# Chemical engineering equivalancy to the spring-mass-damper/RLC circuit

I understand the equivalency between the MSD and RLC circuits. Mass ~ resistance, spring ~ inductor, damper ~ capacitor.

With the equations of the form MSD:

$$m\ddot{x} + c\dot{x}+ kx = F$$

RLC:

$$L\ddot{i} + R\dot{i} + \frac{1}{C}i = V$$

I was thinking a bit about what the chemical engineering equivalent would be for a "plant circuit". For a capacitor, I thought it could be equated to a tank with a inlet at the top and the outlet at the opposite end (also at the top). It would fill without outputting anything until it is full. However, if the inlet stops, the outflow stops and thus doesnt work as a capacitor.

For resistance/mass, i thought the tank size might be the best representation.

I have no idea for an inductor/damper.

After some more thinking, it became clear that a single tank cannot possible approximate such a system, and it has to be a dual tank system. However, this complicates the ODE to such a point where a equivalency is not intuitive at all!

Would be awesome if someone could shed some light on this for me. I might be missing something somewhere.