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Mathematical Modeling for Geometric Design and Calibration of Open Frustum Tank for Expandable Liquid
Subject area: Science,Engineering and Technology · Area of research: Materials and Metallurgical Engineering
Abstract
In order to proffer solution to the sudden failure of liquid tanks, which has been an industrial challenge, this paper presents a proposed mathematical modeling for geometric design and calibration of frustum tank that can hold expandable liquid at elevated temperature and accommodate increase in liquid volume due to temperature rise. In the design, the tank is presented in three segments; the first segment represents the reserved liquid volume below the datum line, the second segment represents the actual liquid volume and the third segment represents the minimum volume of free space above the liquid level, provided to compensate for liquid expansion. Another design condition is that the liquid levels must not fall below the datum. Based on these conditions, mathematical equations have been derived for calculating tank dimensions, volumes of the various tank segments, total tank volume and calibration of the actual liquid volume. By iteration method, the proposed model was used for geometric design of an open frustum tank of 30000litres actual liquid capacity. The dimensions obtained, were used to calculate the total tank volume, which yielded approximately 35000litres. The result of the calibration shows a non-linear relationship between the tank instantaneous height and the corresponding instantaneous volume. It was concluded that open frustum tank of expandable liquid can be designed if the actual liquid capacity and the dimensions of the tank below the datum are known.
Keywords
Geometric, Design, Calibration, Frustum tank
How to cite this paper
@article{1706484,
author = {Kingsley Onyekachi Anyanwu, Harrison Ogochukwu Nzei, Victor Ikechukwu Ehirim, Lambertson Chima Osuchukwu, Chukwudike Onuoha},
title = {Mathematical Modeling for Geometric Design and Calibration of Open Frustum Tank for Expandable Liquid},
journal = {Iconic Research And Engineering Journals},
year = {2024},
volume = {8},
number = {5},
pages = {1346-1355},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1706484.pdf},
abstract = {In order to proffer solution to the sudden failure of liquid tanks, which has been an industrial challenge, this paper presents a proposed mathematical modeling for geometric design and calibration of frustum tank that can hold expandable liquid at elevated temperature and accommodate increase in liquid volume due to temperature rise. In the design, the tank is presented in three segments; the first segment represents the reserved liquid volume below the datum line, the second segment represents the actual liquid volume and the third segment represents the minimum volume of free space above the liquid level, provided to compensate for liquid expansion. Another design condition is that the liquid levels must not fall below the datum. Based on these conditions, mathematical equations have been derived for calculating tank dimensions, volumes of the various tank segments, total tank volume and calibration of the actual liquid volume. By iteration method, the proposed model was used for geometric design of an open frustum tank of 30000litres actual liquid capacity. The dimensions obtained, were used to calculate the total tank volume, which yielded approximately 35000litres. The result of the calibration shows a non-linear relationship between the tank instantaneous height and the corresponding instantaneous volume. It was concluded that open frustum tank of expandable liquid can be designed if the actual liquid capacity and the dimensions of the tank below the datum are known.},
keywords = {Geometric, Design, Calibration, Frustum tank},
month = {November},
}