Samara, Samara, Russian Federation
A graphic construction of six-measured nomogram with its subsequent decomposition on four cell-like three-dimensional spatial axonometries with their physiographic analysis is offered in this work. Compact construction of the six-measured nomogram allows obtain fully a graphic illustration for the current experiment and explicitly characterize its physical entity by means of parametric link. A qualitatively new illustrative model graphically connects all experimental cycle of operating parameters by means of projective dependence for Cartesian coordinate system taking into account the materialization of spot measurements. In the course of receiving geometrical images in the form of straight lines’ segments, curves, planes and surfaces during construction of the six-measured nomogram a question about obtaining of each geometrical image’s physical characteristics is set. Regularity of parameters layout on the epure six-measured nomogram’s planes should define physical evolution or its absence in the experiment. In case of construction a graphic dependence between parameters the applicate axis, certainly, is resultant or functional one and all remaining axes are arguments or variables. Geometrical images, such as horizontal planes of level, are involved in the work, and each of these planes expresses the spot measurement of all projective parameters. Horizontally projecting surfaces have been presented by intersection of generatrixes with directing lines that are the transition link of conformance points between two-phase flow’s phases. The compliance axiom is given that is the graphic confirmation for what has been said.
nomogram, multidimensional geometry, phases, environment, planes of three dimensional dependences, axonometric model, live sections, rating curves, speeds and accelerations of phases.
Номограммы, их значение и применение
В 1906–1908 гг. впервые в Росси начал заниматься вопросами номографии Н.М. Герсеванов.
1. Adler Yu.R. Planirovanie eksperimenta pri poiske optimal'nykh usloviy [Planning an experiment when searching for optimal conditions]. Moscow, Mashinostroenie Publ. 1976, p. 279. (in Russian)
2. Batuner L.M. Matematicheskie metody v khimicheskoy tekhnike [Mathematical methods in chemical engineering]. Khimiya [Chemistry]. Moscow, 1968. 823 p. (in Russian)
3. Chugaev R.R. Gidravlika [Hydraulics]. Moscow, 1971. 648 p. (in Russian)
4. Branovitskaya S.V. Vychislitel'naya matematika v khimii i khimicheskoy tekhnologii [Computational mathematics in chemistry and chemical technology]. Vysshaya shkola, Golovnoe izdatel'stvo [Higher School, Head Publishing House]. Moscow, 1986. 216 p. (in Russian)
5. Glagolev N.A. Kurs nomografii [Course of nomograph]. Vysshaya shkola 2 [Higher School 2]. Moscow, 1961. 270 p. (in Russian)
6. Gordon V.O., Sementsov-Ogievskiy M.A. Kurs nachertatel'noy geometrii [The course of grained geometry]. Moscow, 1988, 2002. 272 p. (in Russian)
7. Klimukhin A.G. Nachertatel'naya geometriya [Descriptive geometry]. Moscow, 1973. 368 p. (in Russian)
8. Kolotov S.M. Nachertatel'naya geometriya [Descriptive geometry]. Kiev, Vishcha shkola Publ. 1975. 262 p. (in Russian)
9. Krylov N.N. Nachertatel'naya geometriya [Descriptive geometry]. Moscow, Vysshaya shkola Publ. 2000. 224 p. (in Russian)
10. Levkin Yu.S. Opredelenie izmeneniy zhivykh secheniy faz dvukhfaznykh potokov pri var'irovanii raskhoda gazovoy fazy [Determination of changes in the live cross-sections of phases of two-phase flows with variation of the gas phase flow rate]. Vestnik Samarskogo gosudarstvennogo aerokosmicheskogo universiteta imeni S.P. Koroleva [Bulletin of the Samara State Aerospace University named after S.P. Koroleva]. 2010, I. 4, pp. 88-91. (in Russian)
11. Levkin Yu.S. Deformatsiya zhivogo secheniya zhidkoy fazy dvukhfaznogo potoka ot vozdeystviya poperechnoy vibratsii [Deformation of the live section of the liquid phase of a two-phase flow from the effect of transverse vibration]. Sbornik trudov II Mezhdunarodnogo ekologicheskogo kongressa Ekologiya i bezopasnost' zhiznedeyatel'nosti promyshlenno-transportnykh kompleksov [Collection of works of the II International Ecological Congress. Ecology and life safety of industrial transport complexes]. Tol'yatti, 2009, V. 8, pp. 271-276. (in Russian)
12. Levkin Yu.S. Psevdolaminarnyy dvukhfaznyy rezhim [Pseudo-laminar two-phase regime]. Samara, 2013. 94 p. (in Russian)
13. Levkin Yu.S. Metod opredeleniya vysoty volny psevdolaminarnogo dvukhfaznogo potoka ot vibratsionnykh vozdeystviy [Method for determining the height of a wave of a pseudo-laminar two-phase flow from vibrational influences]. Ekologiya i bezopasnost' zhiznedeyatel'nosti promyshlenno-transportnykh kompleksov [Ecology and life safety of industrial transport complexes]. Tol'yatti, 2011, V. 4, pp. 169-175. (in Russian)
14. Levkin Yu.S., Lushkin I.A Vliyanie vibratsionnykh uskoreniy 3 g i 4 g na dispersnuyu strukturu nizko i srednechastotnykh kolebaniy [Influence of vibrational accelerations 3 g and 4 g on the dispersed structure of low and medium-frequency oscillations]. Izd. Samarskogo gosudarstvennogo aerokosmicheskogo universiteta [Samara State Aerospace University]. Samara, 2015, V. 14, I. 4, pp. 135-142. (in Russian)
15. Levkin Yu.S. Deformatsiya zhivogo secheniya gazovoy fazy dvukhfaznogo potoka ot vozdeystviya poperechnoy vibratsii [Deformation of the live section of the gas phase of a two-phase flow from the effect of transverse vibration]. Sbornik trudov II Mezhdunarodnogo ekologicheskogo kongressa Ekologiya i bezopasnost' zhiznedeyatel'nosti promyshlenno-transportnykh kompleksov [Collection of works of the II International Ecological Congress. Ecology and life safety of industrial transport complexes]. Tol'yatti, 2009, I. 3, pp. 262-270. (in Russian)
16. Levkin Yu.S. Zavisimost' izmeneniya skorosti dispersnoy i plenochno-dispersnoy struktur ot vibratsionnykh uskoreniy vysokochastotnykh kolebaniy [Dependence of the change in the speed of dispersed and film-disperse structures on vibrational accelerations of high-frequency oscillations]. Izvestiya Vuzov. Severo-Kavkazsky region. Tekhnicheskie nauki [Proceedings of Higher Educational Institutions. North Caucasus region. Technical science]. Novocherkassk, 2016, I. 3, pp. 77-82. (in Russian)
17. Levkin Yu.S. Poluchenie chetyrekhmernykh nomogramm na baze teoremy podobiya [Obtaining four-dimensional nomograms on the basis of the similarity theorem]. Geometriya i grafika [Geometry and graphics]. Moscow, 2017, pp. 69-74. (in Russian)
18. Levkin Yu.S. Vliyanie vibratsionnykh kolebaniy na kharakteristiki struktury dvukhfaznogo potoka [The influence of vibration oscillations on the characteristics of the structure of a two-phase flow]. Izvestiya Vuzov. Severo-Kavkazsky region. Tekhnicheskie nauki [Proceedings of Higher Educational Institutions. North Caucasus region. Technical science]. Novocherkassk, 2016, I. 2, pp. 112-119. (in Russian)
19. Levkin Yu.S., Lushkin I.A Postroenie grafoanaliticheskikh odnoyacheechnykh prostranstvennykh nomogramm nizkochastotnykh i vysokochastotnykh zon pologosti volny [Construction of graphoanalytical single-cell spatial nomograms of low-frequency and high-frequency zones of wave flatness]. Mezhdunarodnyy nauchno-issledovatel'skiy zhurnal [International Scientific and Research Journal]. 2017, I. 11, pp. 98-103. (in Russian)
20. Lysenko A.V. Postroenie nomogramm po fundamental'noy i prikladnoy khimii [Construction of nomograms on fundamental and applied chemistry]. Yugo-Zapadnyy Gosudarstvennyy universitet [South-Western State University]. Kursk, 2016. 17 p. (in Russian)
21. Sal'kov N.A., Nachertatel'naya geometriya - baza dlya geometrii analiticheskoy [Descriptive Geometry - Base for Analytical Geometry]. Geometriya i grafika [Geometry and graphics]. 2016, V. 4, I. 1, pp. 44-54. (in Russian)
22. Sal'kov N.A., Nachertatel'naya geometriya - baza dlya komp'yuternoy grafiki [Descriptive geometry - base for computer graphics]. Geometriya i grafika [Geometry and graphics]. 2016, V. 4, I. 2, pp. 37-47. (in Russian)
23. Sal'kov N.A. Nachertatel'naya geometriya - bazovyy kurs [Descriptive geometry - basic course]. Moscow, INFRA-M Publ., 2013. 184 p. (in Russian)
24. Khvatov B.N. Postroenie nomogramm rezhimov lentochnogo shlifovaniya na osnove matematicheskogo planirovaniya eksperimenta [Construction of nomograms of belt grinding modes on the basis of mathematical design of the experiment]. Tambovskiy gosudarstvennyy tekhnicheskiy universitet [Tambov State Technical University]. Tambov, 2007. 32 p. (in Russian)
25. Chetverukhin N.F. Nachertatel'naya geometriya [Descriptive geometry]. Moscow, Vysshaya shkola Publ. 1963. 420 p. (in Russian)
