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Mass Balance Notes

# Mass Balance Notes - MassBalances Chapter4(pp.134158...

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Mass Balances Chapter 4 (pp. 134-158)   Accumulation = In – Out But, TIME is important, therefore  Rate of Accumulation = Rate of Inputs – Rate of Outputs

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Where (in) and (out) refer to masses coming into and out of a control volume by flow, reaction, or other forms. If we are talking about concentrations of masses in volume V, then a common form is: where: C represents concentration (mg/L, for example) Σ Q in C in is the sum of all the masses (mass/time) coming into V Σ Q out C out is the sum of all the masses (mass/time) going out of V dt d(out) - dt d(in) dt dM = Equation 4-4 in the text (p. 137) ± = reactions C Q - C Q dt d(CV) out out in in
Important Assumptions 1. The control volume is well mixed 2. All flows and reactions are included 3. Usually,  Σ Q in  Σ Q out 4. Often can assume no reactions or first order reactions 5. Often can assume steady state, accumulation = 0 Example Control Volume

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General form of any mass balance: Rate of Accumulation = Rate of Inputs – Rate of Outputs mass/time of units have must reactions that shows analysis Unit min) L/ ie., me, (volume/ti flow a is Q L) (ie., volume control the is V me) (mass/volu volume control in the ion concentrat the is C mg/L) me, (mass/volu inflow any in ion concentrat the is C - dt dCV in reactions QC QC in ± = IMPORTANT:   C is the concentration in the control  volume AND the concentration in the outflow (a result of  assuming the control volume is  well mixed )
Strategy to Solving MB problems 1. Draw diagram  control volume  flows and reactions (use arrows) values where known units 2. Write a general form of the mass balance (see above) 3. Define all the terms in the equation and simplify using the  assumptions  (list your assumptions) 4. Solve reactions QC QC in ± = - dt dCV

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Questions to Ask about Mass Balances 1. Is there flow (i.e., is Q in  and/or Q out  = 0)? 1.
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Mass Balance Notes - MassBalances Chapter4(pp.134158...

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