Suppose we apply an external force as shown.
The pressure from the external force spreads throughout the fluid.
Here, we are in a zero-gravity environment.
Eventually, the pressure of the fluid will be the same everywhere throughout this container.
This principle applies both to fluids and to gasses.
Let’s now consider a slightly different scenario.
Let’s also apply an equal external force on each of the other red rectangles.
Since the pressure of the fluid is the same everywhere, this pressure balances each of these external forces.
As before, we are in a zero-gravity environment.
If we replace the five small rectangles on the right with one large rectangle, all the forces will still balance.
The total external force on the right rectangle is five times the external force on the left rectangle, but the forces from the fluid pressure still balance everything.
In this next example, we are again in zero-gravity, but this time the external force on the right rectangle is only three times the external force on the left rectangle.
Here, the smaller force manages to overcome the larger force.
There are many practical applications of this principle, such as the hydraulic lift, which allows us to raise extremely heavy objects.
This works because the force from the fluid is the pressure multiplied by the surface area, and the larger rectangle has a larger surface area.
This does not violate the conservation of energy, because the energy transfer is the force multiplied by distance travelled.
The left rectangle feels a smaller force, but it travels a longer distance than the right rectangle.
Up until now, we have neglected the effects of gravity on the molecules.
Gravity will cause the pressure to increase at deeper depths, due to the weight of the fluid above.
But, in steady state conditions, at any specific depth below the surface, the pressure is the same throughout the fluid at this specific depth.
This remains true regardless of the shape of the container, due to the thermal vibrations of the molecules.
The effect of gravity on fluid pressure is discussed in detail in the video, "Archimedes' Principle in the Molecular World."
And the rarely discussed explanation of why pressure drops at higher fluid velocities is discussed in the video "Bernoulli's Principle on Atomic Scale."