What is the indicated relationship between speed and pressure according to Bernoulli's principle?

According to Bernoulli's principle, there is an inverse relationship between the speed of a fluid and its pressure. When the speed of a fluid increases, the pressure within that fluid decreases. This principle results from the conservation of energy in a fluid flow, which states that for a streamlined flow, the total mechanical energy of the flowing fluid remains constant.

In practical terms, as the velocity of a fluid rises, its kinetic energy increases, which must be balanced by a decrease in potential energy, manifested as a drop in pressure. This phenomenon can be observed in various real-world applications, such as the lift generated over an airplane wing where the air moves faster over the top surface, resulting in lower pressure compared to the slower-moving air beneath the wing, thus providing lift.

Understanding this principle is crucial in fields such as fluid dynamics, engineering, and aerodynamics, where the behavior of fluids affects design and function significantly.