Bernoulli’s Equation

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


The Bernoulli equation can be viewed as an energy law. It relates blood pressure (P) to flow velocity (v). Bernoulli’s law says that if we follow a blood particle along its path (dashed line in left Figure in the box) the following sum remains constant:
$$ P+{\scriptscriptstyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\cdot r\cdot {u}^{2}+r\cdot g\cdot z=\text {constant}$$
where ρ is blood density, g acceleration of gravity, and z elevation with respect to a horizontal reference surface (i.e., ground level or heart level). The equation of Bernoulli says that as a fluid particle flows, the sum of the hydrostatic pressure, P, potential energy, ρ · g · z, and the dynamic pressure or kinetic energy, ½ · ρ · v 2, remains constant. One can easily derive Bernoulli’s equation from Newton’s law: Pressure forces + gravitational forces = mass × acceleration.




  1. 1.
    Gorlin R, Gorlin SG. Hydraulic formula for calculations of the area of the stenotic mitral valve value, orthocardiac values and central circulating shunts. Am Heart J 1951;41:1–29.PubMedCrossRefGoogle Scholar
  2. 2.
    Wilkinson JL. Haemodynamic calculations in the catheter laboratory. Heart 2001;85:113–120.PubMedCrossRefGoogle Scholar
  3. 3.
    Burton AC. Physiology and Biophysics of the Circulation. 1972, Chicago, Year Book Medical Publ., 2nd edn.Google Scholar

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

Personalised recommendations