Bernoulli’s Equation

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


Bernoulli’s equation relates blood pressure, P, and blood flow velocity, v. It expresses the conservation of energy in the flowing blood. If pressure losses due to friction or turbulence are neglected, Bernoulli’s equation states that the sum of mechanical energy expressed in terms of pressure, P, kinetic energy based on blood velocity, ½ ρ v2, with ρ blood density, and potential energy, ρ g z, is constant. For a blood vessel in the supine human the term ρ g z is usually neglected, and P + ½ ρ v2 = constant. Thus, when velocity is high, as in a stenosis, pressure is low. In reality pressure distal to the narrowing section does not recover completely as suggested by Bernoulli’s equation. The law helps to understand the effect of valvular stenosis and coarctation. The pressure drop over a stenosed valve can be estimated by ΔP = 4vs2 with ΔP in mmHg and vs, the maximal velocity in the stenosis, given in m/s.


Pressure Kinetic energy Potential energy Stenosis Pressure over a heart valve 


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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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