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EXERCISES SYSTEMS OF EQUATIONS FOR SEVERAL METHODS
BY :DUBAN CASTRO FLOREZ
NUMERICS METHODS IN ENGINEERING
2010

2. BALANCE OF MASS
1.In a distillation column it is carried out the process of separation alcohol-water in a food .Thealcohol has high purity and the food has in its composition 20%molar ethylic alcohol. If the feeding during the process is of 45 lbmol/h, being obtained a distilled that it contains 85% molar of ethylic alcohol and a residual that it contains 3% molar of ethylic alcohol it calculates:
-The quantity of having distilled and obtained residuals
-% of food alcohol recovered in the one distilled
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3. BALANCE OF MASS
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B
WATER =15%
ALCOHOL=85%
DISTILLATION COLUMN
A
FOOD 45 lbmol/h
WATER =15%
ALCOHOL=85%
WATER =15%
ALCOHOL=85%
C
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Making a general balance to the column the following
equations is obtained:
45=B+C 1 Equation
0.2A= 0.85B + 0.03C 2 Equation
0.8A= 0.15B + 0.97C 3 Equation
5. 2.To solve for the method de simple Gauss
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1/12f1+f2
12f2
-1/6f1 + f3
6f3
-7/71f2+f3
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3.To solve the following system of equations 2x2 for the graphic method.
The solution of the system of equations is
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4.To solve the following system of equations for the Thomas method.
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d
r
L
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x
U
d
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5.Aplicar la metodologa de Cholesky para descomponer la siguiente matriz simtrica
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Finally as product of the decomposition it was obtained that:
13. BIBLIOGRAPHY
-CHAPRA, Steven C. y CANALE, Raymond P.: Mtodos Numricos para Ingenieros. McGraw Hill 2002.
--http://es.wikipedia.org/wiki/M%C3%A9todo_de_Gauss-Seidel
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