Download presentation

Presentation is loading. Please wait.

Published byJustine Durham Modified over 3 years ago

1
CE 498/698 and ERS 685 (Spring 2004) Lecture 61 Lecture 6: Feedback Systems of Reactors CE 498/698 and ERS 685 Principles of Water Quality Modeling

2
CE 498/698 and ERS 685 (Spring 2004) Lecture 62 Feedback W1W1 W2W2 Q 01 c 0 Q 12 c 1 Q 23 c 2 Q 21 c 2 k1V1c1k1V1c1 k2V2c2k2V2c2

3
CE 498/698 and ERS 685 (Spring 2004) Lecture 63 Lake 1: W1W1 W2W2 Q 01 c 0 Q 12 c 1 Q 23 c 2 Q 21 c 2 k1V1c1k1V1c1 k2V2c2k2V2c2 1 2 Lake 2:

4
CE 498/698 and ERS 685 (Spring 2004) Lecture 64 Lake 1: Lake 2: Steady-state: and

5
CE 498/698 and ERS 685 (Spring 2004) Lecture 65 system parametersloadingsunknowns LINEAR ALGEBRAIC EQUATIONS Matrix algebra

6
CE 498/698 and ERS 685 (Spring 2004) Lecture 66

7
CE 498/698 and ERS 685 (Spring 2004) Lecture 67 Gauss-Jordan method To compute the matrix inverse Identity matrix 3 3 identity matrix: augmented matrix:

8
CE 498/698 and ERS 685 (Spring 2004) Lecture 68 Gauss-Jordan method To compute the matrix inverse 1) Normalize 2) Elimination

9
CE 498/698 and ERS 685 (Spring 2004) Lecture 69 Gauss-Jordan method 1) Normalize Divide by a 11

10
CE 498/698 and ERS 685 (Spring 2004) Lecture 610 Gauss-Jordan method 2) Elimination

11
CE 498/698 and ERS 685 (Spring 2004) Lecture 611 Gauss-Jordan method 2) Elimination

12
CE 498/698 and ERS 685 (Spring 2004) Lecture 612 Gauss-Jordan method 1) Normalization

13
CE 498/698 and ERS 685 (Spring 2004) Lecture 613 Gauss-Jordan method Matrix inverse

14
CE 498/698 and ERS 685 (Spring 2004) Lecture 614 Gauss-Jordan method example augmented matrix

15
CE 498/698 and ERS 685 (Spring 2004) Lecture 615 Gauss-Jordan method example Divide by 3 (normalize)

16
CE 498/698 and ERS 685 (Spring 2004) Lecture 616 Gauss-Jordan method example Divide by 7.003 (normalize)

17
CE 498/698 and ERS 685 (Spring 2004) Lecture 617 Gauss-Jordan method example

18
CE 498/698 and ERS 685 (Spring 2004) Lecture 618 Gauss-Jordan method example

19
CE 498/698 and ERS 685 (Spring 2004) Lecture 619 Gauss-Jordan method Can also be used to solve for concentrations

20
CE 498/698 and ERS 685 (Spring 2004) Lecture 620 Excel - MINVERSE 1.Enter your [A] matrix 2.Block an area the same size 3.Type =MINVERSE(block location of [A]matrix) and press CNTL+SHIFT+ENTER

21
CE 498/698 and ERS 685 (Spring 2004) Lecture 621 We want to solve for {C} Multiply both sides by [A] -1 Definitions of identity matrix

22
CE 498/698 and ERS 685 (Spring 2004) Lecture 622 Homework Problem 6.2(a) Use both Gauss-Jordan method and Excel MINVERSE function

23
CE 498/698 and ERS 685 (Spring 2004) Lecture 623 {C} = response {W} = forcing functions [A] -1 = parameters {response} =[interactions]{forcing functions} Response of reactor 1 Unit change in loading of reactor 2

24
CE 498/698 and ERS 685 (Spring 2004) Lecture 624 Matrix Multiplication (Box 6.1) # columns in matrix 1 = # rows in matrix 2

25
CE 498/698 and ERS 685 (Spring 2004) Lecture 625 Terminology DIAGONAL Effect of direct loading SUPERDIAGONAL Effects of d/s loadings on u/s reactors SUBDIAGONAL Effects of u/s loadings on d/s reactors

26
CE 498/698 and ERS 685 (Spring 2004) Lecture 626 Time-variable response for two reactors where

27
CE 498/698 and ERS 685 (Spring 2004) Lecture 627 Time-variable response for two reactors General solution if c 1 =c 10 at t = 0 where s are functions of s cs are coefficients that depend on eigenvalues and initial concentrations f = fast eigenvalue s = slow eigenvalue f >> s see formulas on page 111

Similar presentations

Presentation is loading. Please wait....

OK

Copyright © Cengage Learning. All rights reserved.

Copyright © Cengage Learning. All rights reserved.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on linux shell scripting Ppt on magnetic field lines class 10 Ppt on water conservation in hindi Ppt on power system harmonics thesis Ppt on reliance life insurance Download ppt on civil disobedience movement in war Ppt on online shopping cart Ppt on tcp ip protocol suite 3rd Ppt on social networking security Ppt on satellite orbit