group
What campus are you from?
Daytona Beach
Authors' Class Standing
Utkarsh Ravi, Junior Zarif Naimul, Junior
Lead Presenter's Name
Utkarsh Ravi
Faculty Mentor Name
Mihhail Berezovski
Abstract
This project investigates Torricelli’s Law, a fundamental principle in fluid mechanics that relates the velocity of fluid exiting an orifice to the height of the fluid above the opening. The experiment compares the drainage rates of two vertical tanks with different diameters but identical outlet sizes, isolating the influence of tank cross-sectional area on flow behavior. Each tank is filled to the same initial height, and water level versus time data are collected as the tanks drain under gravity. Using differential equation modeling and separation of variables, theoretical predictions are derived and compared to experimental results. Data analysis focuses on determining discharge coefficients and evaluating how well the mathematical model captures real-world behavior, accounting for energy losses and fluid friction. The study demonstrates that larger-diameter tanks drain more slowly, with drain times roughly proportional to their cross-sectional areas. The experiment provides a tangible illustration of how geometry affects flow dynamics, while reinforcing key mathematical concepts in modeling and data fitting. This research integrates theory, experimentation, and quantitative analysis, offering a hands-on exploration of physics and applied mathematics for undergraduate learners.
Did this research project receive funding support from the Office of Undergraduate Research.
No
Experimental Validation of Torricelli’s Law Using Dual Tank Geometries
This project investigates Torricelli’s Law, a fundamental principle in fluid mechanics that relates the velocity of fluid exiting an orifice to the height of the fluid above the opening. The experiment compares the drainage rates of two vertical tanks with different diameters but identical outlet sizes, isolating the influence of tank cross-sectional area on flow behavior. Each tank is filled to the same initial height, and water level versus time data are collected as the tanks drain under gravity. Using differential equation modeling and separation of variables, theoretical predictions are derived and compared to experimental results. Data analysis focuses on determining discharge coefficients and evaluating how well the mathematical model captures real-world behavior, accounting for energy losses and fluid friction. The study demonstrates that larger-diameter tanks drain more slowly, with drain times roughly proportional to their cross-sectional areas. The experiment provides a tangible illustration of how geometry affects flow dynamics, while reinforcing key mathematical concepts in modeling and data fitting. This research integrates theory, experimentation, and quantitative analysis, offering a hands-on exploration of physics and applied mathematics for undergraduate learners.