Mathematical Modeling for Geometric Design and Calibration of Open Frustum Tank for Expandable Liquid

References

[1] Koo BS (2021). A Theoretical Approach for Estimating the Effect of Water- Quenching on low-carbon steel beams. Sci Rep 11, 15401. DOI: https://doi.org/10.1038/s41598-021-94819-9.

[2] “Coca-Cola Steam Boiler-Noyakong Group Co., Ltd.”. https://www.noyakong.com/portfolio/coca-cola-boiler/. Accessed 15 Sept., 2022.

[3] Spectac International (2020). Pharmaceutical vessels require a Sterile environment for particular solutions. https://www.spectacinternational.com/blog/pharmaceutical-vessels-require-a-sterile-environment-for-particular-solutions/. Accessed 15 Sept., 2022.

[4] “9 Common Types of Water Storage Tanks and How They’re Used-National Storage Tank”. https://www.nationalstoragetank.com/blog/9-common-types-of-water-storage-tanks-and-how-theyre-used/. Accessed 24 Sept., 2022.

[5] Irie M, Tarhouni (2015). Water reservoir as resource of raw material for ceramic industry. Journal of Physics Conference, Series 596(1). DOI: 10.1088/1742-6596/596/1/012003.

[6] Spark Engineers (2022). Spark Engineers LPG Storage Tanks. https://m.indiamart.com/proddetail/lpg-storage-tank-9315921162.html. Accessed 15 Sept., 2022.

[7] Varkey G (2012). What is the use of Expansion Tank in HVAC. American Wheatley HVAC Products (2012). HVAC. https://www.quora.com/what-is-the-use-of-an-expansion-tank-in-HVAC. Accessed 23 Sept., 2022.

[8] Reigh S (2012). What is the function of an Expansion Tank in cooling water system? American Wheatley HVAC Products. https://www.quora.com/what-is-the-use-of-an-expansion-tank-in-HVAC. Accessed 17 Sept., 2022.

[9] Graham A, Simon C, Simon G, Laurence C (2014). Flammable vapour cloud generation from overfilling tanks: Learning the lessons from Buncefield. Journal of loss prevention in the Process industries. DOI: 10.1016/j.jip.2014.11.011.

[10] Polyprocessing (2015). Tank Geometry and Wall Thickness.

[11] https://blog.poyprocessing,com/blog/tank-geometry-and-wall-thickness. Accessed 20 Sept., 2022.

[12] Huang S and Mannan MS (2013). Technical Aspects of Storage Tank Loss Prevention. Process Safety Progress 32(1):28-36. DOI: https://doi.org/10.1002/prs.11550.

[13] kletz T (2009). Failure of Storage Tanks. What Went Wrong? 5th Edition.

[14] Tribuna F, Simcak F, Bocko J (2009). Failure Analysis of Storage Tank. January 2009. Engineering Failure Analysis, 16(1):26-38. DOI: 10.1016/j.engfailanal.2007.12.005.

[15] Dev AK (2022). Storage Tank Failure: Examples, Causes, and Prevention.https://whatispiping,com/storage-tank-failure-examples-causes-and-prevention/. 14 Accessed Sept., 2022.

[16] Tripathi S, Duby A, Maurya MC (2020). Time History Analysis of Underground Water Tank for Different Seismic Intensity. International Journal of Science and Research, 9(6):5. DOI: 10.21275/SR20612100503.

[17] Kapadia I, Patel P, Dholiya N, Patel N (2018). Desgn, Analysis and Study of the Combined Rectangular Ground Water Tank by Using STAAD proSoftware. International Journal of Current Research 10(4):67632-67635.

[18] Steckler A (2018). Seven Considerations for Tanks.

[19] https://www.wwdmag.com/storage/tanks/article/10936472/seven-considerations-for-tanks Accessed 20 Sept., 2022.

[20] Azzuni E, Guzey S (2016). Design of cylindrical steel storage Tanks: A linear elastic analysi approach. Conference: ASME 2016 Pressure Vessels and Piping Conference. DOI: 10.1115/PVP2016-6320.

[21] Mohamed HJ (2011). Economic Design of Water Concrete Tank. European Journal of Scientific Research 49 (4): 510-520.

[22] Thevendran V, Thambiratnam D (1987). Cylindrical Concrete Water Tank: Analysis and Designation: Panda G. N. Middleton J. (eds) Numerical Technique for Engineering Analysis and Design. Springer, Dordrecht. DOI: https://doi.org/10.1007/978-94-009-3653-9_19.

[23] Mayeux S and Miller J (2016). “CADWorx, CAESAR II & PV Elite: Insider Blog: Designing Storage Tanks in PTQ Magazine”. https://coade.typepad.com/coadeinsider/2016/12/tank-designing-storage-tanks.html. Accessed 20 Sept., 2022.

[24] Instrumentations Tools Ltd. (2021). Types of Level Measurement | Types of Level Sensors. Instrumentation Tool.com.

[25] Farshad A, Rahim KS, Siamak M, Reza S, Ardalan S (2023). Integration of a conical frustum PCM system for enhanced thermal energy storage in a diesel engine cogeneration system. Case Studies in Thermal Engineering 50:103452. DOI: https://doi.org/10.1016/j.csite.2023.103452.

[26] Bensah Y, Damoah L, Nyankson E, Yaya A, Nukpezah D, Azeko S, Mustapha K, Annan E (2020). Theoretical Modeling of Flow for Frustum -Shaped Ceramic Water Filters Via Disc-Shaped Ceramic Water Filters. Journal of Engineering and Applied Sciences 14:4135.

[27] Marco D and Lemay G (2022). “Frustum of Cone & Pyramid | How to Find the Volume of a Frustum –Video & Lesson TranscriptStudy.com”. https://study,com/learn/lesson/frustum-of-a-cone-pyramid-how-to-find-the-volume-of-a-frustum.html Accessed 26 Sept., 2022.

[28] Szczepanek, A. Cubic Equation Calculator. Available at: https://www.omnicalculator.com/math/cubic-equation. Accessed: Oct 10, 2024.

[29] Elert G (2022). “Thermal Expansion – Summary – The Physics hypertextbook”. https://www.engineeringtoolbox.com/cubical-expansion-coefficients-d_sensing/level_gauges. Accessed 15 Sept., 2022.

@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},
  }