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

The indicated relationship between speed and pressure according to Bernoulli's principle is that increased speed decreases pressure. This principle is derived from the conservation of energy for flowing fluids and illustrates how different forms of energy within a fluid can convert into one another.

As the speed of a fluid increases, its kinetic energy increases. To maintain energy conservation, if the kinetic energy increases due to higher velocity, there must be a corresponding decrease in the potential energy represented by pressure. This implies that in a streamlined flow, when the velocity of a fluid increases in a given area, the static pressure in that area must decrease. This relationship is fundamental in various applications, including aerodynamics and the design of various fluid systems, such as airfoils and pipe systems.

The other options do not accurately reflect Bernoulli's principle. Increased speed leading to increased pressure contradicts the basic premise, as does the notion that decreased speed leads to decreased pressure, because a decrease in speed typically results in a higher pressure. The claim that there is no relationship is incorrect as well, as there is a clear and quantified relationship between speed and pressure as outlined by Bernoulli's equation.