Abstract

Citation

Researchers should cite this work as follows:

• deOlivera, P. (2023). 2000-deOlivera-Delfino-Costa-Leite-Pinhole Water Flow From Cylindrical Bottles. SIMIODE, QUBES Educational Resources. doi:10.25334/M3YB-JJ63

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Article Context

Description

deOlivera, Paulo Murilo Castro, Antonio Delfino, Eden Vieira Costa and Carlos Alberto Faria Leite.  2000. Pinhole Water Flow From Cylindrical Bottles. Phys.Educ. 35(2): 110-119.

See http://seniorphysics.com/physics/pinhole_water_flow.pdf . Accessed 27 March 2023.

From the opening of the article,  "We performed an experiment on elementary hydrodynamics. The basic system is a cylindrical bottle from which water flows through a pin-hole located at the bottom of its lateral surface. We measured the speed of the water leaving the pin-hole, as a function of both the time and the current level of water still inside the bottle. The experimental results are compared with the theory. The theoretical treatment is a very simple one based on mass and energy conservation, corresponding to a widespread exercise usually adopted in university basic disciplines of physics.

"We extended the previous experiment to another similar system using two identical bottles with equivalent pin-holes. The water flowing from the first bottle feeds the second one located below it. The same concepts of mass and energy conservation now lead to a non-trivial differential equation for the lowest bottle dynamics. We solved this equation both numerically and analytically, comparing the results with the experimental data.

Keywords: Torricelli’s Law, Conservation of Mass, Conservation of Energy, differential equation, model, data, parameter estimation, Bernoulli’s Theorem