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.

#### Physics

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 (V_{1}) and distal velocity (V2) as they relate to a structure (e.g. valve) of interest, yielding a pressure gradient:

Pressure gradient (ΔP) = 4 (V_{2}^{2 }- V_{1}^{2})

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

ΔP = 4(V^{2})

#### Practical points

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

- aortic stenosis
- right ventricular systolic pressure
- ventricular septal defects
- left ventricular end diastolic pressure