# Bernoulli’s Equation

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

## Abstarct

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.

## Keywords

Mitral Valve Stenosis Fluid Particle Bernoulli Equation Blood Density Vena Contracta
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

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.
2. 2.
Wilkinson JL. Haemodynamic calculations in the catheter laboratory. Heart 2001;85:113–120.
3. 3.
Burton AC. Physiology and Biophysics of the Circulation. 1972, Chicago, Year Book Medical Publ., 2nd edn.Google Scholar

## 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