Why is the pressure at a given point in a fluid equal from all directions ie surely the vertical forces and the horizontal force forces can be different so long as they balance separately?

Answer 1

OK, then consider a diagonal direction, and the forces in that direction.

If the horizontal COMPONENT of force in that direction were not equal to

the horizontal component of force in the opposite direction, then some fluid

would move horizontally until those components were equal. Likewise, if the

vertical component of force in that direction were not equal to the vertical

component of force in the opposite direction, then some fluid would move

vertically until those components were equal. Eventually, once things settle

down, every component of force at that point in the fluid must be equal,

so the pressure on a tiny element of area at that point doesn't depend on

what direction the area is facing. qed

Pretty good for the spur of the moment, eh !

Answer 2

In a fluid at rest, the pressure at a point is the same in all directions due to the fluid's ability to transmit and distribute force through its particles. This is known as Pascal's principle. The different vertical and horizontal forces acting at the point are balanced such that the net force in any direction is zero, resulting in equal pressure from all directions at that point. It allows the fluid to maintain equilibrium and ensures the fluid can support objects immersed in it evenly.