Law of Laplace

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


The original law of Laplace pertains to soap bubbles, with radius r, and gives the relation between transmural pressure, P t , and wall tension, T s , in a thin-walled sphere as T s =P t · r. The law can be used, for example, to calculate tension in alveoli. This tension is directly related to surface tension and has the dimension N/m. The form of the law of Laplace most often used in hemodynamics gives the relation between transmural pressure and the stress in the wall in organs with a wall thickness h. We here use the Cauchy stress formulation, which is defined as the ratio of the normal (perpendicular) force acting on a surface divided by the area of the surface at its deformed configuration. Stress has the dimension N/m2 (see Figure in the box).


Circular Cylinder Fiber Stress Wall Stress Transmural Pressure Wall Tension 
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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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