Determination of hydrostatic pressure force on a spherical surface under conditions of relative equilibrium of fluid using method K123

Автор(и)

  • Yuri Kopanytsia Київський національний університет будівництва і архітектури

DOI:

https://doi.org/10.32347/2524-0021.2020.34.12-18

Ключові слова:

method of three commands, K123, hydrostatic pressure, relative equilibrium of fluid, coordi-nates of pressure force center

Анотація

Lack of modern universal computer algorithms for analytical and numerical modeling as well as for calculation of hydrostatic pressure force proves to be a problem in designing certain component parts of the water-sludge system of the concentrator.

Determination of the vector parameters of the hydrostatic pressure resultant force, namely, the magnitude, direction and calculation of the coordinates of the pressure force center in three dimensions, allows to design reliable components for product unloading in such processes as lighting, thickening and separation in systems using centrifugal acceleration under conditions of relative equilibrium of fluid.

Author’s universal algorithm, the method of three commands K123, has been offered to calculate the vector parameters of the hydrostatic pressure force on a curved surface under conditions of relative equilibrium of fluid. Calculation of the pressure force on an arbitrary surface component has been presented on the example of pressure on a spherical surface rotating with a certain frequency.

Presented algorithms allow to increase the efficiency in designing the component parts of automatic control for unloading the lightened or thickened product in the concentrator water-sludge systems.

Посилання

Konstantinov, Y. M. (2002). Technical mechanics of liquid and gas: Textbook. Kyiv: Higher school.

Konstantinov, Y. M. (2012). Hydrostatics. Examples and problems: Textbook. Kyiv: KNUBA.

Gorchin, N. K. (1927). Hydraulics in problems. Leningrad: Kubuch.

Maxima. Retrieved from https://en.wikipedia.org/wiki/Maxima_(software)

Maxima, a Computer Algebra System. Retrieved from http://maxima.sourceforge.net/

Kopanytsia, Yu. (2018). Multivariance of hydrostatic pressure calculation in CAS MAXIMA system. Underwater technologies. Industrial and civil engineering, 8, 50-51. Retrieved from http://nbuv.gov.ua/UJRN/pidteh_2018_8_11

Kopanytsia, Yu. (2018). Calculation of long pipelines in the web interface of the computer algebra system MAXIMA. Underwater technologies. Industrial and civil engineering, 8, 52-53. Retrieved from http://nbuv.gov.ua/UJRN/pidteh_2018_8_12

Edwards, C. H., Penney, D., & Calvis, D. (2014). Differential Equations and Boundary Value Problems: Computing and Modeling Harlow: Pearson Education Limited. ISBN-13: 978-0-321-81625-2

Turyn, L. (2013). Advanced Engineering Mathematics. CRC Press. ISBN: 9781439834473. doi: 10.1201/b15750

Magrab, E. B. (2014). An Engineer's Guide to Mathematica. John Wiley & Sons Ltd. ISBN: 9781118821268

Mathews, J. H. (2014). Complex Analysis for Mathematics and Engineering. Jones & Bartlett Learning. ISBN: 9781449604455

Harris, F. E. (2014). Mathematics for Physical Science and Engineering. Academic Press. ISBN: 9780128010006

Romano, A. & Marasco, A. (2018). Classical Mechanics with Mathematica. Birkhäuser Basel. ISBN: 9783319775944. doi: 10.1007/978-3-319-77595-1

Cryer, C. W. (2014). A Math Primer for Engineers. IOS Priess. ISBN: 9781614992981. doi:10.3233/978-1-61499-299-8-i

Mathews, J. H., & Howell, R. (2012). Complex Analysis for Mathematics and Engineering. Jones & Bartlett Learning. ISBN: 9781449604455

Geveci, T. (2011). Calculus I. Cognella. ISBN: 9781935551423

Gregor, J., Tišer, J. (2011). Discovering Mathematics: A Problem-Solving Approach to Mathematical Analysis with Mathematica and Maple. Springer. ISBN: 9780857290540. doi: 10.1007/978-0-85729-064-9

Abramovich, S. (2015). Exploring Mathematics with Integrated Spreadsheets in Teacher Education. World Scientific. ISBN: 9789814689908. doi:10.1142/9601

Anastassiou, G. A., & Iatan, I. F. (2013). Intelligent Routines: Solving Mathematical Analysis with Matlab, Mathcad, Mathematica and Maple. Springer. ISBN: 9783642284748. doi:10.1007/978-3-642-28475-5

Borwein, J., & Skerritt, M. P. (2012). An Introduction to Modern Mathematical Computing with Mathematica. Springer Undergraduate Texts in Mathematics and Technology. ISBN: 9781461442523. doi: 10.1007/978-1-4614-4253-0

Bindner, D., & Erickson, M. (2010). Student's Guide to the Study, Practice, and Tools of Modern Mathematics. CRC Press. ISBN: 9781439846063.

Kopanytsia, Yu. D. (2012). Computer calculation of pressure force. Universal al-gorithm of three commands - K123. Problems of water supply, sewerage and hydraulic, 18, 148-163.

Kopanytsia, Yu. D. (2012). Calculation of hydrostatic pressure on a curved surface. Universal algorithm of three commands - K123. Problems of water supply, sewerage and hydraulic, 20, 105-119.

Kopanytsia, Yu. D. (2013). Analysis of the measurement of the plot of hydrostatic pressure on the curved surface. Universal method of calculation K123. Problems of water supply, sewerage and hydraulic, 21, 165-180.

Kopanytsia, Yu. D. (2013). Integral equations of the universal method of three commands K123. Problems of water supply, sewerage and hydraulic, 22, 159-171.

##submission.downloads##

Опубліковано

2020-12-16