Skip to main content
SpringerLink
Log in
Book cover

The Pi-Theorem pp 103–130Cite as

Laminar Flows in Channels and Pipes

  • Chapter
  • First Online:

  • 2355 Accesses

Part of the book series: Experimental Fluid Mechanics ((FLUID,volume 1))

Abstract

Fluid flow in pipes and ducts was a subject of numerous experimental and theoretical investigations performed during the last two centuries. Beginning from the seminal works of Hagen (1839) and Poiseuille (1840), a detailed data on flows of incompressible viscous fluids in pipes and ducts of different geometry was obtained. These results are presented in many review articles, monographs and textbooks. A comprehensive analysis of problems related to laminar and turbulent flows in pipes and ducts (the physical foundations of the theory and its mathematical formulation) can be found in such widely known books as Schlichting (1979), Landau and Lifshitz (1987), Loitsyanskii (1966) and Ward-Smith (1980).

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    \( \left[ {{\rm Re} } \right] = 1 \) since it is defined by the parameter magnitudes.

References

  • Adler M (1934) Stromung in gekruiimmeten. Rohren Z Angew Math 14:257–275

    MATH  Google Scholar 

  • Astarita G, Marrucci G (1974) Principies of non-newtonian fluid mechanics. McGraw-Hill, New York

    Google Scholar 

  • Bahrami M, Yovanovich MM, Culham JR (2006) Pressure drop of fully developed laminar flow in rough microtybes. J Fluids Eng Trans ASME 128:632–637

    Article  Google Scholar 

  • Barua SN (1963) On secondary flow in stationary curved pipes. QJ Mech Appl Math 16:61–77

    Article  MathSciNet  Google Scholar 

  • Berger SA, Tabol L, Yao L-S (1983) Flow in curved pipes. Annu Rev Fluid Mech 15:461–512

    Article  Google Scholar 

  • Bird RB, Armstrong RC, Hassager O (1977) Dynamics of polymeric liquids. In: Fluid mechanics, vol 1. Wiley&Sons, New York

    Google Scholar 

  • Celata GP (2000) Heat transfer and fluid flow in microchannels. Begell Hause, New York

    Google Scholar 

  • Dean WR (1927) Note on the motion of fluid in a curved pipe. Philos Mag 20:208–223

    Google Scholar 

  • Dean WR (1928) The streamline motion of fluid in a curved pipe. Philos Mag 30:673–693

    Google Scholar 

  • Dunkan AB, Peterson GP (1994) Review of micro-scale heat transfer. App Mech 47:397–428

    Article  Google Scholar 

  • Van Dyke M (1978) Extended Stokes series: Laminar flow through a loosely coiled pipe. J Fluid Mech 36:129–145

    Article  Google Scholar 

  • Emery AE, Chen CS (1968) An experimental investigation of possible methods to reduce laminar entry length. Trans ASME Ser D 90:134–137

    Article  Google Scholar 

  • Fargie D, Martin BW (1971) Developing laminar flow in a pipe of circular cross-section. Proc Roy Soc 321A:461–476

    Google Scholar 

  • Friedmann M, Gilis J, Liron N (1968) Laminar flow in a pipe at low and moderate Reynolds numbers. App Sci Res 19:426–438

    Article  MATH  Google Scholar 

  • Gad-el-Hak M (1999) The fluid mechanics of micro-devices. The Freeman Scholar Lecture. J Fluid Eng 121:5–33

    Article  Google Scholar 

  • Gad-el-Hak M (2003) Comments or “critical” view on new results in micro-fluid mechanics. Int J Heat Mass Transf 46:3941–3945

    Article  MATH  Google Scholar 

  • Garimella S, Sobhan C (2003) Transport in microchannels: critical review. Annu Rev Heat Transf 13:1–50

    Google Scholar 

  • Germano M (1989) The Dean equations extended to a helical pipe flow. J Fluid Mech 203:289–305

    Article  MATH  Google Scholar 

  • Hagen G (1839) Uber die Bewegung des Wassers in engen zylindrisghen Rohren. Pogg Ann 46:423–442

    Article  Google Scholar 

  • Hezwig H (2002) Flow and heat transfer in micro systems. Everything different or just smaller? ZAMM 82(9):579–586

    Google Scholar 

  • Hezwig H, Hausner O (2003) Critical view on new results in micro-fluid mechanics: an example. Int J Heat Mass Transf 46:935–937

    Article  Google Scholar 

  • Hezwig H, Gloss D, Wenterodt T (2008) A new approach to understanding and modeling the influence of wall roughness on friction factors for pipe and channel flows. J Fluid Mech 613:35–53

    Google Scholar 

  • Hetsroni H, Mosyak A, Pogrebnyak E, Yarin LP (2005a) Fluid flow in microchannels. Int J Heat Mass Transf 48:1982–1998

    Article  Google Scholar 

  • Hetsroni G, Mosyak A, Pogrebnyak E, Yarin LP (2005b) Heat transfer in micro-channels: comparison of experiments with theory and numerical results. Int J Heat Mass Transf 48:5580–5601

    Article  Google Scholar 

  • Ho C-M, Tai Y-C (1988) Micro-electro-mechanical systems (MEMS) and fluid flows. Annu Rev Fluid Mech 30:579–612

    Article  Google Scholar 

  • Incropera FP (1999) Liquid cooling of electronic devices by single-phase convection. John Wiley&Sons, New York

    Google Scholar 

  • Ito H (1959) Friction factors for turbulent flow in curved pipes. Trans ASME J Basic Eng 81:123–134

    Google Scholar 

  • Kakas S, Vasiliev LL, Bayazitoglu Y, Yener Y (2005) Micro-scale heat transfer. Springer, Berlin

    Google Scholar 

  • Kandlicar SG (2005) Roughness effects at microscale-reassessing Nikuradse’s experiments on liquid flow in rough tubes. B Pol Acad Sci Tech Sci 53:343–349

    Google Scholar 

  • Landau LD, Lifshitz EM (1987) Fluid mechanics, 2nd edn. Pergamon, New York

    Google Scholar 

  • Li ZX, Du DX, Guo ZY (2003) Experimental study on flow characteristics of liquid in circular micro-tubes. Microscale Thermophys Eng 7:253–265

    Article  Google Scholar 

  • Li Z, He Y-L, Tang G-H, Tao W-Q (2007) Experimental and numerical studies of liquid flow and heat transfer in microtubes. Int J Heat Mass Transf 50:3442–3460

    Google Scholar 

  • Loitsyanskii LG (1966) Mechanics of liquids and gases. Pergamon Press, Oxford

    Google Scholar 

  • Ma HB, Peterson GP (1997) Laminar friction factor in micro-scale ducts of irregular cross-section. Micro-scale Thermophys Eng 1:253–265

    Article  Google Scholar 

  • Moody LF (1948) Friction factors for pipe flow. Trans ASME 66:671–684

    Google Scholar 

  • Mori Y, Nakayama W (1965) Study on forced convective heat transfer in curved pipes (1st Report, Laminar flow). Int J Heat Mass Transf 8:67–82

    Article  MATH  Google Scholar 

  • Nikuradse J (1930) Turbulente stromung in nicht kreisfozmigen rohren. Ing Arch 1:306–332

    Google Scholar 

  • Nikuradse J (1933) Stromungsgesetze in rauhen. Rihren Forschg Arb Ing-Wes 361. Translated in NACA Memo. N1292, (1950)

    Google Scholar 

  • Pfund D, Rector D, Shekarriz A (2000) Pressure drop measurements in micro-channel. AIChE 46:1496–1507

    Article  Google Scholar 

  • Plam B (2000) Heat transfer in micro-channels. In: Heat transfer and transport phenomena in microscale. Banff Oct, pp 54–64

    Google Scholar 

  • Poiseuille J (1840) Recherches experimentelles sur le mouvements des liquides dans les tubes de tres petits diameters. Comptes Rendus 11:961–967, 1041–1048

    Google Scholar 

  • Qu W, Mala GM, Li D (2000) Pressure driven water flows in trapezoidal silicon micro-channels. Int J Heat Mass Transf 43:353–364

    Article  MATH  Google Scholar 

  • Schlichting H (1979) Boundary layer theory, 8th edn. Springer, Berlin

    Google Scholar 

  • Schiller L (1923) Uber den Stromungswiderrstand von Rohren verschiedenen Querschnitts-und Rauhigkeitsgrades. ZAMM 3:2–13

    Article  MathSciNet  Google Scholar 

  • Shah RK, London AL (1978) Laminar flow forced convection in duct. Academic, New York

    Google Scholar 

  • Wang HL, Wang Y (2007) Flow in microchannels with rough walls: flow pattern and pressure drop. J Micromech Microeng 17:586–596

    Article  Google Scholar 

  • Ward-Smith AS (1980) Internal fluid flow (The fluid dynamics of flow in pipes and ducts). Clarendon, Oxford

    Google Scholar 

  • White CM (1929) Streamline flow through curved pipes. Proc R Soc London Ser 123A:645–663

    Article  Google Scholar 

  • White FM (2008) Viscous fluid flow, 7th edn. McGraw-Hill, New York

    Google Scholar 

  • Wilkinson WL, Chen AML (1960) Non-Newtonian fluids (Fluid mechanics, mixing and heat transfer). Pergamon Press, New York

    Google Scholar 

  • Yarin LP, Mosyak A, Hetsroni G (2009) Fluid flow, Heat transfer and boiling in micro-channels. Springer, Berlin

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Mechanical Engineering Technion City, Technion-Israel Institute of Technology, 32000, Haifa, Israel

    L. P. Yarin

Authors
  1. L. P. Yarin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Yarin, L.P. (2012). Laminar Flows in Channels and Pipes. In: The Pi-Theorem. Experimental Fluid Mechanics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19565-5_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-19565-5_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-19564-8

  • Online ISBN: 978-3-642-19565-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation