A note on the bathtub analogy

Adapted from “A note on the bathtub analogy,” Pål Davidsen, Erling Moxnes, Mauricio Munera Sánchez, David Wheat, 2011 System Dynamics Conference.


The bathtub analogy has been used extensively to illustrate stock and flow relationships. Because this analogy is frequently used, System Dynamicists should be aware that the natural outflow of water from a bathtub is a nonlinear function of water volume. A questionnaire suggests that students with one year or more of System Dynamics training tend to assume a linear relationship when asked to model a water outflow driven by gravity. We present Torricelli’s law for the outflow and investigate the error caused by assuming linearity. We also construct an “inverted funnel” which does behave like a linear system. We conclude by pointing out that the nonlinearity is of no importance for the usefulness of bathtubs or funnels as analogies. On the other hand, simplified analogies could make modellers overconfident in linear formulations and not able to address critical remarks from physicists or other specialists.

See my related blog post for details.

Units balance.

Runs in Vensim (any version): ToricelliBathtub.mdl ToricelliBathtub.vpm

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