Hydrostatic Paradox

Hydrostatic Paradox 

the seeming contradiction that the weight of the fluid poured into a vessel can be different from the force of the pressure exerted by it on the bottom of the vessel. Thus, in a vessel that is wider at the top, the force of the pressure on the bottom is less than the weight of the fluid, whereas in one that is wider at the bottom, it is greater. In a cylindrical vessel both forces are the same. If the same fluid is poured up to the same height in vessels of different shapes but the same bottom areas, then despite the differences in the weight of fluid poured into the vessels, the force of the pressure on the bottoms is identical for all the vessels and is equal to the weight of the fluid in the cylindrical vessel. This follows from the fact that the pressure of a quiescent fluid depends only on the depth under a free surface and the density of the fluid.

The hydrostatic paradox is explained by the fact that, since the hydrostatic pressure is always normal to a vessel’s walls, the force of the pressure on the inclined walls has a vertical component that compensates for the excess weight of the volume of fluid in a vessel that is wider at the top than a cylindrical vessel with the same bottom area and compensates for the lack of weight of the volume of fluid in a vessel that is narrower at the top. The paradox was discovered by the French physicist B. Pascal.