How does Bernoulli’s theorem connect fluid pressure with fluid speed?

Bernoulli’s theorem describes the relationship between pressure, velocity, and elevation in a moving fluid, serving as a principle of energy conservation for ideal, steady-flowing fluids. It states that the total mechanical energy—comprising energy from fluid pressure, gravitational potential energy, and kinetic energy—remains constant along a streamline.12

In the context of horizontal flow, where changes in gravitational potential energy are negligible, the theorem establishes an inverse relationship between fluid pressure and fluid speed: a decrease in pressure is associated with an increase in fluid velocity.1

This principle explains various physical phenomena, such as the Venturi effect, where fluid accelerating through a constricted area experiences a drop in pressure. While this may seem paradoxical, the pressure drop is the physical cause that allows the fluid to accelerate. These relationships are fundamental to engineering applications, including the operation of venturi tubes and pitot tubes used to monitor fluid flow.12