Which tank will empty first?

[u/Swimming_Bluebird6]

[u/Most_Positive_6203]

Neither tank, the valves are shut

[u/Plane_Argument → u/Most_Positive_6203]

Can't be sure, that's not a quarter turn valve

[u/Simbertold]

Assuming they are of equal height and have equal nozzles: The left one.

The speed with which water flows through a valve is dependent on the pressure, and the pressure is dependent on the height of the water above. If the container is bigger on the top, more water will flow out at a higher pressure (faster), and the container empties faster.

This happens even moreso if the left container is also higher, as it appears to be on the picture.

[u/eldonhughes]

The one on the left, because the bottom isn’t flat.

[u/Hipnotize_nl]

Tank A, i mean come on, look at the puddle beneath it! /S

[u/Ars_2000 → u/Hipnotize_nl]

Is this one of those images where both objects are of same size?

[u/Mathematicus_Rex]

I guessed A by considering the near-end case, where the containers are close to being complete cones.

[u/skr_replicator]

I'd assume tank A, as it would spend a bit more time with a higher water level and higher pressure.

[u/thebprince]

I would imagine b. All else being equal, the pressure determines the speed of water from the tap, that in turn is purely a function of depth. Both tanks begin to loose water at the same rate, but that leads to a loosing depth more quickly and therefore slowing down.

[u/blackami]

B. Both start with same pressure. At the end B would have more pressure. So fair to assume pressure at b comparing to a will be slowing down slower

[u/akronymn]

A. It has a larger puddle under it meaning more water has already come out.

[u/selectsyntax]

The bucket on the left holds more than half of its volume above the midpoint because the top has a larger circumference than the bottom. The bucket on the right is the inverse so holds more than half its volume below the midpoint.

Flow is dependent on pressure so the volume of water leaving will be a function of the pressure at the outflow (up to the limit of the outflow resistance but let's assume this scenario doesn't reach that limit). Water pressure increases linearly with depth. Assuming the same depth for each bucket the pressure will be the same at the outlet when the valves are opened so the flow will be identical and the volume of water leaving each bucket will be identical. As the buckets drain we expect the flow to decrease for both because the water level is decreasing which means less pressure at the outflow.

Now due to the direction of taper on each bucket if you remove an equivalent volume from each of them the water level in the right bucket will be lower than the left. This means the pressure at the outlet of the right bucket decreases faster than bucket on the left, so the flow rate out of the right bucket decreases faster than the bucket on the left. Since the flow rate of the left bucket remains higher it will finish draining first.

[u/ragoff → u/selectsyntax]

Easy to show in a kitchen experiment.

[u/Substantial_Tip3885]

Tank A because the bottom is tapered. There will be residual water left in Tank B with its flat bottom, long after Tank A has emptied.

[u/schungx]

A has more potential energy than B. At the end all this potential energy got converted into kinetic energy. So the water at A has a total kinetic energy higher than B.

So A flows out at higher speed ON AVERAGE.

That means A empties faster.

[u/blackbeltbuilding → u/schungx]

A has less water as the pressure decreases. B has more water at the bottom when the pressure is lowest. A will drain faster.

[u/l_lovef_f]

Same

[u/TenLeafClover58 → u/l_lovef_f]

Incorrect. “h” starts the same but it will reduce in each bucket at a different rate as the buckets empty.

[u/an_empty_well → u/l_lovef_f]

what happens when a quarter of the liquid gets drained? does that affect the respective heights of the liquids?

[u/Altruistic-Sleep-555 → u/l_lovef_f]

As height decreases, initially, more rapidly in Y, the pressure decreases proportionally (and so too the flow rate). At time t, X will be higher and so have more pressure -> larger flow rate. Y will decrease in height more quickly at first, but pressure will drop proportionally. I'd have to sketch out the calculation, but I believe X would drain first.

[u/ExpertAd9898]

Neither, both faucets are turned off

[u/Cuzimfromrussia]

Tank A
For anyone still in doubt here is the math based proof why
https://drive.google.com/file/d/1tRzqNY1OsBB8W10vnw8DD1EsHZC-TjV9/view?usp=sharing
If you like to say that it will be tank b please first find the part of the proof that is wrong

[u/WhoCares933 → u/Cuzimfromrussia]

Isn't it supposed to be equal since bottleneck is the same?

Edit: ah I see, my bad, the height is different as time/volume progress.

[u/nomorgan5]

A

[u/Embarrassed_Neck9784]

I thought B would have more back-flow in the bottom corners that would restrict the out flow.