Hwk_Soln_1

Hwk_Soln_1 - • 332 305 Numerical Modeling in Biomedical...

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Unformatted text preview: • 332: 305 Numerical Modeling in Biomedical Systems Fall 2010 Dr. Shoane Homework Solutions #1 1) Prob. 1.2.1 ( 29 ( 29 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 2 2 1 2 2 1 2 2 2 1 2 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 a) Tank 1: , Tank 2: , b) c) dH H A F F F dt R dH H A F F F dt R dH H A F dt R dH H H dH H H A A dt R R dt R R d H R F A R F F F dt dF A R F F dt d H R F A R F dt + = = + = = + = + = ⇒ + - = = ⇒ + = + = = ⇒ + 2 2 2 2 2 1 1 1 2 d) ( ) , As , F F dF A R F F dt F t F t dH dH t dt dt = + = = ≥ → ∞ = = 1 1 ( ) F t 2 A 1 ( ) H t 2 ( ) H t 2 ( ) F t ( ) F t 1 A 2) Prob. 1.4.3 ( 29 ( 29 1/ 2 1 1/ 2 1 1/ 2 1 a) , 1 Aproximating the first derivative using the first order difference quotient, ( ) ( ) 1 Replacing ( ) with ( ), short for ( ) and ( ) A A dH A F F F H dt dH F H dt A H t t H t F H t A H t H n H n t H t t α α α + = = =- + ∆- ≈- ∆ ∆ + ∆ 1/2 1 3 2 3 1/2 1 1/ 2 with ( 1), short for ([ 1] ), leads to the difference equation ( 1) ( ) ( ) ( ) ( ) 5 ft / min, 10 ft , 2 ft / min per ft ( 1) ( ) 5 2 ( ) 10 b) (0) (0 A A A A A A A A A H n H n t t H n H n F n H n A F t A t H n H n H n H H α α + + ∆ ∆ +- =- = = = ∆ ⇒ + = +- + 1/ 2 1/ 2 1/2 1/2 1/ 2 ) 4 ft, 0.25 min 0 : (1) (0) 5 2 (0) 10 0.25 4 5 2(4) 10 4.025 ft 1: (2) (1) 0.025 5 2 (1) 4 0.025 5 2(4.025) 4.0497 ft 2 : (3) (2) 0.025 5 2 (2) A A A A A A A A A t t n H H H n H H H n H H H = ∆ = ∆ = = +- = +...
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Hwk_Soln_1 - • 332 305 Numerical Modeling in Biomedical...

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