# Hydrostatic Paradox

The hydrostatic paradox is a counterintuitive phenomenon related to fluid pressure. It states the fact that in different shaped containers, with the same base area, which are filled with a liquid of the same height, the applied force by the liquid on the base of each container is exactly the same. However, if the shape of the container is different, the amount of the liquid (and as a consequence the weight) can greatly vary.

The water level in three connected containers is independent of their shapes and sizes. The pressure just above the water surface is equal to the atmospheric pressure. The pressure at the base (where bottles are connected to the rectangular container) is equal to the atmospheric pressure plus the hydrostatic pressure due to the height of the water level.

The pressure P, at depth h below the surface of a liquid open to the atmosphere is greater than atmospheric pressure by an amount $\rho g h$. Note that the height of the fluid column is important and not cross-sectional or base area or the shape of the container. The liquid pressure is the same at all points at the same horizontal level (same depth). The result is appreciated through the example of hydrostatic paradox.

Consider three vessels A, B and C of different shapes. They are connected at the bottom by a horizontal pipe. On filling with water the level in the three vessels is the same though they hold different amounts of water. This is so, because water at the bottom has the same pressure below each section of the vessel.

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