Attempts to describe the fluid flow through pipes were made by domestic and foreign scientists at different times. The article provides an overview of scientific papers in the field of hydraulic studies of pipelines published in the XVIII – XX centuries, based on processing the results of a wealth of experimental data obtained for various hydrodynamic conditions. A significant role was played by work of the French school representatives H. Darcy and G. de Prony, who first demonstrated the dependence of hydraulic losses on the diameter and roughness of the inner wall of pipes. In consequence, up to the end of the 19th century, two competing scientific directions can be observed: the study of hydraulic friction at “low” and “high” fluid velocities. The beginning of the “reconciliation” of the controversial research results was laid by the works of N.P. Petrov and O. Reynolds. The limited use of empirical dependencies does not allow to extend any of the proposed formulas to the whole range of operating modes of pipelines. For each particular case, it is necessary to analyze the accuracy of the equations used by comparison with actual operation data. A retrospective analysis of the scientific and technical literature in the field of pipeline’s hydraulics reveals the variability of methodological approaches and formal decisions in the study of quantitative estimates of the parameters of fluid flow in pipes. It was shown that the concept of using the relative roughness of the inner wall of the pipe D/D as an adaptive factor in determining hydraulic losses in pipes can be traced from Darcy’s works and has gained its methodological substantiation in the works of L. Prandtl’s school.

References

1. Kutukov S.E., Razrabotka metodov funktsional'noy diagnostiki tekhnologicheskikh rezhimov ekspluatatsii magistral'nykh nefteprovodov (Development of methods for functional diagnostics of technological modes of trunk pipelines operation): thesis of doctor of technical science, Ufa, 2003.

2. Shammazov A.M., Kutukov S.E., Arsent'ev A.A. et al., Complex investigation of rheological and adhesion properties of oils in the range of crystallization temperatures (In Russ.), Izvestiya vysshikh uchebnykh zavedeniy. Neft' i gaz, 1998, no. 4, pp. 63–72.

3. Brot R.A., Kutukov S.E., Determination of rheophysical parameters of gas-saturated oil (In Russ.), Elektronnyy nauchnyy zhurnal Neftegazovoe delo, 2005, no. 2, URL: http://ogbus.ru/files/ogbus/authors/Brot/Brot_1.pdf.

4. Al'tshul' A.D., Gidravlicheskie soprotivleniya (Hydraulic resistance), Moscow: Nedra Publ., 1982, 224 p.

5. Brown G.O., The history of the Darcy-Weisbach equation for pipe flow resistance, Proceedings of 150th Anniversary Conf. Environmental and water resources history of ASCE Reston, 2002, pp. 34–43, DOI: 10.1061/40650(2003)4.

6. Chernikin V.I., Gidravlicheskie soprotivlenia svarnykh truboprovodov (Hydraulic connections of welded pipelines), Proceedings of Oil industry academy, 1956, v. 3, pp. 53–56.

7. Isaev I.A., Eksperimental'noe opredelenie koeffitsientov gidravlicheskikh soprotivleniy v pryamykh nefteprovodnykh trubakh i fitingakh (Experimental determination of hydraulic resistance coefficients in straight oil pipelines and fittings), In: Voprosy transporta, khraneniya nefti i mashinostroeniya (Problems of transport, storage of oil and engineering), Proceedings of MOI, V. 17, Moscow: Gostoptekhizdat Publ, 1956, pp. 112–168.

8. Frenkel' N.Z., Gidravlika (Hydraulics), Moscow – Leningrad: Gosenergizdat Publ., 1956, 456 p.

9. Lobaev B.N., Novye formuly dlya rascheta trub v perekhodnoy oblasti (New formulas for calculating pipes in the transition area), Moscow: Sanitarnaya tekhnika Publ., 1954, 121 p.

10. Filonenko G.K., Pipeline hydraulic resistance (In Russ.), Teploenergetika, 1958, Vfi 4, pp.63–68.

11. Konakov P.K., New formula for hydraulic resistance coefficients for smooth pipes (In Russ.), DAN SSSR, 1946, no. 10, pp. 70–77.

12. Churchill S.W., Empirical expressions for the shear stress in turbulent flow in commercial pipe, AIChE Journal, 1973, V. 19, pp. 375–376.

13. Nikolaev A.K., Bykov K.V., Malarev V.I., Determination of the hydraulic resistance coefficient of the main oil pipeline (In Russ.), Gornyy informatsionno-analiticheskiy byulleten', 2013, no. 5, pp. 265–268.

14. Prandtl L., Tietjens O.J., Hydro und aeromechanic, Berlin: Springer-Verlag, 1934, 290 p.

15. White F.M., Fluid mechanics, 3rd ed., New York: Mc-Graw Hill, 1994, 736 p.

16. Rouse H., Ince S., History of hygraulics, lowa City: lowa Institute of Hydraulic Research, Univ. of lowa, 1957, 269 p.

17. Revel'-Muroz P.A. et al., Assessing the hydraulic efficiency of oil pipelines according to the monitoring of process operation conditions (In Russ.), Nauka i tehnologii truboprovodnogo transporta nefti i nefteproduktov = Science & Technologies: Oil and Oil Products Pipeline Transportation, 2019, V. 9, no. 1, pp. 8–19.

Attempts to describe the fluid flow through pipes were made by domestic and foreign scientists at different times. The article provides an overview of scientific papers in the field of hydraulic studies of pipelines published in the XVIII – XX centuries, based on processing the results of a wealth of experimental data obtained for various hydrodynamic conditions. A significant role was played by work of the French school representatives H. Darcy and G. de Prony, who first demonstrated the dependence of hydraulic losses on the diameter and roughness of the inner wall of pipes. In consequence, up to the end of the 19th century, two competing scientific directions can be observed: the study of hydraulic friction at “low” and “high” fluid velocities. The beginning of the “reconciliation” of the controversial research results was laid by the works of N.P. Petrov and O. Reynolds. The limited use of empirical dependencies does not allow to extend any of the proposed formulas to the whole range of operating modes of pipelines. For each particular case, it is necessary to analyze the accuracy of the equations used by comparison with actual operation data. A retrospective analysis of the scientific and technical literature in the field of pipeline’s hydraulics reveals the variability of methodological approaches and formal decisions in the study of quantitative estimates of the parameters of fluid flow in pipes. It was shown that the concept of using the relative roughness of the inner wall of the pipe D/D as an adaptive factor in determining hydraulic losses in pipes can be traced from Darcy’s works and has gained its methodological substantiation in the works of L. Prandtl’s school.

References

1. Kutukov S.E., Razrabotka metodov funktsional'noy diagnostiki tekhnologicheskikh rezhimov ekspluatatsii magistral'nykh nefteprovodov (Development of methods for functional diagnostics of technological modes of trunk pipelines operation): thesis of doctor of technical science, Ufa, 2003.

2. Shammazov A.M., Kutukov S.E., Arsent'ev A.A. et al., Complex investigation of rheological and adhesion properties of oils in the range of crystallization temperatures (In Russ.), Izvestiya vysshikh uchebnykh zavedeniy. Neft' i gaz, 1998, no. 4, pp. 63–72.

3. Brot R.A., Kutukov S.E., Determination of rheophysical parameters of gas-saturated oil (In Russ.), Elektronnyy nauchnyy zhurnal Neftegazovoe delo, 2005, no. 2, URL: http://ogbus.ru/files/ogbus/authors/Brot/Brot_1.pdf.

4. Al'tshul' A.D., Gidravlicheskie soprotivleniya (Hydraulic resistance), Moscow: Nedra Publ., 1982, 224 p.

5. Brown G.O., The history of the Darcy-Weisbach equation for pipe flow resistance, Proceedings of 150th Anniversary Conf. Environmental and water resources history of ASCE Reston, 2002, pp. 34–43, DOI: 10.1061/40650(2003)4.

6. Chernikin V.I., Gidravlicheskie soprotivlenia svarnykh truboprovodov (Hydraulic connections of welded pipelines), Proceedings of Oil industry academy, 1956, v. 3, pp. 53–56.

7. Isaev I.A., Eksperimental'noe opredelenie koeffitsientov gidravlicheskikh soprotivleniy v pryamykh nefteprovodnykh trubakh i fitingakh (Experimental determination of hydraulic resistance coefficients in straight oil pipelines and fittings), In: Voprosy transporta, khraneniya nefti i mashinostroeniya (Problems of transport, storage of oil and engineering), Proceedings of MOI, V. 17, Moscow: Gostoptekhizdat Publ, 1956, pp. 112–168.

8. Frenkel' N.Z., Gidravlika (Hydraulics), Moscow – Leningrad: Gosenergizdat Publ., 1956, 456 p.

9. Lobaev B.N., Novye formuly dlya rascheta trub v perekhodnoy oblasti (New formulas for calculating pipes in the transition area), Moscow: Sanitarnaya tekhnika Publ., 1954, 121 p.

10. Filonenko G.K., Pipeline hydraulic resistance (In Russ.), Teploenergetika, 1958, Vfi 4, pp.63–68.

11. Konakov P.K., New formula for hydraulic resistance coefficients for smooth pipes (In Russ.), DAN SSSR, 1946, no. 10, pp. 70–77.

12. Churchill S.W., Empirical expressions for the shear stress in turbulent flow in commercial pipe, AIChE Journal, 1973, V. 19, pp. 375–376.

13. Nikolaev A.K., Bykov K.V., Malarev V.I., Determination of the hydraulic resistance coefficient of the main oil pipeline (In Russ.), Gornyy informatsionno-analiticheskiy byulleten', 2013, no. 5, pp. 265–268.

14. Prandtl L., Tietjens O.J., Hydro und aeromechanic, Berlin: Springer-Verlag, 1934, 290 p.

15. White F.M., Fluid mechanics, 3rd ed., New York: Mc-Graw Hill, 1994, 736 p.

16. Rouse H., Ince S., History of hygraulics, lowa City: lowa Institute of Hydraulic Research, Univ. of lowa, 1957, 269 p.

17. Revel'-Muroz P.A. et al., Assessing the hydraulic efficiency of oil pipelines according to the monitoring of process operation conditions (In Russ.), Nauka i tehnologii truboprovodnogo transporta nefti i nefteproduktov = Science & Technologies: Oil and Oil Products Pipeline Transportation, 2019, V. 9, no. 1, pp. 8–19.