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    I got a couple questions.

    (1) I need to derive reactor volume as a function of time and volumetric flow rate, from the mass conservation equation. I did the following:

    Q_0 - Q = \frac {dV}{dt}. They said it happened in a semi batch reactor so I went further by doing:

     V = V_0 + \int Q_0 dt

    I think thats right. Is it?

    (2) I need to show that the cell weight in the reactor, can be derived from the cell mass balance equation as a function of mass inflow, volumetric flow rate, μm, and time. They've given the end result which is:

    N_C = \frac {F_0}{\mu_{max}} [e^{\mu_{max}t} - 1]

    I've worked out from my notes that: NC = XV, NC initially is 0, and F0 = X0Q. The hint they gave is to solve the ODE. The thing is I don't know how to express NC as an ODE to evaluate. Any advice please?

    (3) Determine the reactor volume after 1 hour given that: V0 = 0, Q = 2 L/hr, X0 = 0.001 g/Land X1 = 0.05 g/L.

    Also find μm assuming that μm = μg as the substrate is in excess.

    My guess is the answer is obtained from part (1) and (2), or maybe something new entirely? I'm just not sure what to do.

    I'm not asking you to do it for me, I've done what I've could, but now I need some help. If you know anything about this, please tell me.

    You realise this is in biology...

    Edit - actually it might be biology, but I think you'll probably get better answers from the maths forum.

    If you're going to redirect people from the maths forum, you're going to need to spell out the equations. I don't know what the mass-conservation equation is (and I'm not going to bother to look it up).

    Without knowing anything of the subject, it's unlikely your 2nd equation is correct (at least if Q_0 denotes a constant as you'd expect).
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