(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A stirred tank reactor that initially contains a volume V(0) = V_0 of water. Suppose that a stirred solution of salt at concentration S is pumped in at a rate of F_in = F litres/hr and the well-stirred mixture is pumped out at a slight faster rate of F_out = (F + f) litres/hr where f > 0. Let C(t) denote the concentration of salt inside the tank. Find C(t).

2. Relevant equations

3. The attempt at a solution

V(t) = V_0 + F_in*t - F_out*t = V_0 + F*t - F*t + f*t = V_0 + f*t

(C*V)' = C'*V + C*V' = C'(V_0 - f*t) - Cf = SF - C(F + f)

C'(V_0 - f*t) = S*F - C*F

C' + C*F/(V_0 - f*t) = S*F/(V_0 - f*t)

Do I use integration factor to solve for C? I tried it and it was really complicated but the final answer is unusually simple. So I don't think it is right.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Mixing Question - Linear ODE

**Physics Forums | Science Articles, Homework Help, Discussion**