There's a simple explanation that wasn't covered in the last thread about this. Start off with an ideal incompressable fluid with no viscosity in a pipe. The flow rate in the pipe is fixed. The amount of mass per unit time moving past any cross section in the pipe is constant, otherwise mass would be accumulating in the pipe. The fact that the flow rate is fixed is one of the key factors in this explanation of Bernoulli's principle. The pipe transitions through various diameters. Since the flow rate in terms of mass per unit time is fixed, the mass is traveling faster when the diameter of the pipe is smaller, changing speed in proportion to the cross sectional area.This faster speed means that the kinetic energy of the fluid has increased. The pipe doesn't perform any work on the fluid, leaving pressure differential as the only explanation for the changes in speed that are inversely proportional to cross sectional area. Therefore the pressure in the smaller diameter sections must be less than the larger diameter sections, because it's the pressure differential that peforms work and causes the acceleration and deceleration of the fluid as it transitions between sections of the pipe with various diameters (cross sectional area changes). I'll leave to others here to show the math, but if pressure is treated as a form of energy, then the total energy (the sum of pressure and kinetic energy), per unit mass, at any point in the pipe, is constant. So an increase in kinetic energy corresponds to a decrease in pressure energy, and vice versa, keeping the total energy constant. For all of this to work requires a closed system. There are no holes in the walls of the pipe that would allow the fluid to escape and/or re-enter the pipe. What's missing from this explanation is what is causing the initial and constant flow rate (maybe a pump), and what is going on at the ends of the pipe, but the cause doesn't have to be known, the important thing is that the flow rate is constant.