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Unformatted text preview: Announcements • Prelim 1 • Quiz 4: Wednesday April 7: esponse equations for CSTR and PFR (no – Response equations for CSTR and PFR (no dispersion) to pulse and continuous inputs of conservative materials. SIMPLIFIED MODELS FOR RIVERS, STREAMS, & AFR'S Recall continuity equation (point form): i i J r∇ • + h i i C u C E h + ∇ i J h C t ∂ = ∂ also Ex. Consider our earlier model for BOD L in a stream. The simplifying assumptions were: 1. 2. Plug flow (no mixing). ∴ E = 0 Complete lateral mixing (width and depth averaging). 1D problem. The continuity equation in this case reduces to: the 1D part no dispersion for first order kinetics ( 29 29 29 ( 29 29 29 x x i C J i r t X ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ =  + =  + =  + =  + ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ a a ( 29 29 29 x i u C r X ∂ =  + =  + =  + =  + ∂ C C u kC t X ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ =  =  =  =  ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ so & this is exactly the same as the equation we had for BOD in the plug flow model. dL = u dLk r L dt dx We solved this at steadystate ( dL = ) dt 0 with boundary conditions of L = L O @ X = 0. The point here is that the continuity equation gives the same result, given the same simplifying assumptions. previously used so O L x r L dL k dX L u =  =  =  =  ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ r O L X ln k L u =  =  =  =  r X k u O L L e = and We used the same assumptions for D.O. in the stream, however, r i also included a reaeration term: 1 2 dC dC u k L k (C* C) dt dX =  + =  + =  + =  + Predicted results (for BOD L ) @ steadystate with continuous discharge were: r r w w o r w Q L Q L L Q Q + = + + + L O ) u / X ( r k o x e L L = mass of the pulse input Let W' = the mass rate of pollutant discharge....
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This note was uploaded on 04/13/2010 for the course CEE 3510 taught by Professor Lion during the Spring '10 term at Cornell University (Engineering School).
 Spring '10
 Lion

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