Watering Cans
The two watering cans above have equal base areas. Their spouts are both open. Which of the two cans can hold a greater volume of water in equilibrium in the upright positions as shown above?
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13 solutions
@Tony Witham Better clarity to say: tip the can back to raise the spout; then the can could hold half it's empty volume of water, and the comparison depends on the relative depths of the two cans.
If the two cans are rotated clockwise by about 40 degrees, the blue can can hold more water than the red one
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Why is that so? Do you want to rotate it left or right?
In problem solving, our solution is based from the given facts in the problem. And we must use our common sense. Rotating the can in 4 0 ∘ is not part of the problem.
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@Marvin Kalngan - the question simply asked which can could hold the most water. It did not specify that the cans had to remain in the upright position. I was simply pointing out that there were situations where the blue can could hold the most water
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@A Former Brilliant Member – Okay. Now I understand.
Wow, it was a great explanation. Kudos!
Wondering, will it be a good idea to have a smaller spout but make it at the upper part of the can?
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Well, the diameter of the spout opening doesn't not play a big role here.
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What I meant here is, what if we move the spout of the blue can higher towards its rim, so that the blue container will hold more water even with a smaller spout. Will that be a good idea?
@Marvin Kalngan - how did you create these images?
We can use the formula for the volume of a right circular cylinder, , the volume of water in the red can is greater than than
But the water won't stay at the same height ,right? Because the velocity at the opening is different than the velocity inside at top of the water ,so this will be at a particular moment?
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The logic here is, after sometime the water stops moving ...
It depends on your definition of the word "holds" you can put more water in the blue can but it will spill out .It will hold more - for a while- . If you mean permanently then eventually both cans will rot away at some point and neither will exist let alone contain water.
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The problem is fixed now. It says, " Which of the two cans can hold a greater volume of water in equilibrium in the upright positions?
It depends on what your definition of 'holds' is. Indeed the red can will fill to a higher level assuming that the quantity of the water filling the cans is not more than the quantity of water exiting the spout or the flow of water has stopped after the cans have reached capacity. If the water is at a higher intake than outtake then it is safe to assume that if the water intake is consistent the blue will hold more water than the red can.
If we do not consider the spout, then Blue container would be the answer?
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We must consider the spouts because they are open.
While Red is definitely the right answer once the system comes to rest, Blue can hold more water for a short period of time. You can fill it all the way to the top. The water will run out until it reaches the level of the top of the spout, but for some period of time it will hold more than the Red can.
It's a matter of definition as you say. Which of these cans can hold more water - under what condition? When a finger is placed over the spout's end, then blue will hold more.
Agreed, this is the common sense answer. Imagine if you had a firehose and started to fill the blue container - due to the pressure of the water flow you would definitely fill the blue can to the top faster than it would run out of the spout. Forget formulas here peeps, use your brain!
You really need to add the words "in equilibrium". The narrower diameter of the blue spout will greatly reduce the rate of flow cf the red.
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The problem is now corrected, it reads " Which of the two cans can hold a greater volume of water in equilibrium in the upright positions?"
The word "hold is key. Blue is not holding more water even if you attempt to fill it to the top the way you described. The blue can is a pipe with water flowing through it. When the water stops flowing and is held we can compare it to the red can.
This is due to the known force of gravity pulling down on the water in both containers applying pressure to the spouts from the bottom outward. Under a vacuum, these containers are free of such pressure and without open ends the blue will hold more. The physics are relevant to a period of time and space in a said location or condition. Gravity or other external forces in that location must be taken into account and applied. Here is a better question, what time would it take in T for the blue container to lose water out of its spout due to the gravity of Jupiter compared to Earth's?
The length and height of spout of red can is more as compare to blue can. so red can hold more water
Does the length of the spout play a role in deciding the height up to which the can could hold water? What if the smaller spout of the blue watering can be at its upper portion to have a greater height than the red can?
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The trick here is to see\look which spout opening is higher or lower. The lower the spout opening, the lower the height of water. The diameter of the spout opening doesn't play a big role here.
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Ahh, by smaller I meant in length and not in the diameter.
More importantly, who in their right mind would design, make or buy a can like blue one?
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Right, the blue one is an impractical design. This explains why the spouts in watering cans open above rim of the can: it helps store more water in the can.
The specs did not say if water was continually added. Us engineers used to solve all these problems of how fast a container would empty with a hole. Before both buckets would empty down to the spout level the blue would have a great deal more liquid. Also, if you tip the buckets away from the spout the blue would hold more liquid. If you want to ask technical questions please be more specific. I would have gotten fired for not asking more questions before providing an engineering solution. Richard the Engineer
Gravity and the pressure it applies to the water over time is one big factor along with the fact the container is open ended and the length of its spout - this is where the formula V = a * h applies.
Because of how liquids occupy space the water is limited to the height of the tip of the spout. The red spout is considerably higher assuming the cans are the same distance away from the viewer. This means that the red pot (in this position) will hold more water.
The radii of both the cans are equal as given in the question.
Wrong!
The blue can, being larger, can obviously hold more water for a short time (until ithe water has run out through the spout)! No minimum time for holding water was specified in the question.
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Naw bro you lost
The problem is now corrected, it reads " Which of the two cans can hold a greater volume of water in equilibrium in the upright positions?"
I hope this clarifies your point.
It depends on what your definition of 'holds' is. Indeed the red can will fill to a higher level assuming that the quantity of the water filling the cans is not more than the quantity of water exiting the spout or that the flow of water has stopped after the cans have reached capacity. If the water is at a higher intake than outtake of water then it is safe to assume that, if the water intake is consistent, the blue will hold more water than the red can.
Volume in this case is dictated by the height of the end of the spout, not the height of the container.
Yes, the height of the container does not matter as long as it is higher than the height of the spout. We only need to compare the heights of the lowest opening of both containers.
It's a issue of equilibrium. The spout of the red can is bigger than that of the blue one, but it is also longer and higher. Therefore, more water pressure is need to push the water through the spout. Meaning: More water is required to push the water through the spout of the red can than through the blue can. The red can will hold more water before it starts to lose water.
the water spout for the red can is higher , and thus the water will equalize at a higher level between the main tank and the water spout. Whereas the blue water can the spout is lower and only water to that level can accumulate in the blue can, before it drains out of the spout.
If radius of both the container are similar, the level of water in a container is determined on the basis of orifice (outlet). The distance from the base to the orifice is larger in the red can compared to the blue can. In short, higher the outlet or spout is, there will be more volume available to hold liquids.
I was confused at first because the blue can is higher. Now I know what's wrong :)
Exactly, it is the height of the outlet that decides how much water a container can hold. If we drill a hole at the bottom of the can, it won't hold any water in it irrespective of how high the can is.
The blue although taller in size the sprout will leak out a large volume of water as it is much lower than the red.
Right, increasing the height of the can won't help store more water if it is above the opening of the spout.
The red one by the principle of communicating vessels. The jet of irrigation is higher than the one of the blue therefore if it is less high it will be able to maintain more water in its interior in vertical position
What is the principle of communicating vessels?
https://www.youtube.com/watch?v=XXWloodBwnA
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This is a nice video, thanks for sharing. It is amazing that the water surface in a container is flat even in an irregular shape container.
The level of the spout is the maximum resting volume of either can. The red can's spout is higher, with the same diameter, yielding a larger volume than the blue can.
Great, we just have to look which can has the higher "lowest opening".
A somewhat different approach-first assume both the spouts to be 'blocked' ( by a cork or something). In this case, clearly the blue can holds more water, as it is larger. Now, simultaneously 'unblock' the spouts. A little thought should convince you that the can which spurts out water at a lower speed would be the same as the can which which holds more water when spouts are open ( a CRUDE way to say this would be to say that both the situations essentially hinge around the same principle- you want to reduce the rate at which you lose your volume, in other words you want to maximize the volume inside your can ). One can also imagine this mathematically- if you assume your volume to be a function of,say time, (even height would work), then your maximum volume(or minima) occurs when the rate of change of volume goes to zero.
The rest is simple. The blue can has a greater amount of water above it; and hence greater pressure to push it out from the spout. So it has a greater rate of change of volume, as water spurts out more quickly(remember that the speed varies directly as the square root of height.) On the other hand, the red can, being shorter, allows us to conclude that the pressure to push out water from the spout will be less( a simple application of Bernoulli/Toricelli law), and hence it loses its volume at a slower rate. Consequently, it can hold a greater amount of volume.
A pretty badly defined question; if we tilt the cans 45deg and therefore they will not be in vertical Position, the blue one will hold more water.
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Thanks for catching this. I see that the problem has been edited to address this issue. It now says that the cans are in upright positions.
Tilt the blue can
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The problem is now fixed, it is mentioned that the cans are placed in the upright positions.
Not a well defined question. Certainly the position of the spout is important but the problem leaves too much room for speculation. Good for discussion but not for a black and white answer.
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Thanks for catching this. I see that the problem has been edited to address this issue. It now says that the cans are in upright positions.
As usual the issue is in the questions and what we interpret its meaning to be - that is, people who miss this are likely not wrong, they are just misinterpreting the question. First, the perspective and realism of the drawing is suspect. Second, OK, the spouts are open, but the question asks - which container "can", as in is able to hold a greater volume. The blue can would have the greater volume, so it should be the right answer, but the information about the spout must be considered ... why is it there? To add to the information or confuse the issue. This becomes a non-question if you draw the containers in schematic form, and define what you are asking clearly.
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Thanks for catching this. I see that the problem has been edited to address this issue. It says "Which of the two cans can hold a greater volume of water in equilibrium..."
We can use the formula for the volume of a right circular cylinder, V = a r e a o f t h e b a s e × h e i g h t , the volume of water in the red can is greater than the volume of water in the blue can because the height of water in the red can is larger than the blue can. Note that they have equal base areas.