Pressure is equal or force is equal at the bottom?

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In the discussion about pressure at the bottom of two equal-volume containers, participants agree that while the pressure at the bottom is the same due to the fluid's height and density, the forces exerted on the bottom differ because of the container's shape and sidewalls. The upward force from the fluid on the bottom is influenced by the sloping sides, which affects how the total force is distributed. Although the weight of the fluid remains constant in both scenarios, the net force acting on the bottom varies due to the geometry of the containers. The conversation emphasizes that pressure is isotropic and independent of the container's shape, but the resultant forces differ based on the configuration. Ultimately, the key takeaway is that while pressure is equal, the forces acting on the bottom are not, highlighting the importance of considering the entire system's geometry.
  • #31
Again volume of both the fluid is same ; so the density. That means weighing machine would read same for both.
Pressure will be same at the bottom of container because it is dependent only on the height of water column.

In the first figure the slanted wall will exert force on the downward direction plus the weight of the fluid also acting downward, that will be compensated by larger flat base
In the 2nd figure slanted wall will exert force on upward direction, that will compensate only weight of the fluid; no need of larger flat base.

Moral of the story; same net force, same pressure on the bottom of the two tank.
 
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  • #32
Ravi Singh choudhary said:
Moral of the story; same net force, same pressure on the bottom of the two tank.

Yes, that's correct. If one draws a free body diagram of a small patch of each container bottom, then the force applied to the inside is the same in both cases while the force applied to the outside of the elements changes depending on the bottom area. The net force on these elements must be zero. This additional force is applied at he edges of the elements and originates from stresses applied from the slanted walls.
 

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