Release:
2026. Vol. 12. № 2 (46)About the authors:
Nikolay G. Konoplev, Senior Lecturer, Department of Transport and Storage of Oil and Gas, Ufa State Petroleum Technological University, Ufa, RussiaAbstract:
This article addresses the problem of reducing hydraulic resistance. Since early studies of the relation between the applied pressure difference at the ends of a pipeline and the fluid flow rate in it, researchers have been concerned with determining the energy losses of a fluid during its motion. Faced with the turbulence — understanding the laws and principles of motion of individual fluid particles and determining hydraulic resistance during turbulent fluid flow — researchers have put forward several theories describing the laws of motion. Solving these tasks for a stationary state led to a new problem — reducing hydraulic resistance during turbulent flow. Based on the theory of the relative displacement of fluid particles, established by the founders of turbulent flow research, and works on the analogy between energy and fluid motion, the authors hypothesize the possibility of controlling hydraulic resistance using an energy source — a pump supplying fluid to the pipeline at a certain frequency. The article presents the results of a study of fluid flow in a pipeline with a variable flow rate, i.e., the movement of fluid under the periodic action of a pump. A model is presented that describes the pressure at the starting point of a pipeline and the fluid flow rate based on an electrohydraulic analogy, in which frictional energy losses are expressed through a complex quantity reflecting the action of the viscous, inertial, and elastic forces of the fluid. As our measurements have shown, the complex hydraulic resistance, which consumes energy during fluid flow through a pipeline, underlies the determination of the attenuation coefficient of a propagating pressure wave, suggesting an analogy between wave propagation and the turbulent movement of fluid through a pipeline.Keywords:
References:
Akulov, V. A. Pulse wave model and its implementation in Excel. In E. A. Rapoport (ed.), Mathematical Modeling and Boundary Value Problems. Proceedings of the Third All-Russian Scientific Conference. Part 4. Mathematical Models in Information Technology (pp. 13–16). Samara State Technical University. [In Russian]
Altshul, A. D. (1982). Hydraulic Resistances (2nd ed. revised and enlarged). Nedra. [In Russian]
Burgers, J. (1936). On the application of statistical mechanics methods to the theory of turbulent fluid motion. In M. A. Velikanov, N. T. Shveikovsky (eds.), Turbulence Problems. Collection of Translated Articles. Onti. Glav. red. obshchetekhn. lit-ry i nomographii. [In Russian]
Gromeka, I. S. (1952). Collected Works (Exec. Ed. A. P. Kochina). Academy of Sciences of the USSR. Retrieved May 29, 2026, from http://books.e-heritage.ru/book/10079943 [In Russian]
Konoplev N. G, & Korobkov G. E. (2020). Resiliency and liquid inertia effects at transient process in the pipeline. Transport and Storage of Oil Products and Hydrocarbons, (3), 44–53. https://doi.org/10.24411/0131-4270-2020-10309
Korshak, A. A., & Khusain, M. N. (2008). Conditions for effective use of anti-turbulence additives in existing oil pipelines. In Proceedings of the 4th International Educational, Scientific and Practical Conference “Pipeline Transport – 2008” (pp. 68–69). Ufa State Petroleum Technical University. [In Russian]
Merkulov, V. I. (2011). Propagation of pulse wave through large blood vessels. Actual Problems of Modern Science, (5), 132–140. [In Russian]
Navruzov, K., Begjanov, A. Sh., Sharipova, Sh. B., & Zhumaev, Zh. (2023). Mathematical modeling of hydrodynamic resistance in an oscillatory flow of a viscoelastic fluid. Russian Mathematics (Iz. VUZ), (8), 45–55. https://doi.org/10.26907/0021-3446-2023-8-45-55 [In Russian]
Radnaev, B. B., Tsybikov, A. S., & Khabituev, B. V. (2017). ARIMA-model of pulse wave. BSU Bulletin. Mathematics, Informatics, (1), 78–85. [In Russian]
Simakov, S. S. (2018). Modern methods of mathematical modeling of blood flow using reduced order methods. Computer Research and Modeling, 10(5), 581–604. [In Russian]
Simonenko, A. P. [et al.]. (2019). Hydrodynamically Active Compositions in Energy Saving and Ecology. DonNU. [In Russian]
Umov, N. A. (1874). Equations of Motion of Energy in Bodies. Printing house of Ulrich and Schulze. [In Russian]
Usanov, D. A., Skripal, A. V., Kalinkin, M. Yu., & Baatyrov, R. T. (2017). Estimation of total peripheral resistance based on the elastic reservoir model. In D. A. Usanov (ed.), Proceedings of the All-Russian School-Seminar “Methods of Computer Diagnostics in Biology and Medicine — 2017” (pp. 23–25). Saratovskii istochnik. [In Russian]
Fedotov, A. A. (2015). Mathematical model of hemodynamic processes of peripheral pulse wave formation. Biophysics, 60(2), 343–347. [In Russian]
Schauberger, V. (2007). Energy of Water (Ed. by A. Krysenko). Yauza, Eksmo. [In Russian]
Schlichting, G. (1974). Boundary Layer Theory (Transl. from German by G. A. Volper, ed. By L. G. Loitsyanskii). Nauka. [In Russian]
Murakami, М., Kikuyama, K., & Nishibori, K. (1983). Flow in axially rotating pipes. Nagoya University, Faculty of Engineering. Memoirs, 35, 1–35.
Ohmi, M., & Iguchi, M. (1980). Flow pattern and frictional losses in pulsating pipe flow: Part 2, effect of pulsating frequency on the turbulent frictional losses. Bulletin of the JSME, 23(186), 2021–2028. https://doi.org/10.1299/jsme1958.23.2021
Schultz-Grunow, F. (1940). Pulsierender Durchfluss durch Rohre. Forschg. Ing. Wes, 11, 170–187. [In German]
Shukurov, Z. K., Yuldoshev, B. Sh., & Begjanov, A. (2022). Investigation of hydraulic resistance of pulsating flows of viscous fluid in elastic pipe. E3S Web of Conferences, 365, 03026. https://doi.org/10.1051/e3sconf/202336503026
Sundstrom, L. R. J., & Cervantes, M. J. (2018). On the similarity of pulsating and accelerating turbulent pipe flows. Flow, Turbulence and Combustion, 100, 417–436. https://doi.org/10.1007/s10494-017-9855-5
