The Bernoulli equation is a fundamental principle in fluid dynamics that describes the relationship between the pressure, velocity, and elevation of a fluid in steady flow. It states that an increase in the fluid's speed occurs simultaneously with a decrease in pressure or potential energy. This principle is derived from the conservation of energy and is applicable to incompressible, non-viscous fluids. In its simplest form, the Bernoulli equation can be expressed as P + \frac12 \rho v^2 + \rho gh = \textconstant , where P is the fluid pressure, \rho is the fluid density, v is the flow velocity, g is the acceleration due to gravity, and h is the height above a reference point. This equation helps explain various phenomena, such as how airplanes generate lift and how fluid flows through pipes.