Which Triangle Experiences Greater Force in a Water Tank?

[nasu]

If prism no 2 is sealed at the bottom, the "hydrostatic force" is larger on it, as in the proposed answer. It is not really buoyant force, as it points downwards.

On prism 1 we have the two equal forces on the sides, 2Fs (up) minus the force on the flat top Ff (down).
For the prism 2 we just have 2Fs (down). 2Fs> (2Fs-Ff)

 

[DTM]

Equal volumes submerged in fluid of equal density. Unless you are going for second order effects where the fluid is more dense when deeper.

Although the net buoyant forces are equal, the magnitude of the forces on the individual faces are different. If you had one scuba diver 10 feet down and another 100 feet down, their net buoyant forces are equal as they are both neutrally buoyant, but we would say the deeper diver has more force on him as the pressure all around him is greater. Another example would be if, instead of triangles under water, you had 2 weight lifters, one lifting a 10 lbs barbell above his head and another lifting a 100 lbs barbell. Which lifter has more force on him? Would anyone honestly answer they are both equal to 0, because they are not accelerating? In practical terms, when we speak of forces on things, we are concerned with stresses and strains. (Can you guess I'm an ME?) For every statics problem in the world, the net force is 0, but the load on the object creating stress is non-zero.

 

[eltodesukane]

The question is part of a mechanical aptitude test. The correct answer is 2, but there is no explanation.

I do not understand why is 2, and not "equal on both". Can anyone give me some clues?.

-- because 2's center of gravity is deeper than 1's center of gravity

 

[georgir]

the liquid may be subject to compression with increase of pressure, so the densities arent really equal. though that effect is minimal for water, the liquid and the distances here are unspecified so it is a possibility. so even the archimedes force could be different for the two triangles.

 

[votingmachine]

-- because 2's center of gravity is deeper than 1's center of gravity

This was also said in another post, and I have to echo it.

Look at the very bottom of the tank (say it is 10 meters in depth) ... that is the highest pressure. And the upside down triangle has a single point at that depth, while the rightside up triangle has an entire side at that pressure. The upside down triangle has an entire side at the lowest submersion, while the rightside up has a single point.

It is intuitive to think they are the same. The same shapes at the same depths. But the orientation actually puts one as deeper than the other, due to the center of cross sectional area. And due to the distribution of the asymmetry along the depth, there is difference in cumulative pressure.