Assignment_3_2007_Solutions

Thecomponentbalanceonthenonreact

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Unformatted text preview: e component balance on the nonreact ing species in the first tank looks like: d ( rVc1 ) = rqc - rqc 0 1 d t The densit y, vo lume and the vo lumetric flowrate are constants, thus, the equat ion reduces to: V dc 1 = q 0 - c ) (c 1 d t This is a linear equation, so one can re­write it in deviat ion variable form trivially, V dc 1 = q 0 - c ) (c 1 d t We are interested in the transfer funct ion that relates the exit concentration to the inlet concentration. Taking the Laplace transform yields, V sc ( = c ( - c ( 1 s) 0 s) 1 s) q c1 ( s ) 1 = c ( s (V / q + 1 )s 0) Recognizing that all tanks are the same, we can generalize to the fo llowing relat ionships: c ( s 1 i) = c -1 ( s (V / q + 1 )s i ) c ( s 5 c ( s æ ) ö 1 5) =Õ i =ç ç (V / q + 1 ÷ ÷ c ( s i =1 c -1 ( s è )s ø 0) i ) 5 If the input is changed by 0.15, then, the so lut ion in t ime do main can be written using partial fract ion expansio ns, leading to the standard result (with V / q = 10 ), 2 3 4 é æ t 1 æ t ö 1 æ...
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  • Fall '08
  • Hjortso,M
  • funct ion, FPTD Linear, transfer  funct ion, Alternat ive Linear, ive Linear  model, inco ming  stream.

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