B 'splain this hydrostatic paradox in tiny words

[DaveC426913]

TL;DR

I understand how hydrostatic pressure works in a straight walled container but this makes no sense.

This is (ostensibly) not a trick shot or video*.

1. The scale was balanced before any blue water was added.
2. 550mL of blue water was added to the left side.
3. only 60mL of water needed to be added to the right side to re-balance the scale.

Apparently, the scale will balance when the height of the two columns is equal.
The left side of the scale only feels the weight of the column above the lower "tail" of the funnel (i.e. 60mL).

So where does the weight of the remaining (550-60=) 490mL go??



* Sorry, Facebook's auto-refresh has made the source material vanish.
UPDATE: Found on Youtube:

 

[jbriggs444]

So where does the weight of the remaining (550-60=) 490mL go??

I assume that the mechanism includes some sort of identical pistons inside the vertical glass walled tubing. The scale pans are then responsible for supporting the bottoms of the two pistons.

You see the clamps that hold up the two containers? That is where the extra weight goes. The extra weight of fluid on the left is supported by the clamp on the left.

The extra fluid pushes down on the diagonal container walls in the left hand container. By Newton's third law, the container walls push up on the extra fluid.

One can do the analysis in a number of ways. A way that pleases me is to draw imaginary boundary lines (as has been done in the image) and add up all the forces on each partitioned parcel.

 

[Ibix]

I assume that the mechanism includes some sort of identical pistons inside the vertical glass walled tubing

Yes - that's shown explicitly in the YouTube video (which may have been edited in after your post).

 

[A.T.]

So where does the weight of the remaining (550-60=) 490mL go??

As a general rule: If the walls are not vertical, they will exert vertical forces on the fluid, which depending on which way they deviate from vertical, can act upwards or downwards.

That's 'where the weight goes' or 'the extra weight comes from' in those paradoxes.

 

[DaveC426913]

As a general rule: If the walls are not vertical, they will exert vertical forces on the fluid, which depending on which way they deviate from vertical, can act upwards or downwards.

That's 'where the weight goes' or 'the extra weight comes from' in those paradoxes.

Why does the scale not seem to feel 550g on the left side? What if we scaled that up by a few kg?

 

[DaveC426913]

You see the clamps that hold up the two containers? That is where the extra weight goes. The extra weight of fluid on the left is supported by the clamp on the left.

? Aren't the clamps just there to keep the pistons upright? Don't the apparati float freely in the clamp's grasp?

That might be where I am misapprehending the setup.

Ah. Yes. That's is exactly it. I misunderstood the apparatus.

The clamps and bases feel the extra weight.

Thank you.

 

[Ibix]

Why does the scale not seem to feel 550g on the left side? What if we scaled that up by a few kg?

If you put the two clampstands on scales, the left one would show the "missing" weight.

The walls of the vessels exert force on the water normal to their surface. In the vertical cylinder, therefore, they only exert horizontal force on the water and support no weight. The cone, though, exerts forces with a vertical component and supports some of the weight of the water - so the left clampstand carries extra weight.

 

[Baluncore]

By hiding some important details, they would get more clicks on the video.

I expect identical glass pistons, that press on the scale pan at the bottom of each column, would slide freely in the column, probably with Vaseline as the seal and lubricant.

 

[Motore]

Everything is neatly explained in the video, also how the clamps support the remaining weight.

 

[sophiecentaur]

this hydrostatic paradox​

When the word "paradox" is used, it usually means that the questioner doesn't know enough, hasn't been rigorous enough or has read something that's deliberately designed to fool the reader. Paradoxes (at least unexplained ones) are extremely rare in Physics.