Approximation of Torricelli's law with Euler's method and an instrumented water tank with ultrasonic sensor

Authors

DOI:

https://doi.org/10.15332/iteckne.v18i1.2540

Keywords:

Computing platforms, learning and material, Sensor applications and deployments

Abstract

In this work, the development of a computer system that has as processing core, an Arduino Nano based board, that collects and processes the signals of a low-cost ultrasonic sensor is presented. The computer system allows monitoring the evolution over time of the height of the water into a container once it begins to empty through a hole in the bottom of it, thus revisiting Torricelli's law with a technological approach using a instrumented container by a computerized electronic data capture and processing data system. The work presents the electrical connection diagrams to interconnect the microcontroller based board and the ultrasonic sensor, as well as the source code used during data acquisition and processing. A comparison of the experimental results is made with results obtained when using the particular analytical solution for the problem, also with the results obtained from implementing the Euler method in obtaining an approximate numerical solution. The presented computer system can be modified and adapted for various academic, educational and research purposes in the various fields of computer engineering, computer systems and mechatronics.

Downloads

Download data is not yet available.

Author Biography

Edgar Serrano Pérez, Universidad Tecnológica de México

Universidad Tecnológica de México - UNITEC MÉXICO - Campus Atizapán

References

Sears and Zemansky’s/ Hugh D. Young, Roger A. Freedman ; contributing author, A. Lewis Ford., University physics : with modern physics, 13th ed. Pearson, p.388, 2013.

Dennis G. Zill, A First Course in Differential Equations with Modeling Applications, 11th ed. Cengage Learning, p. 26, 2016.

Steven C. Chapra, Raymond P. Canale, Numerical Methods for Engineers, 5th ed. McGraw-Hill, Inc, p. 725, 2005.

Đ. HERCEG and D. HERCEG, “Arduino and Numerical Mathematics,” Inform. Educ., vol. 19, no. 2, pp. 239–256, 2020, doi: 10.15388/infedu.2020.12.

D. Guerra, A. Plaisted, and M. Smith, “A Bernoulli’s Law Lab in a Bottle,” Phys. Teach., vol. 43, no. 7, pp. 456–459, Sep. 2005, doi: 10.1119/1.2060646.

L. F. P. Gálvez, “Modelamiento Matemático para vaciado de Tanques,” Sci. Tech., vol. 22, no. 1, Art. no. 1, Mar. 2017, doi: 10.22517/23447214.9185.

H. G. R. Rotgé, A. I. O. Arias, and J. E. C. Hernández, “Flujo de agua en botellas como experimento,” Lat.-Am. J. Phys. Educ., vol. 5, no. 1, p. 24, 2011.

H. M. Aguilar, “Level sensor for hydrodynamics experiments,” Phys. Educ., vol. 43, no. 1, p. 46, Jan. 2008, doi: 10.1088/0031-9120/43/01/003.

K. Atkin, “Investigating the Torricelli law using a pressure sensor with the Arduino and MakerPlot,” Phys. Educ., vol. 53, no. 6, p. 065001, Aug. 2018, doi: 10.1088/1361-6552/aad680.

C. Román-Herrera, D. Loza-Matovelle, L. Segura, and R. Dabirian, “The construction of an open source based low cost turbidity sensor,” ITECKNE Vol 13 No 1 2016 17-22, Apr. 2016, doi: 10.15332/iteckne.v13i1.1431.

K. C. Ramos-Castañeda, J. J. Gil-Peláez, J. F. Panesso-Narváez, and R. Claros-Lamus, “Design of a measurement equipment of the unevenness in a railway line,” ITECKNE, vol. 12, no. 2, Art. no. 2, Nov. 2015, doi: 10.15332/iteckne.v12i2.1243.

V. P. Jiménez, A. R. Fonseca, and D. Amaya, “Diseño y construcción de un sensor capacitivo de nivel,” ITECKNE, vol. 7, no. 2, Art. no. 2, Dec. 2010, doi: 10.15332/iteckne.v7i2.288.

M. El-Abd, “A Review of Embedded Systems Education in the Arduino Age: Lessons Learned and Future Directions,” Int J Eng Pedagog, vol. 7, pp. 79–93, 2017.

S. L. Mohammed, A. Al-Naji, M. M. Farjo, and J. Chahl, “Highly Accurate Water Level Measurement System Using a Microcontroller and an Ultrasonic Sensor,” IOP Conf. Ser. Mater. Sci. Eng., vol. 518, p. 042025, Jun. 2019, doi: 10.1088/1757-899x/518/4/042025.

K. E. Supriya and K. R. R. lowast Nbsp, “IoT based real time water level monitoring using Texas instruments’ CC3200,” Indian J. Sci. Technol., vol. 13, no. 17, pp. 1720–1729, Jun. 2020, doi: 10.17485/IJST/v13i17.295.

C. J. Jeswin, B. Marimuthu, and K. Chithra, “Ultrasonic water level indicator and controller using AVR microcontroller,” in 2017 International Conference on Information Communication and Embedded Systems (ICICES), Feb. 2017, pp. 1–6, doi: 10.1109/ICICES.2017.8070773.

Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition. Wiley, pp. 16-17, 2011.

R. Santos and S. Santos, “18+ Arduino Projects,” p. 169.

Published

2021-01-01

How to Cite

Serrano Pérez, E. (2021). Approximation of Torricelli’s law with Euler’s method and an instrumented water tank with ultrasonic sensor. ITECKNE, 18(1), 52–56. https://doi.org/10.15332/iteckne.v18i1.2540

Issue

Section

Research and Innovation Articles