14b_InteractingTanksBlockDiagramsW12

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Unformatted text preview: Page - 1 - of 5 Interacting Tanks – Block Diagrams CHE 361 Chapter 6, page 103 = Classical interacting states example = two tanks where flow between tanks depends on both heights. A non-classical example is the CHE 361 Bioreactor project, which also has two states. Review = Cha. 4 pgs 6 1-65 starting with Transfer Functions of Complicated Models. Fig. 4.1 = “additive”, Fig. 4.2 = “multiplicative” relationships for transfer functions Figs 4.3/4.4 for two liquid surge tanks in series. Here we look at a quantitative example of the interacting tank problem. Let the area of tank 1 (A1) be 10 m2 and the area for tank 2 (A2) be 4 m2 and assume constant density for the liquid. Also let R1 = R2 = 1 m2/min. Then q1 = q2 = ( h1 − h2 ) R1 = flow from tank 1 to tank 2 h2 = flow through R2 valve R2 dh1 = qi − h1 + h2 from a mass balance on Tank 1 dt dh 4 2= h1 − 2h2 from a mass balance on Tank 2 dt 10 1 ′ 1 ′ = Qi ( s ) + From the first ode we get : H1′( s ) H 2 (s) 10 s + 1 10 s + 1 0.5 ′ ′ From the second ode we get: H 2 ( s ) = H1 ( s ) 2s + 1 Page - 2 - of 5 These transfer function relationships can be represented in transfer function block diagrams as: Page - 3 - of 5 Page - 4 - of 5 Page - 5 - of 5 InterTanks.mdl Either block diagram yields the same plot. Step Input 4s+2 2+24s+1 40s h_Tank1 M ux PC_graph 1 40s2+24s+1 h_Tank2 M ux Interacting Tanks = Tank 1 = Solid, Tank 2 = Dashed 2 Tank Heights, h' 1.5 1 0.5 0 0 20 40 60 Time , [min] 80 100 InterTanksFB.mdl Sum 1 Step Input 10s+1 G1 0.5 M ux 2s+1 PC_graph G2 M ux ...
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This note was uploaded on 03/01/2012 for the course CHE 361 taught by Professor Staff during the Winter '08 term at Oregon State.

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