Bernoulli’s Equation

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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.