Rotating Pipes
Water is flowing out from the 8 holes of a star-shaped sprinkler. When the sprinkler is stationary, the water flows as indicated by the blue dots in the diagram above (when seen from above).
How does the water stream appear from the top when the sprinkler is rotated counterclockwise?
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11 solutions
Great solution, you have explained it quite nicely! As shown in the gif, each "particle" is moving away from the center of the sprinkler, and their direction is fixed. However, each particle moves in a different direction depending on which direction it was released, so the stream appears to be curved.
PS: ezgif.com is great tool to compress gifs.
Relevant wiki: Newton's First Law
Newton's first law of motion tells us that the water leaving the sprinkle tends to move in a straight line.
Ignoring gravity to understand the pattern (in reality the water will also fall down), this means that when the sprinkler turns counterclockwise, the water stays behind, resulting in pattern B.
Certainly the water will appear to move in an arc as shown in B, but it will actually flow in a straight line once it has left the sprinkler and no external force is applies to it other gravity.
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That is indeed the case, as I tried to explain. In reality, with small droplets, friction will also have a significant role.
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What I meant was that A is the correct answer to the question. It only LOOKS like B when viewed from above. The question asks 'How does the water flow?' NOT 'How does the water APPEAR to flow?'
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@Michael Jarvis – Yeah, I'll let a more native speaker handle that interpretation. I get what you (and some others) mean though.
@Michael Jarvis – The images are snapshots of the setup. They show the position of water droplets at a single instant of time. I have updated the problem statement to better clarify this.
Michael Jarvis is correct; the water FLOWS in exactly the same way regardless of the motion of the sprinkler, either rotational or transversely. In the rotational counterclockwise case, the water APPEARS as shown in B.
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The question is worded poorly. Way too many questions on this site are worded either poorly or incorrectly. Where is the "quality control?"
Thanks. The images show a snapshot of the positions of a series of drops in one instant of time. I have updated the problem statement to clarify this.
I recently answered this question on the Coriolis effect - https://brilliant.org/practice/coriolis-force/?p=3 - and I tried to apply these principles to this problem and came up with the answer C, even though I knew intuitively that B was right. I deduced that taking the particle at the 10 o'clock position for example, that the drops of water will leave the sprinkler with tangential velocity pointing left and down, therefore causing the spiral arm shape of C. I know this is wrong, but I'm having a hard time understanding why. Is there any frame of reference from which the pattern would look like C?
Thanks in advance!
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Why would a drop leaving the sprinkler have a leftward component of velocity (relative to the pipe where it flows in before)? It only has a radial component, i.e. a component in the direction of the pipe it comes from and that is (ignoring friction, gravity, ...) the only one it will keep, so from above we will get pattern B, which is exactly what happens in Earth's atmosphere as well with winds moving Northwards seemingly deflecting eastwards (Southwards/ westwards).
When doing your physics in the rotating frame, the fictitious Coriolis force pops up, but in essence this is just a manifestation of Newton's first law.
There is however no frame of reference in which the pattern would be like C.
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I think that C is right, because when you spin it, water hits the side which pushes it further, making a shape like C. This was shown in the Exploritorium in California.
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@Eric S – Right, this setup is often seen in science exhibits. The direction depends on whether water is moving radially outwards or inwards while leaving the sprinkler. Both directions are shown in this gif:
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@Pranshu Gaba – So it's also a Coriolis Effect? :)
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@Wenjin C. – Please see my comment to Chris Cross above. If you are tracking the path of one particle for a period of time, and if you are in the rotating frame of the sprinkler, then a particle will appear to move clockwise because of the coriolis force. The coriolis force is an imaginary force which arises because we are in a rotating frame of reference.
The images in the problem are like photographs of the setup. They show the position of all the drops at one instant of time, so the image of the drops of water will appear the same regardless of our frame of reference.
If you are tracking the path of one particle for a period of time, then yes, the path will look different depending on your frame of reference.
In the inertial frame, a particle will move in a straight line, because net force on the particle is zero.
In the rotating frame of the sprinkler, a particle will appear to move clockwise because of the coriolis force.
If you are in a rotating frame in which the sprinkler appears to be rotating clockwise, then the path of the water will appear like C.
I agree that this is a poorly worded description, along with an ambiguous diagram. Each individual droplet of water will exit in a straight line; only the perception of a stream describes an arc. The question is stated "How does the water flow?", which begs the question. If the row of dots represents the path over time of a single droplet, then "A" is the answer. If It represents a moment in time for a series of droplets, then "B" is correct.
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Thanks. The images show a snapshot of the positions of a series of drops in one instant of time. I have updated the problem statement to clarify this.
The water cannot bend backwards unles an additional external force is applied. Therefore once the water leaves the sprinkler, it will continue in s straight line. Due to the sprinkler turning, however, it will appear as if it is bending backwards but in reality, it will still be a straight line.
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Right, if you look at a small section of the water stream, it moves away from the center in a fixed direction. The sprinkler is rotating, so the new section of the stream moves in a different direction.
"how does the water flow, not 'appear' to flow " agreed, but not only direction, but pressure...water will reach the center holes BEFORE it reaches the perimeter holes and thus will leave the sprinkler first. This can be seen quite clearly with drip irrigation tubing. there will be a delay between the time water leaves holes near the hub, and the perimeter. No wait, depending on how fast it spins and the tank pressure, the pressure may be reversed due to centrifugal effects
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I don't think there are any "center holes" or "perimeter holes". The problem (now?) says there are eight holes. Presumably that's one hole at the end of each arm. (That would be a typical sprinkler design.) Dots instead of a solid line to show individual drops at different points in time.
Relevant wiki: Conservation of Angular Momentum
I find conservation of angular momentum to be the more intuitive way to solve this one. As each droplet move away from the center they need to travel less degrees per second in order to compensate for the greater distance to the center, around which they spin.
It is nice to see a different approach! Since there is no net torque on the water particles, angular momentum is constant.
Angular momentum becomes inapplicable after the water leaves the sprinkler arm as it is no longer in the sprinkler system, therefore no longer in rotation about the sprinkler axis, there is no centripetal force on the droplets. Its motion is entirely linear, combining both the moments of the forward tangential vector of the rotating tip(sideways) and the outward spurting vector. The water spurt continues travelling in that Straight line, does not curve and has no additional forces on it. Angular or rotational motion is zero. The sprinkler tip however continues to rotate away with no change of its angular momentum. All water mass ejected is continually replaced assuming a constant flux of water. The centrifugal flow aspect of the water is irrelevant because each instant is identical to the next.
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The water droplets will always spin around the center of the sprinkler unless there is a torque that does the "braking". As Pranshu Gaba, the person who submitted this question, has already mentioned. There is no net torque on the water particles, thus my solution is satisfactory.
I must emphasis that your statement, "Angular or rotational motion is zero", is false, you can calculate the angular momentum by computing (r X mv), which will never be zero for any of the droplets.
Centripetal/centrifugal force has nothing to do with this, I think you are over-thinking a really simple question.
edit:grammar
When the sprinkles goes in counter clockwise direction, the water needs to retain its original position (due inertia) which is straight line. Newton's first law.
Is it also Coriolis Effect? :)
Water flows against the motion given to the sprinkler in order to conserve energy. Since the notion of the sprinkler is counterclockwise, the motion of the water would be clockwise. So the answer is B.
Could you explain how moving against the motion conserves energy?
How about Coriolis effect? :)
The force acting on the water ejected from the sprinkler nozzles reduces as the distance increases and the water droplets slow down. Therfore when the sprinkler rotates the pattern at B results. This follows Newtons laws of motion which state that a body will stay at rest or in motion until a force acts on it.
What force is acting on the water once it is ejected from the sprinkler?
if we give force to the sprinkler to rotate it anticlockwise..it will start to move anticlockwise.
so,there is 3 conditions......
at first...it will move slightly & move with all his particles at the same time if there is no force against it and if we are able to give same force to all of its particles .[then it is A]
secondly--the pressure against it(any outer pressure) will create the most impact on the outer part of it.so the outer part will be unable to move with same slightness with the inner part.[then it is C]
thirdly--as we have to rotate the system anticlockwise,the initial force must be from the center. as ,we are giving more pressure in the center ,the particles of center will get more energy than the far parts of the system.so,the middle parts will move quickly than the far parts of the sprinkler...[then it is B]
as rotating anticlockwise mostly means giving force from the center,so the answer will be B.
This is a very poorly written question. momentum means that if the sprinkler is in motion, the water coming out of each hole will have the same initial velocity and direction as the hole it came from when it came out of the sprinkler. C would be correct
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You can always report it if you want clarification.
What's happening, is known as the Coriolis effect. I found a fantastic video on youtube illustrating the principle, you can watch it here: https://youtu.be/XHGKIzCcVa0?t=4m44s The water is spinning around with the sprinkler, when released it moves directly outwards, it doesn't rotate around the sprinkler, instead it moves on a path tangent to where it got spat out, as illustrated in this gif: https://goo.gl/f3sDsx (the blue ball is moving with the same speed as the blue outline.) The gif was taken from the video above. The reason for this is because the further it gets from the center of it's rotation, the faster it needs to move to stay on a straight line from the center. Because nothing is speeding up the water drops, they appear to lag behind the sprinkler.
You are all wrong. Remember the question is "how does the water flow".
If the sprinkler is rotating then the water will have two motions:
1) straight line motion as if the sprinkler is stationary and
2) angular motion from the rotating sprinkler.
The sprinkler is rotating counterclockwise hence C is the correct answer.
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B is correct to how the question is described.
there is nothing wrong.even u are not.i calculated the term thinking water flow constant.
Due to inertia, the water resists movement and stays behind, thus resulting in it moving clockwise, i.e opposite to the initial movement of the sprinkler
What would happen if the holes were opening towards the center, like in this problem ?
Inertia keeps the water away from the direction of rotation. Hence answer B
What would happen if the holes were opening towards the center, like in this problem ?
Easy the water flow from the 8 hole when stationary rotate the hole clockwise the water still flow from the same point the 8 hole or if you move it anti-clockwise it will still flow from the 8 hole
that doesn't make any sense.need clear explanation.
This doesn't explain why the stream of water should look like the image in B. Water flows out of 8 holes in all three options.
I got this correct but it is actually a poorly written problem.
You can report it if you want clarification.
Why do you think it was poorly written?
Relevant wiki: Angular Kinematics
I wrote this in a comment below, but decided to also post it as an answer here:
What's happening, is known as the Coriolis effect. I found a fantastic video on youtube illustrating the principle, you can watch it here .
The water is spinning around with the sprinkler, when released it maintains it's sideways speed, it no longer rotates around the sprinkler, instead it moves on a path tangent to where it got spat out, similar to what is illustrated in this gif. (The only difference being the water droplets gets pushed out away from the center as well, so the path the droplets take is not quite as curved as the yellow path.)
The reason for this is because if an object is orbiting around a center of rotation, the further it is from the center, the longer the distance it has to travel around to make one full rotation around the center. It'll have to move further around the center, the further away it is from the center.
The droplets, when released and moving away from the center is not expected to change their speed, so they appear to lag behind the sprinkler.