Abstract
We explore the dynamics of the water in a PVC pipe during the drain using two independent sensors simultaneously. We track the height of the water column and the discharge velocity of the water through the hole made in the lower part of the pipe. The ultrasonic distance sensor and the flow meter used as sensors were controlled by an Arduíno board. The acquired data follows the theoretical models but, with a coefficient of discharge smaller than 1.
Highlights
A very common question/problem presented in physics textbooks [1] related to fluid dynamics is: What is the speed of water flowing from a hole in the lower side of a vessel?
Evangelista Torricelli (1608-1647) discovered the answer showing that the speed of the fluid that leaks through a small hole is proportional to the square root of the water column, and later, its equation was demonstrated as a particular case of Bernoullis principle
Were Ad and A are the hole and the vessel cross-sectional areas, respectively, g is the gravitation acceleration, and h is the height of the water column
Summary
A very common question/problem presented in physics textbooks [1] related to fluid dynamics is: What is the speed of water flowing from a hole in the lower side of a vessel?. Were Cd is the coefficient of discharge (the ratio of the measured discharge to the theoretical discharge), a number smaller than one This coefficient includes all factors cited that are responsible for decreasing the real discharge velocity. Another fact is that Equations (2) and (3), as presented, are valid only if the water level in the vessel is constant. We use an Arduino connected to two sensors: one to measure the water column height, another the discharge velocity Measuring these two parameters independently, we fitted Torricelli's law equation, considering the correction due to the system not being ideal
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