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

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.