Thread 16837780

pressure is a function of depth, so they will empty at the same rate (assuming the bottom of tank y is funneled like x)

>>16837787
>At the same rate
First, not fastest. At least you're already disagreeing with Reddit.

>>16837793
underage? retarded? never took calculus?
if both are emptying at the same rate and they have the same starting capacity, then they run out at the same time

>>16837787
>>16837795
>sci is confidently retarded
They will drain at the same rate at t=0, but the level will decrease faster in Y so it will drain slower for t>0.

>>16837780 (OP)
X's tank is less full than Y's tank but Y's faucet pipe holds less.

>>16837780 (OP)
Tank X, based on the image. Tank Y looks like it has a flat base with a hole in it instead of a funnel to the hole like X does, so there will be water that forms stable droplets at the bottom of tank Y so that it will never empty completely.

Y because it has no fucking bottom lmao

>>16837780 (OP)
I would imagine that the shallow angle at the bottom of y even if there is a taper would cause more turbulence, but knowing physics there's probably some weird effect in fluid mechanics that make it dump at twice the speed completely counterintuitively, therefore y

>>16837780 (OP)
"These are not tanks.", but in French.

X_h would start out dropping slowly and then accelerate.
Y_h would start dropping fast and then decelerate.
This means P_X at the pipe will be higher for a longer duration = more water drained ?
Assuming this is true it should drain faster.
It also makes sense the inverted cone shape would have lower flow impedance than the wide flat bottom to small pipe transition.

>>16837807
It's okay anon. I saw what you were saying before reading down.

Thought about it for around 10 seconds and saw that bottom loading the water meant it would drain at a lower average pressure.

>>16837876
Welcome to /sci/ Mon-Agh-Mi Mon-Sherri

>>16837923
Wee-wee, but it's a drawing of a penis, but when you turn it upside down it's a banana instead, or an older family/social focused video game console. I can never remember.
Did reddit figure it out?

>>16837780 (OP)
It's really simple. If I drop a rock from 10 meters and I drop a rock from 1 meter at the same time, which one will hit the ground first? Tank Y.

>>16837998
>which one will hit the ground first?
the one that doesn't hit a random pedestrian in the head

Left tank. As they drain, the water level in the left tank will be higher than the right one with the wide base. Taller water column = more pressure = faster flow.

Same cross sectional area for exit pipe so the flow rate upon exit must be the same.

The tautochrone of spigoted tanks, if it exists, is the shape that drains in constant time no matter what the initial level.

>>16837780 (OP)
fuck reddit. also: the speed of flow depends on pressure, pressure depends on depth only. so they start at the same speed but the depth decreases faster in the right side, reducing outflow faster than the left side, so the left side will empty first.

>>16837780 (OP)
My gut says that pressure doesn't matter and they will empty at the same rate since they pass through an aperture of the same area and the only force acting on them is gravity
I'm going to assume they have the same funnel at the tap and the appearance is just an artistic choice instead of a gotcha
I'm not going to check what reddit says

>>16837780 (OP)
I fail to see how OP's pic is different in principle from picrel. Left one should have higher pressure.

t. programmer

>>16838456
P.S consider what happens if you gradually reduce the height of the smaller part: you approach the situation where it's just the big square at two different elevations.

>>16838456
The bottom of both of those have the same pressure

>>16838501
I didn't ask you, retard.

>>16837780 (OP)
X, level falls slower meaning higher pressure for longer.

>>16837780 (OP)
Left will empty faster because it maintains the highst pressure for slightly longer resulting in more peak flow.

>>16837780 (OP)
I know water pressure will be equal for both faucets at the start. Tank X will lose pressure slower than Tank Y at the start, and the reverse when they're almost empty. I dunno which would empty first.

>>16838043
Flow rate is a function of pipe diameter and pressure. Turbulent losses will be somewhat similar in both setups, but left has an advantage in turbulent losses due to having a smaller throat near the drain.

But left really wins because although the initial pressure (water column height) is the same, the right side's water column gets much shorter as the same volume of water is drained. Left maintains higher pressure for longer and thus drains faster and has less volume remaining at the same water column height.

>>16838213
>empty at same time
Just dump the entire thing at once. Or set a timer to dump it all and then pour the last milliliter at time t
>empty at constant rate
Possible with a resistive and turbulent pipe geometry or just a pendulum timer that measures a volume that it pumps.

>>16838213
I don't think such a thing exists.
There's no analog to momentum for fluids draining (except perhaps a small amount initially) so no matter what at higher initial levels you must necessarily pass the height of lower initial levels at about the same flow rate, which means it will always take the lower level's time plus some extra time for higher initial levels. Therefore, such a shape cannot exist.

>>16837780 (OP)
tank x gravity with heavier force cuh

>>16838213
that can't be, since the water that's not in contact with the tank isn't subject to the tank's shape

>handwavy bullshit
>no calculation
/sci/ is dead

>>16839070
The "tank" can be thin or branchy to make viscosity or momentum important.

same amount of water = same weight = same speed it goes down
QED

>>16839303
X has higher potential energy = higher average kinetic energy of outflowing water = higher average flow speed = X is empty earlier

>>16838368
Until they pass halway and the depth decreases faster on the left side of course

>>16837780 (OP)
The answer is none will empty: because it's an illustration and doesn't actually physically exist.

Assuming a vacuum, X.

Sci has average intelligence of a 18 year old.

>>16837780 (OP)
The left one.
It's more top heavy so it flips over and spills out all the water

>>16837780 (OP)
Tank X. Because the water is stacked on top of each other, meaning it'll push out faster.

>>16837780 (OP)
Though they will start emptying at the same rate, It is tank X because the level of the water in tank y will lower faster, decreasing the water pressure faster and thus decreasing the discharge. The water level in tank X will stay higher for longer, keeping the pressure higher, and thus the discharge rate will be higher for longer.

>>16839529
I regret to inform you that water only experiences pressure from water in the column above it, so the two tanks are equal in that regard

>>16838456
this only tells you A has more potential energy compared to B, not how fast each drains.

>>16839441
That's the peak intelligence though

>>16839640
When they are empty they have 0 potential energy, so what happened to the energy? It got turned into kinetic energy like anon said.
The mass of the water doesn't change, therefore the velocity does = faster flow rate.

X is evaporating more water per unit of time. Therefore, X drains faster.

Additionally, the coriolis force is greatest at the surface for X and the base for Y. So, for Y more than X, the coriolis effect would be counteracted by friction at the base -> heat. Therefore, given any friction at the base of Y, X would drain faster.

>>16839326
Depth is different to volume.

>>16839640
>this only tells you A has more potential energy compared to B
And what can this extra potential energy translate into?

>>16839640
>>16839973
Actually... yeah, I see more potential energy doesn't mean anything in and of itself, but in this case there's more water higher up relative to the opening, not just the ground. If it takes more energy to elevate a certain amount of water from the opening to the top then surely it has to dispense of more energy as it tries to come back down.

>>16839640
>>16838456
Consider the following MS paint scribble for a more rigorous scientific proof: even if you assume an equal drain rate for both tanks most of the way through, by the time 2/3rds of each tank are drained, you can just apply Torricelli's law v=sqrt(2gh) to the remaining columns of liquid and conclude the rightmost tank with the higher water level will finish draining faster.

Top wide empties first. Flow rate slows down slower because effective depth also reduces slower, and the effective remaining volume continues to decrease. The top narrow will initially appear to outpace top wide, but will be surpassed because the flow rate both drops faster, and the volume obligation grows faster relative to height of remaining water.

>>16837780 (OP)
X starts slow but the decrease in area increases pressure which increases flow rate.
Y starts fast but the increase of area decreases pressure which decreases flow rate.
Given the same volume, occam's razor would be saying they'll both drain in the same amount of time, BUT:
The bottom of X is a steep funnel, the bottom of Y is either a flat surface with a hole or a shallow funnel.
Thus, X should drain first.

looking at real-world systems where this matters, the answer is very clearly X

a low wide bowl or a tall narrow column which voids fastest?

If we agree that a pressurized container drains faster - like a closed tank and a compressor - then it stands to reason that the container with the most amount of pressure for the longest duration will drain faster - which is X due to more water being stacked on top of each other

Times will be the same if potential energies in the vessels are the same.

>>16837780 (OP)
shouldn't that be a pretty simple calculus problem? I'm a little rusty in my fluid mechanics but it seems like a textbook exercise one could calculate exactly instead of trying to guesstimate.

>>16840342
>shouldn't that be a pretty simple calculus problem? I'm a little rusty in my fluid mechanics but it seems like a textbook exercise one could calculate exactly
I guess? Couldn't you just integrate Torricelli's law over the varying cross-section of a tank?

X.
Reminds me of this Steve Mould vid.
https://www.youtube.com/watch?v=U7NHNT3M-tw

>>16840347
8:22 seems relevant to the problem

>>16840391
Ok back to old people what is our current cut age

>>16837787
if pressure is a function of depth then x will empty faster since it spends longer at a higher level

>>16840178
Shut up hindpoo faggot

>>16840446
>>16840446
>if pressure is a function of depth then x will empty faster since it spends longer at a higher level

That would be equalized below half height of water column.

>>16837780 (OP)
Water has viskosity wich is lower on greater cross section. So Y will be faster because that section is higher at lower pressure/level.

>>16840446
i realized that as soon as anon called me dumb.
but there is the competing effects of pressure and remaining volume to drain, and i haven't sat down to work out a mathematical description of the solution yet

>>16841554
Am i gonna have to just print the solution?

Simple matter of integrating the bernoulli matrix rotation over the cylindrical hedronic constant, effectively neutralizing the codeterminant flow rate factor and then we just solve for y.

>>16841556
nah, give it another day

>>16840347
i fear you didn't understand steve's video. according to it, they should empty at the same rate. the force on the bottom of the water is the same in both cases, meaning the flow rate in the spigots is the same. at least, initially. the spigots of X and Y will dynamically have different flow rates to balance out in the end. to wit: his video asserts that both funnels function as is there is invisible water in the empty space.

>>16838368
Pressure is force per area
Force is mass times acceleration (simplified)
As area changes, for proper calculation an integral over area and over time is necessary
I suspect that the left will drain faster as there is more mass applying force on atoms below
>Hurr durr pressure is le depths dependant
Are you retarded? It's simplification not accounting geometry, you are literally wrong

Water is incompressible. If vessels have same volume. Both vessels are equally tall, and spigot are identical and at the same height. Each element of volume has a potential which, upon exit at the spigot, turns into k.e., determining rate of depletion. Integrate potential over vessel. Vessel with higher potential empties earlier.