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There are 3 containers ,having the same base area ,having being filled with the liquid of same density to the same volume as shown in the figure.

the three vessels

What will be the force exerted on the base in each case?

I think that the forces must be equal since equal masses are present in each case , hence force must be mg.

But thinking in another way, writing force as the product of pressure into area, i get that the force will be maximum in the third vessel since height will be the highest.

Which argument is correct and why?

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  • $\begingroup$ Is this the fluid force only, or also the sides of the container pushing down on the base. Please clarify. $\endgroup$ Commented Nov 29, 2020 at 21:11

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It depends.

The Pressure * (Base area) is different as you said.

But total force (weight) must be the same

In the vessels with inclined sides, you have the pressure working on the sides, that has a vertical component, down (first vessel) or up (third vessel). This component should fix the paradox.

See same question Vessels paradox

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