Influence of an ellipse in the calculation of the partial volume of an inclined right cylindrical tank with an interface tangent to it
DOI:
https://doi.org/10.15648/invefor.v5i1.4571Keywords:
Volume calculation, cylinder, ellipse, inclination, tangentAbstract
The present research aimed to develop a mathematical model to calculate the partial volume of a liquid contained in a straight inclined cylindrical tank, considering the influence of an ellipse in its geometry with an interface tangent to it.
The study was framed within a quantitative approach, as it involved the manipulation of variables with numerical values; analytical, because analyses were performed on certain parameters of the cylinder's geometry in relation to the ellipse; and applied, as it provided a solution to a concrete real-world problem using theoretical tools and mathematical modeling techniques. The research level was analytical, and the research design was quantitative.
This study developed an efficient method for estimating partial volumes, considering the angle of inclination and the dimensions of the container. To obtain precise data, the software GeoGebra 3D was used to model the elliptic function within the cylinder, while SolidWorks enabled numerical simulations and validation of the results through comparison with other methods. The main finding of the mathematical model is given by V(b)=(1/2 l+b)πr^2, where "l" is the length of the container, the number π (pi) is a constant with a value of 3,1451… , "r" is the radius of the circumference that forms the base of the cylinder, and "b" is the target variable arising from the relationship between the ellipse and the tangent liquid surface.
Author Biography
Samuel Suarez-Cabarcas, Universidad del Atlántico
Facultad de Ciencias Básicas. Matemáticas. Semillero de Investigación Sistemas Dinámicos y EDO.
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