Bernoulli's equation is a physical equation that describes the conservation of energy in a flowing fluid or gas medium. The equation is named after the Swiss mathematician and physicist Daniel Bernoulli, who first formulated it.
Bernoulli's equation, in its basic form, states that the total mechanical energy in a flowing liquid or gas medium is constant in the absence of external forces such as friction or resistance. This energy consists of three parts: the kinetic energy of the fluid movement, the potential energy of the gravitational field, and the pressure energy.
Mathematically, the Bernoulli equation is expressed as follows:
P + ½ ρv² + ρgh = constant
P is the pressure of the liquid or gas,
ρ is the density of the liquid or gas,
v is the fluid or gas velocity,
g is the gravitational acceleration,
h is the height above the reference level.
The equation therefore expresses a balanced relationship between pressure, velocity and height in a flowing environment. If any of these factors change, then the other energy in the equation changes as well.
Bernoulli's equation is a useful tool for analyzing the flow of liquids or gases in various situations, for example when studying the flow of liquid in a pipe, the movement of air over an airplane wing, or when calculating pressure differences in plumbing and HVAC systems.