# Hydrostatic pressure at lateral directions

I just read that, with respect to a stationary tiny cube, suspended in a fluid, that has a negligible weight and dimensions:

Pressure is the same in every direction in a fluid at a given depth, if it weren't the fluid would start to move.

This made sense to me the first time, but then I realised that the condition for the fluid not to move is that the net force is zero. However, the net force being zero doesn't necessarily require that forces in all directions are equal, just that two forces pointing in opposing directions are equal?

So say, the vertical forces on a cube, pointing up and down, are 1N each, but then all the other forces pointing towards the sides of the cube, may as well be 10N each, and yet all the forces would cancel each other out, resulting in a net force of zero.

Am I missing something here?

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## 1 Answer

Here pressure is hydrostatic pressure.

http://en.wikipedia.org/wiki/Buoyancy#Simplified_model

Look at the above link of Wikipedia. It is well explained there with cartoons.

Pressure is not vector, it is a scalar quantity. Also, have a look here for fluid statics : http://en.wikipedia.org/wiki/Fluid_statics#Pressure_in_fluids_at_rest

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From the first link, "The sides are identical in area, and have the same depth distribution, therefore they also have the same pressure distribution, and consequently the same total force resulting from hydrostatic pressure, exerted perpendicular to the plane of the surface of each side." Can you care to elaborate on this? I still do not really understand why the pressure acting on the top face must be equal to the pressure acting on the side, directly below the top face. –  Soyuz Apr 2 '13 at 17:14
Ah I think I get it now -- "the same pressure distribution" leading to "the same total force resulting from hydrostatic pressure" is a result of pressure itself not being a vector, but being a scalar quantity. –  Soyuz Apr 2 '13 at 17:22