Pipe Flows

Part of the Advances in Geophysical and Environmental Mechanics and Mathematics book series (AGEM)


In this chapter pipe flows are studied for laminar Hagen-Poiseuille flows as well as turbulent flows; this situation culminates via a dimensional analysis in the well known Moody diagram based on the pioneering work of Johann Nikuradse’s hydraulically smooth and rough pipes. Plane turbulent flow is mathematically modeled by Prandtl and von Kármán on the basis of Prandtl’s mixing length parameterization of the turbulent shear stress. Wall parallel flows can computationally be determined by two additional assumptions, (1) that the mixing length grows linearly with distance from the wall and (2) the shear stress velocity is constant across the turbulent boundary layer. The result is the well known logarithmic velocity profile. It culminates in Prandtl’s and von Kármán’s universal representation of the coefficient of resistance, \(\lambda \). This universality property, assumed to hold since the 1930s, has been challenged by Barenblatt and associates in the 1990s and later on. These authors negate the logarithmic law and show that the laminar sub-layer influences the outer turbulent boundary layer.


Hagen-Poiseuille flow Laminar flow in cylindrical pipes of arbitrary cross section Turbulent flows in pipes Moody diagram based on Nikuradse’s experiments Prantl-von Kármán plane turbulent flows Universal logarithmic turbulent boundary layer velocity profile Barenblatt et al.’s negation of the logarithmic velocity profile 


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Versuchsanstalt für Wasserbau, Hydrologie und GlaziologieETH ZürichZürichSwitzerland
  2. 2.Department of Mechanical EngineeringTechnische Universität DarmstadtDarmstadtGermany

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