Lecture 10

# Lecture 10 - Mass Balance Equations Lecture#10 finish up...

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1 Mass Balance Equations ± Lecture#10 ± finish up ICP#8 (residence time) ± review mass flow balance equation (CMFR) ± review steady state ± identifying steady vs. non steady state problems ± ICP#9 ± Reading: V: Ch. 5 (95-102); course pack Mi: pg. 43- 44 ; DFE1 Handout Overview ± How can you determine whether a system should be treated as a steady-state problem? ± What does the form of the solution look like for a non steady-state, conservative pollutant problem? ± How does one solve a non steady-state mass flow balance problem (ICP#9)? Residence time ( τ d ) ± residence time τ is the average time a “particle” of water or pollutant spends in the system ± gives estimate of how long it takes a system to respond to inputs or how quickly a system can flush out a conservative pollutant ± τ = (mass in system)/(all mass rates out) ± note in Text:V ( τ = t ) Residence Times for common water bodies Residence time ( τ d ) ± water residence time: τ W =V ρ /(Q ρ ) = V/Q ( d) ± pollutant residence time (non-reacting), τ p = VC/(QC) = V/Q (units d) τ p = τ W ± water residence time with evaporation: τ W = V ρ /((Q out + Q EVAP )( ρ )) = V/(Q out + Q EVAP )( d) ± pollutant residence time with water evaporation (pollutant non-volatile and non-reacting) τ p = VC/(Q out C) = V/Q out (units d) τ p > τ W ICP#8 (cont.) Q R C R shallow lake V L = 1.0x10 7 m 3 A L = 1.0 x 10 7 m 2 Q Evap C Evap Q Ef C Ef Q R = 5m 3 /s C R = 01.mg/L Q S C S Q S = 0.5 m 3 /s C S = 0.2 mg/L Q Ef = ? C Ef = ?

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2 ICP#8 (cont.) ± a) Does the effluent from the lake exceed the drinking water standard for arsenic of 0.01 mg/L? ± MFB on water (no evap): Q Ef = Q R + Q S = 5m 3 /s + 0.5 m 3 /s = 5.5 m 3 /s ± MFB on arsenic (no evap): Q Ef C Ef = Q R C R + Q S C S = 5.0x0.1 + 0.5x0.2 = 0.6 mg/L 11 . 0 s)
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## This note was uploaded on 04/17/2008 for the course CEE 260 taught by Professor Kimf.hayes during the Fall '06 term at University of Michigan.

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Lecture 10 - Mass Balance Equations Lecture#10 finish up...

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