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Application of Log and Exponential Functions for Velocity Calculation in Axis Symmetrical Conductor’s Cross-Section

Received: 16 November 2022     Accepted: 6 December 2022     Published: 15 December 2022
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Abstract

The paper is occupied with laminar and turbulence flow in round conductors having as main theme velocity division in pipes cross – section. For this problem there are existing formulas that are analyzed, and also some new formulas are presented. Rectilinear flow is researched with constant cross – section therefor flow through all cross – sections is parallel and normal on cross – section. Flow is uniform through flow direction, average velocity is constant value. Laminar flow where analytic solution is existed and turbulence flow where experimental formulas are applied, were analyzed. Log and exponential formulas for velocity division in turbulence flow are analyzed through short calculation and the graphic for identical flow conditions with same Re number. Reynolds equation applied for steady turbulence flow, for flow plane do not allowed determination of velocity division in cross – section. Therefor relations between average values and fluctuations were assumed as log or exponential functions and they were experimentally validated. Some existing formulas are shown below. Laminar uniform axis symmetrical flow having analytic solution as square parable is shown. Formula for turbulence axis symmetrical flow with log velocity division called ”velocity deficit” is analyzed. Also formula for turbulence axis symmetrical flow with exponential velocity division for smooth wall has been analyzed. At the end new and original formulas for turbulence flow with log and exponential velocity division are presented having significant advantages. These mathematical formula have to be validated experimentally and justified for use in some areas of fluid mechanics. Analyze is valid also for plane flow between two plane boards.

Published in American Journal of Applied Mathematics (Volume 10, Issue 6)
DOI 10.11648/j.ajam.20221006.12
Page(s) 236-239
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2022. Published by Science Publishing Group

Keywords

Log, Exponential, Function, Velocity, Division, Original

References
[1] G. Hajdin, Fluid Mechanics (Mehanika fluida), Gradjevinska knjiga, Faculty of Civil Engineering, University of Belgrade, 1983.
[2] G. Hajdin, Fluid Mechanics book II Introduction in hydraulics (Mehanika fluida knjiga druga Uvodjenje u hidrauliku), Faculty of Civil Engineering, University of Belgrade, 2002.
[3] J. Hinze, Turbulence, New York – London, 1959.
[4] G. De Marchi, Idraulica, Milano, 1942.
[5] G, Hajdin, O praktičnom značaju statističke analize pulzacija pritisaka vode na konture hidrotehničkih konstrukcija, VIII Kongres YUCOLD, 1970.
[6] G. Hajdin, Contribution to the evaluation of fluctuation pressure on fluid currents limit areasbased on the pressures recorded at several points of the area, VIII Conference of Yugoslav Hydraulics Association. Portorož, 1982.
[7] G. Hajdin, Two contributions to spillway designing based on experimental studies13th ICOLD, Q50, R 45, New Delhi, 1979.
[8] A. Rajčević, S. Djordjević, M. Ivetić and Č. Maksimović, An Approach to the Simulation of Street Flooding in the Modelling of Surcharged Flow in Storm Sewers, Proc. UDT `91 Conference, Dubrovnik, 1991., Elsevier.
[9] A. Rajčević, S. Djordjević, M. Ivetić and Č. Maksimović, Modelling of Surcharged Flow in Storm Sewers with Water Exchange Through The Inlet Openings, Hydrocomp `92 Conference, Budapest, 1992.
[10] Č. Maksimović, D. Obradović and M. Radojković, Computational sanitary hydrotechnique (Računari u komunalnoj hidrotehnici), Gradjevinska knjiga, Beograd, 1990.
[11] M. Boreli, Hydraulics (Hidraulika), Naučna knjiga, Građevinski fakultet Univerziteta u Beogradu, 1984.
[12] D. Prodanović, D. Pavlović and N. Branisavljević, Flow measurment in the short structures in hydraulic complex conditions – HE “Djerdap 2” case study (Merenje protoka na kratkim objektima u hidraulički neregularnim uslovima na primeru HE “Djerdap 2”), Vodoprivreda Vol. 43 No. 252-254, Beograd, 2011.
[13] P. Petrović, Sadd – El – Kafara dam in Egypt, Vodoprivreda Vol. 43 No. 249-251, Beograd, 2011.
[14] Ž. Erčić, Application of the results of contemporaneous hydraulic investigations in the designs of spillways for large dams, Vodoprivreda Vol. 43 No. 252-254, Beograd, 2011.
[15] B. Djordjević and T. Dašić, Method for determing the environmental flow downstream of the dams and water intakes, Vodoprivreda Vol. 43 No. 252-254, Beograd, 2011.
Cite This Article
  • APA Style

    Aleksandra Rajcevic. (2022). Application of Log and Exponential Functions for Velocity Calculation in Axis Symmetrical Conductor’s Cross-Section. American Journal of Applied Mathematics, 10(6), 236-239. https://doi.org/10.11648/j.ajam.20221006.12

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    ACS Style

    Aleksandra Rajcevic. Application of Log and Exponential Functions for Velocity Calculation in Axis Symmetrical Conductor’s Cross-Section. Am. J. Appl. Math. 2022, 10(6), 236-239. doi: 10.11648/j.ajam.20221006.12

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    AMA Style

    Aleksandra Rajcevic. Application of Log and Exponential Functions for Velocity Calculation in Axis Symmetrical Conductor’s Cross-Section. Am J Appl Math. 2022;10(6):236-239. doi: 10.11648/j.ajam.20221006.12

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  • @article{10.11648/j.ajam.20221006.12,
      author = {Aleksandra Rajcevic},
      title = {Application of Log and Exponential Functions for Velocity Calculation in Axis Symmetrical Conductor’s Cross-Section},
      journal = {American Journal of Applied Mathematics},
      volume = {10},
      number = {6},
      pages = {236-239},
      doi = {10.11648/j.ajam.20221006.12},
      url = {https://doi.org/10.11648/j.ajam.20221006.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20221006.12},
      abstract = {The paper is occupied with laminar and turbulence flow in round conductors having as main theme velocity division in pipes cross – section. For this problem there are existing formulas that are analyzed, and also some new formulas are presented. Rectilinear flow is researched with constant cross – section therefor flow through all cross – sections is parallel and normal on cross – section. Flow is uniform through flow direction, average velocity is constant value. Laminar flow where analytic solution is existed and turbulence flow where experimental formulas are applied, were analyzed. Log and exponential formulas for velocity division in turbulence flow are analyzed through short calculation and the graphic for identical flow conditions with same Re number. Reynolds equation applied for steady turbulence flow, for flow plane do not allowed determination of velocity division in cross – section. Therefor relations between average values and fluctuations were assumed as log or exponential functions and they were experimentally validated. Some existing formulas are shown below. Laminar uniform axis symmetrical flow having analytic solution as square parable is shown. Formula for turbulence axis symmetrical flow with log velocity division called ”velocity deficit” is analyzed. Also formula for turbulence axis symmetrical flow with exponential velocity division for smooth wall has been analyzed. At the end new and original formulas for turbulence flow with log and exponential velocity division are presented having significant advantages. These mathematical formula have to be validated experimentally and justified for use in some areas of fluid mechanics. Analyze is valid also for plane flow between two plane boards.},
     year = {2022}
    }
    

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  • TY  - JOUR
    T1  - Application of Log and Exponential Functions for Velocity Calculation in Axis Symmetrical Conductor’s Cross-Section
    AU  - Aleksandra Rajcevic
    Y1  - 2022/12/15
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    N1  - https://doi.org/10.11648/j.ajam.20221006.12
    DO  - 10.11648/j.ajam.20221006.12
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 236
    EP  - 239
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20221006.12
    AB  - The paper is occupied with laminar and turbulence flow in round conductors having as main theme velocity division in pipes cross – section. For this problem there are existing formulas that are analyzed, and also some new formulas are presented. Rectilinear flow is researched with constant cross – section therefor flow through all cross – sections is parallel and normal on cross – section. Flow is uniform through flow direction, average velocity is constant value. Laminar flow where analytic solution is existed and turbulence flow where experimental formulas are applied, were analyzed. Log and exponential formulas for velocity division in turbulence flow are analyzed through short calculation and the graphic for identical flow conditions with same Re number. Reynolds equation applied for steady turbulence flow, for flow plane do not allowed determination of velocity division in cross – section. Therefor relations between average values and fluctuations were assumed as log or exponential functions and they were experimentally validated. Some existing formulas are shown below. Laminar uniform axis symmetrical flow having analytic solution as square parable is shown. Formula for turbulence axis symmetrical flow with log velocity division called ”velocity deficit” is analyzed. Also formula for turbulence axis symmetrical flow with exponential velocity division for smooth wall has been analyzed. At the end new and original formulas for turbulence flow with log and exponential velocity division are presented having significant advantages. These mathematical formula have to be validated experimentally and justified for use in some areas of fluid mechanics. Analyze is valid also for plane flow between two plane boards.
    VL  - 10
    IS  - 6
    ER  - 

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Author Information
  • Faculty of Civil Engineering, University of Belgrade, Belgrade, Serbia

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