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Laminar Flow of a Viscous Liquid in the Entrance Region of a Circular Pipe

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Abstract

An approximate theory of stationary axisymmetric laminar flow of a viscous incompressible fluid in the entrance region of a circular pipe is presented. It gives correct (within ±2%) calculated values of different physical characteristics of the established flow, which coincide with the known calculated and experimental data. Instead of the traditional Bernoulli equation for the entire length of the entrance region, the work at hand uses the equation of the axial pressure gradient averaged over the pipe section to determine the pressure value.

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REFERENCES

  1. Targ, S.M., Osnovnye zadachi teorii laminarnykh techenii (Basic Problems of the Theory of Laminar Flows), Moscow-Leningrad: Gos. Izd. Tekhniko-Tekhnicheskoi Literatury, 1951.

  2. Schiller, L., Strömung in Röhren, Leipzig: Akademische Verlagsgesellschaft, 1932.

    MATH  Google Scholar 

  3. Slezkin, N.A., Dinamika vyazkoi neszhimaemoi zhidkosti (Dynamics of a Viscous Incompressible Liquid), Moscow: Gos. Izd. Tekhniko-Tekhnicheskoi Literatury, 1955.

  4. Volarovich, M.P., Poiseuille’s works on the flow of liquid in pipes, Izv. Akad. Nauk SSSR, Ser. Fiz., 1947, vol. 11, no. 1.

  5. Prandtl, L. and Tietjens, O.G, Fundamentals of Hydro and Aeromechanics, New York: McGraw-Hill, 1934.

    MATH  Google Scholar 

  6. Schiller, L. and Kirsten, H., Über den Widerstand strömender Flüssigkeit in kurzen Rohrstücken (in connection with the discussion of the results of experimental studies V. Zarkow), Phys. Z., 1921, vol. 22, pp. 523–528.

    Google Scholar 

  7. Durst, F., Ray, S., Ünsal, B., and Bayoumi, O.A., The development lengths of laminar pipe and channel flows, J. Fluid Eng., 2005, vol. 127, no. 6, pp. 1154–1160.

    Article  Google Scholar 

  8. Poole, R.J. and Ridley, B.S., Development – length requirements for fully developed laminar pipe flow of inelastic non-Newtonian liquids, J. Fluid Eng., 2007, vol. 129, pp. 1281–1287.

    Article  Google Scholar 

  9. Mehrotra, A.K. and Patience, G.S., Unified entry length for newtonian and power-law fluids in laminar pipe flow, Can. J. Chem. Eng., 1990, vol. 68, pp. 529–533.

    Article  Google Scholar 

  10. Shimomukay, K. and Kanda, H., Numerical study of normal pressure distribution in entrance pipe flow, Electron. Trans. Num. Anal., 2008, vol. 30, pp. 10–25.

    MathSciNet  MATH  Google Scholar 

  11. Landau, L.D. and Lifshits, E.M., Teoreticheskaya fizika (Theoretical Physics), vol. 6: Gidrodinamika (Hydrodynamics), Moscow: Nauka, 1986.

  12. Loitsyanskii, L.G., Laminarnyi pogranichnyi sloi (Laminar Boundary Layer), Moscow: Gos. Izd. Fiz.-Mat. Lit., 1962.

  13. Kamke, E., Differentialgleichungen: Losungsmethoden und Losungen, I, Gewohnliche Differentialgleichungen, Leipzig: B. G. Teubner, 1977.

    Book  Google Scholar 

  14. Hornbeck, R.W., Laminar flow in the entrance region of a pipe, Appl. Sci. Res. A, 1964, vol. 13, pp. 224–236.

    Article  Google Scholar 

  15. Kazakov, L.I., Razvitie techeniya Puazeilya v krugloi trube (Development of the poiseuille flow in a round tube), Available from VINITI, 2019, Sevastopol, no. 80-B2019.

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  1. Federal State Unitary Enterprise “NIIAE”, 299006, Sevastopol, Russia

    L. I. Kazakov

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  1. L. I. Kazakov
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Correspondence to L. I. Kazakov.

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Translated by L. Trubitsyna

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Kazakov, L.I. Laminar Flow of a Viscous Liquid in the Entrance Region of a Circular Pipe. Fluid Dyn 56, 954–966 (2021). https://doi.org/10.1134/S0015462821070053

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  • DOI: https://doi.org/10.1134/S0015462821070053

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