# Tema12 - 12.9 + + F x F y = 0 : P cos 21.5 M cos 37 M cos...

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12.9 ) 2 ( 0 383 . 0 3665 . 0 0 80 sin 37 sin 5 . 21 sin : 0 ) 1 ( 0 9723 . 0 93042 . 0 0 80 cos 37 cos 5 . 21 cos : 0 = - = - + = + = - = - - = + M P M M P F M P M M P F y x Use any method to solve equations (1) and (2): = - + - = 0 0 ) 80 sin 37 (sin 5 . 21 sin ) 80 cos 37 (cos 5 . 21 cos B A Apply Ax = B where x = M P Use Matlab or calculator for results P = 314 lb M = 300 lb

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12.10 Mass balances can be written for each reactor as 1 , 1 1 1 , in in , in 0 A A A c V k c Q c Q - - = 1 , 1 1 1 , in 0 A B c V k c Q + = 2 , 2 2 2 , 32 in 3 , 32 1 , in ) ( 0 A A A A c V k c Q Q c Q c Q - + - + = 2 , 2 2 2 , 32 in 3 , 32 1 , in ) ( 0 A B B B c V k c Q Q c Q c Q + + - + = 3 , 3 3 3 , 43 in 4 , 43 2 , 32 in ) ( ) ( 0 A A A A c V k c Q Q c Q c Q Q - + - + + = 3 , 3 3 3 , 43 in 4 , 43 2 , 32 in ) ( ) ( 0 A B B B c V k c Q Q c Q c Q Q + + - + + = 4 , 4 4 4 , 43 in 3 , 43 in ) ( ) ( 0 A A A c V k c Q Q c Q Q - + - + = 4 , 4 4 4 , 43 in 3 , 43 in ) ( ) ( 0 A B B c V k c Q Q c Q Q + + - + = Collecting terms, the system can be expresses in matrix form as [ A ]{ C } = { B } where [ A ] = - - - - - - - - - - - - - - 13 5 . 2 13 0 0 0 0 0 0 5 . 15 0 13 0 0 0 0 3 0 18 50 15 0 0 0 0 3 0 68 0 15 0 0 0 0 5 0 15 5 . 7 10 0 0 0 0 5 0 5 . 22 0 10 0 0 0 0 0 0 10 25 . 1 0 0 0 0 0 0 0 25 . 11 [ B ] T = [10 0 0 0 0 0 0 0 0 0] [ C ] T = [ c A ,1 c B ,1 c A ,2 c B ,2 c A ,3 c B ,3 c A ,4 c B ,4 ] The system can be solved for [ C ] T = [0.889 0.111 0.416 0.584 0.095 0.905 0.080 0.920]. A B 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 12.11 Assuming a unit flow for Q 1 , the simultaneous equations can be written in matrix form as
= - - - - - - - 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 3 1 0 0 0 0 0 1 2 1 0 0 0 0 0 1 2 1 7 6 5 4 3 2 Q Q Q Q Q Q These equations can be solved to give [ Q ] T = [0.7321 0.2679 0.1964 0.0714 0.0536 0.0178].

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12.20 Find the unit vectors: k j i k j i B k j i k j i A ˆ 873 . 0 ˆ 218 . 0 ˆ 436 . 0 4 2 1 ˆ 4 ˆ 1 ˆ 2 ˆ 873 . 0 ˆ 436 . 0 ˆ 218 . 0 4 2 1 ˆ 4 ˆ 2 ˆ 1 2 2 2 2 2 2 - + = + + - + - - = + + - - Sum moments about the origin: 0 ) 4 ( 218 . 0 ) 4 ( 436 . 0 0 ) 4 ( 218 . 0 ) 4 ( 436 . 0 ) 2 ( 50 = - = = - - = B A M A B M oy ox In the form 2 2 22 2 21 1 2 12 1 11 b x a x a b x a x a = + = +

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0 872 . 0 744 . 1 100 744 . 1 872 . 0 = - + - = - + - B A B A Plug into equations 9.10 and 9.11: N a a a a b a b a x N a a a a b a b a x 87 . 45 80192 . 3 4 . 174 94 . 22 80192 . 3 2 . 87 21 12 22 11 1 21 2 11 2 21 12 22 11 2 12 1 22 1 = = - - = = = - - = 12.21 k j i k j i T ˆ 549 . 0 ˆ
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## Tema12 - 12.9 + + F x F y = 0 : P cos 21.5 M cos 37 M cos...

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