Options for calculating the hydrostatic pressure force using the K123 method on the walls of a paraboloidal channel

The development of modern microprocessor technologies in personal gadgets and computers, the distribution on the Internet of open client-server calculation services of almost all known computer mathematics systems (Wolfram Mathematica, Waterloo Maple, MATHLAB, PTC Mathcad, R, CAS MAXIMA, etc.) allows anyone to use modern engineering calculations in open access. But this theoretical statement has certain practical limitations. The complexity of modern engineering calculations, due to the development of the software component, has been significantly simplified for typical tasks and increases or goes beyond the capabilities of the program for any atypical or non-standard task. The standard mechanism for expanding program functionality to define non-standard solutions is also known and implemented by a built-in internal programming language, additional modules, and libraries. It is this standard mechanism for using modern software products that requires a significant increase in the general mathematical culture, which combines analytical, numerical, and graphical calculation methods in implementation algorithms within the framework of one modern engineering problem. The article presents a study of calculation methods using the example of a seemingly simple standard problem of determining the magnitude, direction, and coordinates of the center of pressure for a hydrostatic pressure force vector on the lateral curved surface of a parabolic channel. The proposed solutions are based on a new theoretical basis and corresponding methods, which underlie the universal author's method of three commands K123 (c) Kopanitsa Y.D. [1-14]. The principle of multi-variant solutions to standard problems by conducting computational experiments in computer mathematics systems using methods from different branches of mathematics should be the basis of the educational process. At the same time, a secure client-server calculation program based on CGI technology with a web form for entering input data for the Internet with open access has been developed. The web form of the program is available on the Internet without restrictions at https://www.k123.org.ua/_jh_ex2b_3b.html. The program implements calculations for all proposed new algorithms, generates detailed reports of intermediate results, and allows modeling and conducting computational experiments on a wide range of data for this class of problems. The graphical component of the solution is visualized in SVG vector format, and mathematical notation is in TEX format. Various operating modes, password access, output data set restrictions, and format and dimension checks of input and output data based on regular expression technology are provided. The program interface is designed with the use of mobile devices with limited Internet bandwidth in mind. New calculation formulas are proposed for a certain class of standard problems based on the author's method of three commands K123 (c) Kopanitsa Yu.D. Until now, this class of standard problems was absent from modern textbooks.