Which one will fill first?
Four open containers of equal volume are connected as shown.
If the capacity of the pipes is greater than the flowrate from the tap, which container will fill first?
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15 solutions
What program did you use in drawing the water (color blue).
Container 3 is the lowest one, can we infer that irrespective of the connections, the lowest container will fill the first?
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It seems like the position of the connections don't matter at all, only the heights of their rim determine the order in which they are filled. This is a bit counterintuitive to me.
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Yes, the height of containers or even their widths won't matter. The container with the lowest rim will fill the first.
No... The problem specifies "three containers of equal volume..." I actually thought that 2 & 3 would fill at the same rate. Water will flow out of 1 faster than it flows in. And water will not flow into 4 until the level in 3 equals the level of the input pipe for 4. But as water flows into #2 and #3, I thought their levels would rise at the same rate.
Still confused...
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Note that container 3 is below 2. Is it possible for the water level in 2 to rise above its outlet if 3 isn't filled yet?
It is stupid task! If the FLOW = (aria x mass x velocity) of incoming water from nose in cap #1 =, or <, or > than opening from cup #1 to cup #2 there will be different results. Picture with blue flow is not correct. There is very big flow according drops and pressure is ~normal.in open top of cups, and so on, etc........
Question: Which container will fill first?
Answer:Container 3
Assumptions needed about whether there are water and air tight lids on the 'containers', whether they are on the same level (e.g. resting on the same table top), and whether they are all the same size (is there perspective to think about?). Not a well stated problem.
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If all are in the same level the way it connected is not possible. The diagram indicates all are same size containers and in the problem statement it is stated as "equal volume".
I agree with Venkatachalam J ...... . . . .
Considering the water flow from the tap to be slow, are you sure that the other containers will ever fill?
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Nah.....Container 1 & 2 will never fill i guess
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Other containers 1,2 & 4 will not get fill if the containers are open. The question is "Which container will fill first?". So it is clear that the container 3 will fill first.
container 3 will fill 1st...yes but my question comes in here....the inflow of container 3 and 4 are on the same level hence same p according to ehg..where=density h= height and g=gravity since the containers are not closed
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see my diagram container 4 is little higher then container 3 marked in the orange color. It is clearly marked "Low Level Container 3" and container 4 lower bound and upper bound marked with green line.
Will the water ever flow into the container 4 before the container 3 gets filled up to the brim ?
I'm new to Brilliant, have seen only a few problems, and am wondering about assumptions. I got this problem right at a glance, but only because I assumed that the rate of flow from the faucet ("slow" is not very informative) and the diameters of the connecting pipes are such that water in 1 and 2 can flow out as fast as it flows in. This and other Brilliant problems give me the impression that problem solving in Brilliant has as much to do with making reasonable assumptions and learning conventions as it does with mathematics, physics, etc. I'm not sure this is a good thing. I would prefer that critical assumptions be stated explicitly in the problem, if only as footnotes.
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I think this problem is more on logical thinking and it will not affect the problems on brilliant as a whole. In addition, this is just a level 1 question. There is nothing to worry about.
I agree with your concern, I originally thought that mentioning that the water from the tap fills the container slowly would suffice. However, now, I agree with you and I've edited the problem to explicitly mention this condition.
Hey, thank you for the problem.
I'm afraid there is another issue of unstated assumptions, with an impact on what the right solution is.
Container 3 will only fill up if the containers are open at the top just like container one. If the containers are closed at the top (except for container 1) air will get stuck in containers 2 to 4 above the connecting tubes (the upper connecting tube in case of container 2), making it impossible for them to fill up. In such a scenario, container 1 will be the only one to fill up, hence the answer to the problem being that it willo be the first one to fill. (Some problem solvers might also be tempted to think that this is actually a trick question designed to make one choose incorrectly container 3 as the apparent solution.) I think the problem should be formulated more clearly, in such a way as to prevent this misunderstanding.
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I think your concern is valid. I have edited the problem statement and mentioned that the containers are open.
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Thank you for your feedback. Keep up the good work and have fun!
I think it is clearly seen in the photo that all containers are open at the top. So containers 1,2 and 4 will not fill up.
"Four open containers of equal volume are connected as shown." Please read the problem.
The order of the altitudes of their tops is the order in which they would fill if we were to put a (sufficiently watertight) lid on each tank when it becomes full.
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Right, it's strange that the order in which the containers are filled does not depend on the position of the connecting pipes.
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The water moves from the higher gravitational region to lower, which is controlled by the height of the water in the containers and not by the position of the connecting pipes.
Tank 3 is the only one that will not yield any outflow water until it fills up.
3 is the only one that will ever be full. 4 and 2 will be filled upto the top of 3's level.
1 filled upto the bottom of overflow pipe. There after water will overflow from top of 3. Assuming overflow pipes can flow all incoming water. If overflow pipes are sufficiently small, 1 will fill first!!
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We ALSO assume that the inflow rate does not exceed the pipes' capacity to carry it.
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Thank you for adding what I missed. I added the comment since it was for level 1.
I agree that number 1 will fill first, and that 3 will remain full after filling next. I am interpreting the flow of water from the depiction which appears quite heavy, enough to overflow as the small amount exiting from the relatively insignificant outflow pipe can't keep up.
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The question mentions that the flow from the tap is slow, so, you should submit your answer based on it. Yes, If the image would have also depicted the same, then it would have been perfect.
I don't get it ... well, the answer at least. It looks like a heavy flow, there's a small outlet at the bottom of tank 1 which the output of which will gain pressure as 1 fills up, the fundamental question then is, is the pressure of the output of the smaller pipe of tank 1, greater than the pressure of the original tap? If all is equal, then tank 3 has the advantage of the extra long exhaust pipe, hence that will be 1st to fill, if not then Brilliant is wrong and am glad I haven't subscribed.
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The image might be a little misleading, but the problem stated that water slowly comes out of the tap, so I assume the flow cannot saturate the pipes connecting the containers.
And Mr Mendrin yes it will . Albeit a trickle. If the pipe was higher ...
wrong. it outflows immediately.
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We're assuming that the piping have negligible volumes. Tank 3 will not lose significant water until the water level reaches to the top bend of the outflow piping.
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You are absolutely correct. I ignored the heights.
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@Jack Higbie – Container 3 is the lowest one, can we infer that irrespective of the connections, the lowest container will fill the first?
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@Rohit Gupta – No. Consider what happens if the outflow pipe in tank 1 was near the top. Then it will fill up first before any water reaches any of the other tanks.
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@Michael Mendrin – No, it would remain almost full, and never fill up completely.
Depends on the flow rate possibly 1
The flow from the tap is slow. So, if it the water if carried by the connected pipes immediately then which container will fill first?
You're right, different flow rates would have different outcomes but it says "If the capacity of the connecting pipes is greater than the rate of flow of water from the tap" so that leaves 3 as the only correct answer
The first thing to consider here is the elevations of the containers. We can see that container 3 has the lowest elevation. The next thing to consider are the heights of the containers. Since it was stated in the problem that the containers have equal volumes, and we can see by our naked eye that the containers in the photo have equal heights, we can conclude that the heights of the containers are equal. Therefore, container 3 will be filled with water first since it has the lowest elevation. (Refer to my drawing). After container 3 is fully filled with water, the other containers will not be fully filled with water because water will overflow in container 3.
If the containers were not of equal heights but still of equal volumes then which container will fill first? The one with the lowest base or the one with the rim at the lowest elevation?
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Of course with the rim of lowest elevation, as seen in my drawing.
I feel like there's a minor catch in the problem's description that might impact the solution; please bear in mind english is not my first language.
If the rate of water from the faucet is greater than the "leak" from Tank 1 to Tank 2 - and how much water can flow through these tanks is in part determined by the width of connection between them - then Tank 1 might fill up first.
(As in: the rate of water coming in to Tank 1 [faucet] is larger than the rate of water coming out of it [Tank 1 - Tank 2 connection])
The question says that the water comes out "slowly" from the tap to fill in the containers. I think this can be taken as implied that the rate of water from the faucet is greater than the leak from tank 1 to tank 2.
The solution to this problem is rooted in Blaise Pascals Law of physics. https://en.wikipedia.org/wiki/Pascal's_law Pressure is equidistant and undiminished in all directions, thus the other containers cannot fill until the container at the lowest point fills due to gravity and the location of the pipes exiting the lowest container. 1 winter I worked in a hydraulic shop, and to me (Grade 11) this principle is the root of all hydraulic principles. IMHO
Because of the way the pipes are shown, container 3 would be almost filled by the time any water reached container 4. This is because the pipe from 3-4 must fill up before any water can go into 4, but 2 and 1 cannot fill until 3 has. Sorry, it was not my best explanation of a problem
Depends on the rate of flow from the tap! Interestingly, this graphic is different than the one in the email which suggests a much higher rate of flow.
Container 3 is the lowest, and will overflow eventually. However I take exception to the question of "Which container will fill first ". Container 3 will fill, and then overflow, so none of the others will ever fill up.
You are right, water will keep spilling out of container 3, and 1, 2, 4 will not fill up. If we seal the containers after they have filled up, then they fill up in the increasing order of heights of their rims.
The question is clear enough. But container 4 can't fill up. A slow flow rate will have low pressure...the water isn't going to flow uphill to 4
Yeah, 4 will never fill to the brim, before that the water will overflow from the 3.
Container 3 is in the lowest level and it has to fill up in order to fill tank 4.
What if the pipe from the container 3 is connected to the bottom of the container 4, then which one would have filled first, 3 or 4?
I believe it is container four because it feeds off container 3.
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Water flows from the higher potential to lower. Does not to feed from container 3, the water level in 3 should be higher?
The container 3 is on the lowest ALTITUDE.
Hence, it will fill first before anyone else.
Ans. CONTAINER 3
Are you suggesting that irrespective of the connections the lowest container will fill first?
The 3rd tank has the minimum potential. So water will prefer going there in order to minimize its potential.
Cosidering all tanks are of equal size, and tank3 has the lowest base.
3rd container will fill first because water flows from higher potential to lower .so...the rate at which the water is entering to 3rd container is greater than the rate at which the water escapes from that container
Container 3 is the only container to fill- it has the lowest top, and as soon as it fills it will begin to overflow (assuming the water flow rate from the tap is low enough to not cause tank 1 to overflow first).