Bernoulli's equation is a fundamental principle in fluid dynamics that describes the relationship between the pressure, velocity, and elevation of a fluid in motion. It states that in a steady, incompressible flow, the total mechanical energy of the fluid remains constant along a streamline. This means that as the speed of the fluid increases, its pressure decreases, and vice versa. The equation is often 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 relationship helps explain various phenomena, such as how airplanes generate lift and how water flows through pipes.