For a fluid with viscosity to flow through a pipe that has the same cross-sectional area at both ends, at a constant velocity, there has to be a pressure difference according to Poiseuille's Law. Why exactly is there a change in pressure required to keep the velocity constant?
Is it because according to Bernoulli's principle that Pressure or Pressure-Energy gets converted to Kinetic Energy to speed up the fluid so the mass flow rate at both ends of the pipe stays the same?
So if that's the case in light of Bernoulli's principle, that means the change in pressure in Poiseullie's Law is there so that pressure energy gets converted to Kinetic Energy to fight off the viscosity of the fluid to keep the velocity of the fluid constant?
What exactly is Pressure? I know it is the Force divided by the area. I understand that concept, but I've seen the terms Pressure and Pressure Energy used interchangeably when talking about fluids, which creates for some amount of confusion. Aren't Pressure and Pressure Energy different? But when we talk about fluids in light of Bernoulli's principles, it seems as if Pressure and Pressure Energy are the same, which is pretty confusing.