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 |
Log, Exponential, Function, Velocity, Division, Original
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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
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
@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} }
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 PY - 2022 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 -