Study of fluid layer gravity motion over vertical surface

Keywords: fluid, boundary layer, viscosity, velocity profile, mean velocity, shearing stresses


This paper presents the results of studying the motion of a liquid layer along the walls of a vertically installed pipe under the action of gravity. Two-dimensional boundary layer is formed by the fluid motion relative to the hard wall on surfaces of structures (pipes, turbines, heat-and-mass transfer equipment, aircrafts, ships, etc.), which are of positive interest in engineering practice. Further upgrading of the above-mentioned structures is possible only by increasing accuracy of momentum in the boundary layer, heat and mass transfer rates calculation. It is confirmed that in the boundary layer transfer phenomena intensity (perpendicular to the wall) is due to the fluid particles velocity distribution regularities in the cross-section of the layer. Fluid velocity distribution regularities in turn are conditioned by Reynolds number according to current notions. The principal method of quantitative analysis of turbulent flow in a boundary layer suggested by Reynolds continues to be the velocity and pressure fluctuations averaging method for some timespan. The suggested model of fluid movement enables to prognosticate conditions under which in cross-sections of the boundary layer reshaping of velocity profile takes place, to carry out analytic calculation of such hydrodynamic characteristics as mean velocity of motion, layer thickness and shearing stresses acting on the wall. The difference between the suggested methods developed for calculation of flow parameters from the well-known ones is in that that calculations are made based on an integrated approach regardless of such conceptual definitions as laminar and turbulent regimes widely used in modern hydrodynamics. Obtained results and design formulas known in the literature have been compared. It has been found that the thickness of the sliding layer, determine by the proposed calculation formula, 1.17 times smaller than that determined by the currently used formula


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Author Biographies

Arestak Sarukhanyan, National University of Architecture and Construction of Armenia

Department of Education Reforms

Norik Sarkisyan, National University of Architecture and Construction of Armenia

Department of Architecture

Vache Tokmajyan, Shushi University of Technology

Department of Technology

Arevshad Vartanyan, Moscow Aviation Institute (National Research University)

Department of Management and Marketing of High-Tech Industries


Schlichting, H., Gersten, K. (2017). Boundary-Layer Theory. Springer, 805. doi:

Loitsyanskii, L. G. (1966). Mechanics of liquids and gases. Pergamon. doi:

Anderson, D. A., Tannehill, J. C., Pletcher, R. H., Ramakanth, M., Shankar, V. (2020). Computational Fluid Mechanics and Heat Transfer. Boca Raton, 974. doi:

Repik, E. U., Sosedko, Yu. P. (2007). Turbulent boundary layer. Moscow: Fizmatgiz, 312. Available at:

Sarukhanyan, A., Vartanyan, A., Vermishyan, G., Tokmajyan, V. (2020). The Study of Hydrodynamic Processes Occurring on Transition of Sudden Expanding of Hydraulic Section of Plane – Parallel Full Pipe Flow. TEM Journal, 9 (4), 1494–1501. doi:

Sarukhanyan, A. A., Vartanyan, A. A., Vartanyan, G. G., Tokmajyan, H. V. (2021). Estimation of hydraulic structures safety by comparison of strength and stability theories. IOP Conference Series: Earth and Environmental Science, 677 (4), 042085. doi:

Tokmajyan, H. V. (2016). On Movement of Suspended Particles in Turbulent Flow. Bulletin of High Technology, 1, 3–10. Available at:

Lykov, A. V. (1978). Heat-and-mass transfer. Мoscow: Energia, 480. Available at:

Pavelyev, A. A., Reshmin, A. I., Teplovodskii, S. K., Fedoseev, S. G. (2003). On the lower critical Reynolds number for flow in a circular pipe. Fluid dynamics, 38 (4), 545–551. doi:

Kutateladze, S. S. (1982). Analysis of similarity in thermal physics. Novosibirsk: Science, 280. Available at:

Nadaoka, K., Hino, M., Koyano, Y. (1989). Structure of the turbulent flow field under breaking waves in the surf zone. Journal of Fluid Mechanics, 204, 359–387. doi:

Corino, E. R., Brodkey, R. S. (1969). A visual investigation of the wall region in turbulent flow. Journal of Fluid Mechanics, 37 (1), 1–30. doi:

Belotserkovskii, O. M. (2009). Constructive modeling of structural turbulence and hydrodynamic instabilities. Singapore: World Scientific, 488. doi:

Bykov, L. V., Molchanov, A. M., Yanyshev, D. S., Platonov, I. M. (2018). Current approaches to calculation of flow characteristics in laminar-turbulent transfer at boundary layer. Thermophysics of high temperatures, 56 (1), 104–120. doi:

Gorbushin, A. R., Zametev, V. B. (2017). Asymptotic analysis of viscous pulsation in turbulent boundary layer. Materials of the XXVIII Scientific and Technical Conference on Aerodynamics, 102. Available at:

Aktershev, S. P., Bartashevich, M. V., Chinnov, E. A. (2017). A semi analytic solution method for heat transfer in a fluid film in condition of constant heat stream on a wall. Thermophysics of high temperatures, 55 (1), 115–121. doi:

Vigdorovich, I. I. (2016). Reynolds analogy and a new formulation of temperature defect law for turbulent boundary on a plate. Reports of the USSR Academy of Sciences, 466 (4), 412–417. doi:

Laptinski, V. N. (2013). On an analytic method of a problem solution on dynamic laminar boundary layer in an auto model case. Scientific notes TsAGI, 44 (5), 72–93. Available at:

Bird, R. B., Stewart, W. E., Lightfoot, E. N. (1974). Transport phenomena. Мoscow: Himiya, 692. Available at:

Nagasaki, T., Akiyama, H., Nakagawa, H. (2002). Numerical analysis of flow and mass transfer in a falling liquid film with interfacial waves. Thermal Science and Engineering, 10 (1), 17–23. Available at:

Chinnov, E. A., Abdurakipov, S. S. (2013). Thermal entry length in falling liquid films at high Reynolds numbers. International Journal of Heat and Mass Transfer, 56 (1-2), 775–786. doi:

Sarkisyan, N. M. (2010). On mass transfer in fluid film, dripping over surface of vertically installed pipe. Chemical technology, 11 (3), 169–175. Available at:

Mellor, G. L. (1972). The large reynolds number, asymptotic theory of turbulent boundary layers. International Journal of Engineering Science, 10 (10), 851–873. doi:

Demikhin, E. A., Kalaidin, E. N., Rastaturin, A. A. (2005). Influence of wave modes on mass transfer in flowing liquid films. Thermophysics and aeromechanics, 12 (2), 259–269. Available at:

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How to Cite
Sarukhanyan, A., Sarkisyan, N., Tokmajyan, V., & Vartanyan, A. (2021). Study of fluid layer gravity motion over vertical surface. EUREKA: Physics and Engineering, (6), 28-38.
Chemical Engineering