 2 0.5 11 0.4 2 0.8 11.5 0.7 2 1.4 12 1.4 2 2.8 12.5 2.4 2 4.8 13 4 2 8 13.5 5.5 2 11 14 6.85 2 13.7 14.5 8 2 16 15 9 2 18 15.5 9.35 2 18.7 16 9.2 2 18.4 16.5 8.7 2 17.4 17 7.95 2 15.9 17.5 7 2 14 18 5.95 2 11.9 18.5 4.85 2 9.7 19 4.1 2 8.2 19.5 3.5 2 7 20 3 2 6 20.5 2.55 2 5.1 21 2.2 2 4.4 21.5 1.8 2 3.6 22 1.5 2 3 22.5 1.3 2 2.6 23 1.1 2 2.2 23.5 0.9 2 1.8 24 0.8 2 1.6 24.5 0.64 2 1.28 25 0.55 2 1.1 25.5 0.47 2 0.94 26 0.4 2 0.8 26.5 0.34 2 0.68 27 0.29 2 0.58 27.5 0.24 2 0.48 28 0.2 2 0.4 28.5 0.16 2 0.32 29 0.14 2 0.28 29.5 0.125 2 0.25 30 0.1 1 0.1 Sum of Products = 236.46 Trapezoidal Approximation = 59.115 Cardiac Output = [56 mg/59.115 mg*sec/L]*60 = 5.68 L/min 24.11 The following Excel Solver application can be used to estimate: k = 0.09915 and A =6.98301. 24.12 The following Excel spreadsheet is set up to use (left) a combination of the trapezoidal and Simpsons rules and (right) just the trapezoidal rule: 24.13 The extremes for both cases are at 16 and 92 24.43 y = -0.0005x 2- 0.3154x + 472.24 R 2 = 0.9957 y = 7E-05x 2- 0.3918x + 372.41 R 2 = 0.9921 y = -0.0004x 2- 0.0947x + 286.21 R 2 = 0.9645 y = -0.0003x 2- 0.0404x + 256.9 R 2 = 0.9463 y = -0.0003x 2- 0.0491x + 238.62 R 2 = 0.99 50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 300 350 400 450 mean stress stress amplitude 10^4 cycles 10^5 cycles 10^6 cycles 10^7 cycles 10^8 cycles Poly. (10^4 cycles) Poly. (10^5 cycles) Poly. (10^6 cycles) Poly. (10^7 cycles) Poly. (10^8 cycles) Finding roots in Matlab: a=[-0.0005 -0.3154 472.24]; roots(a) b=[7E-05 -0.3918 372.41]; roots(b) c=[-0.0004 -0.0947 286.21]; roots(c) d=[-0.0003 -0.0404 256.9]; roots(d) e=[ -0.0003 -0.0491 238.62]; roots(e) Roots: 706.3, 1213.7, 735.75, 860.5, 813.77 Using the AVERAGE command in Excel, the ultimate strength, u σ , was 866 MPa. Plot with σ μ included: y = -0.0005x 2- 0.3307x + 472.76 R 2 = 0.9992 10^4 cycles y = 7E-05x 2- 0.3894x + 372.32 R 2 = 0.9988 10^5 cycles y = -0.0004x 2- 0.0746x + 285.51 R 2 = 0.996 10^6 cycles y = -0.0003x 2- 0.0389x + 256.84 R 2 = 0.9969 10^7 cycles y = -0.0003x 2- 0.0474x + 238.56 R 2 = 0.9993 10^8 cycles-100 100 200 300 400 500 600 200 400 600 800 1000 1200 mean stress stress amplitude 10^4 cycles 10^5 cycles 10^6 cycles 10^7 cycles 10^8 cycles Poly. (10^4 cycles) Poly. (10^5 cycles) Poly. (10^6 cycles) Poly. (10^7 cycles) Poly. (10^8 cycles) It can be seen from the higher R 2 values that the polynomial fit including the ultimate stress, u σ , is more accurate than the fit without including u σ . 24.44 This problem was solved using Excel. 0.01 0.02 0.03 0.04 0.05 0.06 0.07 2 4 6 8 10 12 ti me , mi n The following values were calculated beginning with the ninth data point of the series....
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This note was uploaded on 03/13/2012 for the course AEROSPACE 301 taught by Professor Pfchang during the Spring '12 term at Shandong University.

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Tema24 - 24.9 24.10 Time After Injection(sec Semilog Dye Concentration Constant Product 9 0.11 1 0.11 9.5 0.14 2 0.28 10 0.18 2 0.36 10.5 0.25 2

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