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Equation Sheet

# Equation Sheet - Useful Equations CEE 3510 Spring 2010...

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Carbonaceous Oxygen Demand C a H b O c N d + 1 2 2 a + 1 2 b ! 3 d ( ) ! c " # \$ % & O 2 ( aCO 2 + 1 2 b ! 3 d ( ) H 2 O + dNH 3 Nitrogenous Oxygen Demand dNH 3 + 2 dO 2 ( dNO 3 ! + dH 2 O + dH + Biological Oxygen Demand (BOD) BOD L ( ) = L 0 e ! k 1 t BOD Y ( ) = L 0 1 ! e ! k 1 t ( ) where L 0 = ultimate BOD concentration [mg/L] BOD L ( ) = BOD remaining at time = t [mg/L] BOD Y ( ) = O 2 consumed during time = t [mg/L] k 1 = 1st order BOD decay rate coefficient [1/day] t = time Substrate utilization kinetics ! dS dt X = kS K S + S where S = substrate concentration mass vol " # \$ % k = maximum rate of substrate utilizaton 1 time " # \$ % K s = half velocity constant mass vol " # \$ % t = time X = biomass concentration mass vol " # \$ % Useful Equations CEE 3510 Spring 2010

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PFR to model BOD degradation in river with no longitudinal mixing L = L 0 e ! k r x u k r = k 1 + k 3 where k r = BOD removal rate coefficient in the river k 1 = BOD degradation rate coefficient in the river k 3 = BOD sedimentation rate coefficient x = distance along the river in the direction of flow u = water velocity
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