Why is there a relationship between speed and pressure? What is that relation? Why are they inverses of each other?
When a fluid is flowing smoothly and steadily through a stationary environment, its energy is conserved. As long as it doesn’t lose much energy to frictional effects, you can count on its total energy remaining essentially constant as it flows downstream. Since it only has three forms for its energy: gravitational potential energy, pressure potential energy, and kinetic energy, you can expect that a decrease in one of these forms of energy will be accompanied by an increase in one of the other forms. That’s when speed and pressure are inversely related. When the fluid slows down, its kinetic energy drops so its pressure potential energy (and its pressure) must rise.