Process vessels utilized for liquids and liquid-phase processes are important in the chemical process industries as they are employed for a number of purposes which include use as reservoirs, surge tanks, transportation tankers and as reactors. It is therefore often desired to have real-time data about the liquid volume and level especially for partially-filled vessels. While obtaining volume-level data for filled tanks for common geometries are simple tasks, this is not so for partially-filled vessels with complex geometries. This paper therefore sets out to develop a useful theoretical tool which can assist process engineers with the task of calibrating process tanks for these complex yet widely-used geometries. The paper presents a mathematical analysis of these geometries and develops equations and charts which could be used to estimate tank volumes from given depth of liquid for any geometry of partially-filled process vessel. The paper also develops a useful methodology which can assist in the design and sizing of process vessels using the developed charts. The paper is unique in that it utilized a normalization technique in the mathematical analyses of the partially-filled process vessels. Fractional volume and fractional depth were introduced as key variables in addition to dimensionless geometric parameters.
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