Law of Poiseuille

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


With laminar and steady flow through a uniform tube of radius r i , the velocity profile over the cross-section is a parabola. The formula that describes the velocity (v) as a function of the radius, r is:
$$ {v}_{r}=\frac{\Delta P \cdot \text ({r}_{i}-{r}^{2})}{4 \cdot \eta \cdot \text l}={v}_{\mathrm{max}}(1-{r}^{2}/{r}_{i})$$
ΔP is the pressure drop over the tube of length (l), and η is blood viscosity. At the axis (r = 0), velocity is maximal, v max , with v max = ΔPr i 2 /4ηl, while at the wall (r = r i ) the velocity is assumed to be zero. Mean velocity is:
$$ {v}_{mean}=\Delta P \cdot \text {r}_{i}^{2}/8\text h \cdot \text l=v_{\mathrm{max}}\text /2=Q/\pi {r}_{i}^{2}$$
and is found at r ≈ 0.7 r i .


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Copyright information

© Springer US 2010

Authors and Affiliations

  • Nicolaas Westerhof
    • 1
  • Nikolaos Stergiopulos
    • 2
  • Mark I. M. Noble
    • 3
  1. 1.Departments of Physiology and Pulmonology ICaR-VUVU University Medical CenterAmsterdamthe Netherlands
  2. 2.Laboratory of Hemodynamics and Cardiovascular TechnologySwiss Federal Institute of TechnologyLausanneSwitzerland
  3. 3.Cardiovascular MedicineAberdeen UniversityAberdeenScotland

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