Modelling tank drainage using a simple apparatus

Research output: Contribution to journalComment/debatepeer-review


A straightforward experimental set-up, requiring a two-liter bottle, a ruler and a stopwatch, is used to provide data appropriate for modelling with Torricelli's Law in the simplest case, and a more sophisticated differential equation when losses are taken into account and a pipe extension is considered. With only an exit hole included in the model, the governing equation can be integrated analytically to find the liquid height in the tank as a function of time. In the more complicated instance, the governing equation requires numerical integration. In both cases, a discharge coefficient can be employed as a fitting parameter. Excellent agreement between the experimental data and the theoretical modelling results has been obtained. An analytical solution with comparable accuracy to the numerical version is also possible for a pipe extension under the operating conditions considered here. Student reception of the experiment was generally positive, although some nuances were not fully grasped.

Original languageEnglish (US)
Pages (from-to)295-307
Number of pages13
JournalInternational Journal of Mathematical Education in Science and Technology
Issue number2
StatePublished - 2024
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2023 Informa UK Limited, trading as Taylor & Francis Group.


  • Tank draining
  • discharge coefficient
  • experiment
  • frictional losses


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