The for C-14 excess relaxation can be modeled using water buckets and valves which gives similar solutions. The buckets are set at different heights and the valves can be used to adjust the flow rates. The flow rste is proportional to the opening of the valve and the relative pressure at the height of the valve which is dependent on the amount of water in the bucket. The air gap between buckets ensures that the flow is oneway.
The equations for the water bucket model are the same as those for the approximation used and the system mimics the excess C-14 relaxation with the flow approching an equilibrium state.
The analogy can also be used to show how seasonal changes in the removal rate can alter the observed amount of water in the intermediate state.