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# 03-05 - II PLUG FLOW MODEL This particular model results in...

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II. PLUG FLOW MODEL This particular model results in the "Streeter-Phelps Equation" which describes the oxygen-sag curve in a river. Consider a simple geometrical analog of a river. Q L C X = 0 X lateral direction longitudinal direction Flow = X BOD = DO = Flow = Q BOD = DO = L O C O A = cross sectional area

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Simplifying Assumptions: 1. Plug Flow : each packet of fluid (such as that contained within X ) moves from one end of the river to the other without any longitudinal mixing with neighboring fluid packets. 2. Complete mixing in the lateral direction i.e., all fluid within the volume ( X) ( A) has uniform D.O and BOD concentrations. ( X)(A) = V 3. Q, L O , C O and A are constant. Stream velocity is also constant. Flow velocity= u = Q/A
With this flow regime (Q, A and u constant) the distance a fluid element has traveled is directly related to time distance traveled = X = ut so: t = x/u This will let us replace the variable time (t) with its distance equivalent: Ex. For first order BOD kinetics: L=L O e -k 1 t L=L 0 e -k(x/u) Remember : k 1 is different in the laboratory and in the river. Use k 1 for river and k 1 L for lab.

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Other Complications (already!) The organic matter in our river has several possible routes (or reactions) including: a. biological oxidation: dL = -k 1 (L) dt b. sedimentation - handle this by assuming sedimentation rate is directly proportional to organic concentration (Ex., organic particles) dL = -k 3 L dt c. resuspension - from previous deposition (we'll assume this is either negligible or taken care of in the rate constant k 3 )
• Remember expressing the waste concentration in

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03-05 - II PLUG FLOW MODEL This particular model results in...

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