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04-05 - Expected results C For a conservative material C =...

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Upstream , J = u/E and C = C O e JX , AND X is negative, so C decreases exponentially. Upstream, J is positive but X is negative so Expected results X=0 C For a conservative material C = C O downstream i.e , J= (1-1) = 0 2 u E For a non conservative material, k 0, and J will be negative downstream , so C decreases exponentially. Upstream , J is positive but X is negative so C still decreases exponentially. Note that the magnitude of C O is smaller (for the same Q W and C W )when k 0.
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Example (an old CEE 351 Exam problem) A sewage outfall is to be located downstream from a bathing area. If the waste and river characteristics are as specified below, how far downstream must the outfall be if 200 MPN/100 mL (coliform conc.) is allowable at the beach?
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Given: Q river = 10 10 L/dy u = 40,000 m/dy (constant) E = 10 7 m 2 /dy Q waste = 10 7 L/day C waste = 10 8 MPN coliforms 100 mL coliform die off may be modeled with first order kinetics i.e., dC = - kC dt and k = 0.1/day u = 40,000 m/dy beach Q = 10 10 L/dy continuous input Desire C = 200 MPN/100mL at this point.
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