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According to what I've gathered, in static fluid, the pressure at any point in the fluid depends on the depth within the fluid, because there is more fluid weighing down on an object the deeper into the fluid it is. However, for some reason, the forces due to pressure are acting in every direction, which means at a given depth, the net force acting on an object would be the pressure*SurfaceArea at the bottom of the object - the pressure*surfaceArea at the top of the object, and horizontal forces would cancel out because they're going in opposite directions and there's no difference in pressure horizontally through a fluid.

A question I have though:

a) If Pascal's principle is true that pressure is evenly distributed throughout a fluid, what does this really mean if at different heights within a fluid, there is a different amount of pressure? Is the pressure being exerted on a particular point of the side of the fluid container greater than the pressure exerted on a lower point on the side of the fluid container?

Further, what I don't understand then is pressure in fluid in motion. Regarding a (steady-flow, nonviscous) fluid flowing through a horizontal tube, my questions are:

b) How is the fluid moving in a direction? How come the horizontal forces due to pressure in this case don't cancel out horizontally like they do in static fluid? Or is the pressure referred to in things like Bernoulli's equation referring to the pressure the fluid exerts on the tube and not the pressure within the fluid?

c) Is the pressure the fluid exerts on the top wall of the tube less than the force it exerts on the bottom wall of the tube? Or does something about the fact that it is moving cause the pressure to be equal throughout.

Even if you don't explicitly answer all my questions, if someone could provide maybe an evident gap in my understand that's causing my misunderstandings I would greatly appreciate it, thank you.