mws_che_sle_txt_seidel_examples

mws_che_sle_txt_seidel_examples - Chapter 04.08...

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04.08.1 Chapter 04.08 Gauss-Seidel Method – More Examples Chemical Engineering Example 1 A liquid-liquid extraction process conducted in the Electrochemical Materials Laboratory involved the extraction of nickel from the aqueous phase into an organic phase. A typical set of experimental data from the laboratory is given below. Ni aqueous phase, ( ) l g a 2 2.5 3 Ni organic phase, ( ) l g g 8.57 10 12 Assuming g is the amount of Ni in the organic phase and a is the amount of Ni in the aqueous phase, the quadratic interpolant that estimates g is given by 3 2 , 3 2 2 1 + + = a x a x a x g The solution for the unknowns 1 x , 2 x , and 3 x is given by = 12 10 57 . 8 1 3 9 1 5 . 2 25 . 6 1 2 4 3 2 1 x x x Find the values of 1 x , 2 x , and 3 x using the Gauss-Seidel method. Estimate the amount of nickel in the organic phase when 2.3 g/l is in the aqueous phase using quadratic interpolation. Use = 1 1 1 3 2 1 x x x as the initial guess and conduct two iterations. Solution Rewriting the equations gives 4 2 57 . 8 3 2 1 x x x = 5 . 2 25 . 6 10 3 1 2 x x x = 1 3 9 12 2 1 3 x x x =
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04.08.2 Chapter 04.08 Iteration #1 Given the initial guess of the solution vector as = 1 1 1 3 2 1 x x x we get 4 1 1 2 57 . 8 1 × = x 3925 . 1 = 5 . 2 1 3925 . 1 25 . 6 10 2 × = x 11875 . 0 = 1 11875 . 0 3 3925 . 1 9 12 3 × × = x 88875 . 0 = The absolute relative approximate error for each i x then is 100 3925 . 1 1 3925 . 1 1 × = a % 187 . 28 = 100 11875 . 0 1
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This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida - Tampa.

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mws_che_sle_txt_seidel_examples - Chapter 04.08...

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