Bernoulli equation (physics)

Last revised by David Carroll on 29 Oct 2021

The Bernoulli equation utilizes the assumptions delineated in the law of conservation of energy to calculate a pressure gradient between two points from a velocity 1. In its simplified form, discussed below, it is often used to quantify severity of valvular derangements in echocardiography.


In a closed system total energy is a constant 2. Flow across a narrowed orifice results in an increase in kinetic energy with a concomitant loss in potential energy; this translates clinically to an increase in velocity with flow through a narrowed valvular orifice and a decrease in pressure. The modified Bernoulli equation relates these variables, using a proximal (V1) and distal velocity (V2) as they relate to a structure (e.g. valve) of interest, yielding a pressure gradient:

Pressure gradient (ΔP) = 4 (V22 - V12)

As the square of the proximal velocity is typically orders of magnitude smaller than the square of the distal velocity, the former variable (V1) is often ignored (generally acceptable when the proximal maximum velocity is less than 1 meter/second) resulting in the simplified Bernoulli equation:

ΔP = 4(V2)

Practical points

The simplified Bernoulli equation is commonly utilized to assess and/or quantify the severity of the following:


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