Law of Poiseuille

  • Nicolaas Westerhof
  • Nikolaos Stergiopulos
  • Mark I. M. Noble
  • Berend E. Westerhof


The law of Poiseuille describes the relation between pressure drop, ΔP/l, and blood flow, Q, in a stiff tube under steady flow conditions. For a tube with circular cross-section and when the blood flows in a laminar fashion, i.e., each fluid layer stays at the same constant distance from the center, the flow depends strongly on the radius of the tube (fourth power), the pressure drop over the tube length (ΔP/l) and viscosity of blood (η) as Q = π ri4P/l)/8η. The velocity profile, v(r), is parabolic. The wall shear stress, τ, acting on the intimal layer (endothelium) equals τ = 4 η Q/(π ri3) = (ΔP/l)·(ri/2). Resistance can be calculated as R = ΔP/Q = 8 ηlri4.


Laminar flow Fourth-power law Parabolic flow profile Wall shear stress 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Nicolaas Westerhof
    • 1
  • Nikolaos Stergiopulos
    • 2
  • Mark I. M. Noble
    • 3
  • Berend E. Westerhof
    • 1
  1. 1.Department of Pulmonary Diseases, Amsterdam Cardiovascular SciencesVU University Medical CenterAmsterdamThe Netherlands
  2. 2.Laboratory of Hemodynamics and Cardiovascular TechnologyEcole Polytechnique Fédérale de Lausanne (EPFL), Institute of BioengineeringLausanneSwitzerland
  3. 3.Cardiovascular Medicine, Department of Medicine and TherapeuticsUniversity of AberdeenAberdeenUnited Kingdom

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