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Thread: Computing an Integral

  1. #1
    Super Member sakonpure6's Avatar
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    Computing an Integral

    Hey folks!

    Long time since I posted here!

    I would just like to run by you a differential equation that models the mass flow in a Completely mixed reactor under step input that I have solved, but my lecture notes present a different solution.

    V \frac{dc_e}{dt} = Qc_i-Qc_e-kVc_e

    V, c_i , Q and k are constants.

     V \cdot \int_c_i^{c_e}\frac{1}{Qc_i-c_e(Q+kV)} dc_e = \int_0^t dt

    I came up with the final answer of :

    c_e = \frac{QC+ kVc_ie^{-\frac{Q+kV}{V} \cdot t}}{Q+kV}

    My lecture notes present a final solution of:

    c_e = \frac{Qc_i - Qc_i e^{- \frac{kV+Q}{V} \cdot t} }{Q+kV}

    If some one could shed some light on this, I would really appreciate it!

    Thank you.
    Last edited by sakonpure6; Jul 13th 2017 at 04:59 PM.
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  2. #2
    Super Member sakonpure6's Avatar
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    Re: Computing an Integral

    Nevermind, please disregard, I was missing a critical piece of information that at t=0 C_e = 0. I was under the impression that at t=0 C_e = C_i
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