Does water flow through a pipe affect its moment of intertia?
May 7, 2011 11:33 PM Subscribe
Does water flow through a straight pipe change its rotational inertia about an axis perpendicular to the pipe? i.e. Compared with the same pipe filled with (non-flowing) water.
Response by poster: > "Strictly speaking I would think no - Rotational inertia is a measure of the distribution of mass, which wouldn't change for a fixed volume of water, whether it's moving or not. "
OK. This is my guess too.
> "That said, if you're asking the broader question - will moving water affect the forces seen by a rotating system, the answer is probably yes, "
I don't really understand what you mean.
> "... but there is a lot missing from your question. Where are you drawing the boundaries to your system (is the water flowing in a self contained loop, or entering and leaving the control volume?) "
Yes, in practice, it is difficult to set up a pipe on a center pivot with water flowing continuously thru, while being free to pivot.
> "Does the measuring axis pass through the pipe centerline?"
Yes, you can assume this is so.
> "Is the system at steady state, or undergoing a transient change in flow / pressure / volume?"
Yes, you can assume steady flow.
posted by gluino at 12:09 AM on May 8, 2011
OK. This is my guess too.
> "That said, if you're asking the broader question - will moving water affect the forces seen by a rotating system, the answer is probably yes, "
I don't really understand what you mean.
> "... but there is a lot missing from your question. Where are you drawing the boundaries to your system (is the water flowing in a self contained loop, or entering and leaving the control volume?) "
Yes, in practice, it is difficult to set up a pipe on a center pivot with water flowing continuously thru, while being free to pivot.
> "Does the measuring axis pass through the pipe centerline?"
Yes, you can assume this is so.
> "Is the system at steady state, or undergoing a transient change in flow / pressure / volume?"
Yes, you can assume steady flow.
posted by gluino at 12:09 AM on May 8, 2011
I don't really understand what you mean.
The flowing water will impart a reaction force on the system wherever it changes direction or diameter, and will also impart viscous drag forces. If these forces are unbalanced, it could make your system do all kinds of weird accelerations, but it shouldn't affect its inertia (I think).
posted by Popular Ethics at 12:29 AM on May 8, 2011
The flowing water will impart a reaction force on the system wherever it changes direction or diameter, and will also impart viscous drag forces. If these forces are unbalanced, it could make your system do all kinds of weird accelerations, but it shouldn't affect its inertia (I think).
posted by Popular Ethics at 12:29 AM on May 8, 2011
Rotational inertia is a very specific measure of a system, and (in the nomrelativistic limit) it is not dependent on the velocity of the water.
posted by Salvor Hardin at 6:08 AM on May 8, 2011
posted by Salvor Hardin at 6:08 AM on May 8, 2011
I can't think of anything that would make water rotate around an axis perpendicular to a straight pipe. If the pipe itself is rotating the water will rotate with it assuming a steady state. At start or stop of rotation you will have some transient turbulence but by nature this is chaotic and really can't be predicted very well. If the water is somehow rotating independently inside a pipe it will impart a moment on the pipe equal to the weight of the water by the velocity and some friction factor (sorry, don't want to look up the equation right now). The direction of the moment will follow the right hand rule. This is the kind of thing that really requires a free body diagram. Use that and the answer will likely be very clear.
posted by bartonlong at 9:00 AM on May 8, 2011
posted by bartonlong at 9:00 AM on May 8, 2011
If I understand what you're getting at, I think the answer is yes, the flowing water will display greater inertia (assuming you are using the term 'inertia' to mean resistance to motion that requires you to put in more work to keep it going, rather than the more technical usage in the context of Newtonian dynamics).
In a center pivot irrigation system, for example, if no water is flowing, you would have to use enough force to balance the frictional forces to keep it moving at any given speed.
If the water is flowing, you would have to use more force because the frictional forces are unchanged, but you have to use additional force to accelerate the water that replaces the water that has flowed out of the system onto the ground, because the replacement water has no initial rotational motion with respect to the pivot axis, and the water it replaces did.
In other words, when the water is flowing, you lose the kinetic energy of the water that flows out, and you have to replace that to keep things going.
posted by jamjam at 10:44 AM on May 8, 2011
In a center pivot irrigation system, for example, if no water is flowing, you would have to use enough force to balance the frictional forces to keep it moving at any given speed.
If the water is flowing, you would have to use more force because the frictional forces are unchanged, but you have to use additional force to accelerate the water that replaces the water that has flowed out of the system onto the ground, because the replacement water has no initial rotational motion with respect to the pivot axis, and the water it replaces did.
In other words, when the water is flowing, you lose the kinetic energy of the water that flows out, and you have to replace that to keep things going.
posted by jamjam at 10:44 AM on May 8, 2011
I am thinking of a couple of potential experiments while trying to divine the OP's intent.
(1) Spin a closed length of pipe filled with water around an axis. Measure the force applied to keep the pipe rotating at a steady state.
Spin a pipe of the same dimension as in (1) filled with water, but with a small hole at the end of the pipe permitting water to flow out. Does the force change?
You have to be careful not to impart energy through the flow of water - pressurized water (by pump or gravity) will impart energy to the pipe. Sprinklers work because of this.
(2) Take a hoop of pipe, closed, filled with water. Stand the hoop up so that the diameter is perpendicular to the ground. Spin the hoop along the axis perpendicular to the ground, the axis running through the center of the hoop.
Do the same thing again, but this time, pump the water so that it is moving.
Will the inertia in the moving water in the hoop act like precession in a gyroscope and force you to impart more energy to keep the hoop moving? This would be becuase of friction at the point of rotation.
(3) Same as 2, but instead of the axis of rotation being through the center of the hoop, move the axis off to one side, outside the hoop, so that the entire hoop is rotating around the axis. Will this affect the precessive inertia of the moving water in the hoop?
You could simulate this without the water. Spin a metal hoop like a wheel, and rotate the spinning wheel around the axes described above. The spinning of the wheel would be like the water without the enclosing pipe.
Note that I am assuming the water in the pipe is to actually have rotational inertia around an axis perpendicular the pipe as stated in the OP's question. Water running through a non rotating pipe doesn't have rotational inertia. Although water running through a pipe that bends incurs rotational inertia in turbulent flow. Analyzing fluid flow in pipe involves some really heavy duty math, if you are interested in what's going on in the fluid itself. I don't do that kind of math.
Here's something to think about. A river that has a bend in it will erode the bank on the outside of the bend and deposit silt on the inside of the bend, do to flow variations caused by the bend itself. This partly is how oxbow lakes form. Don't buy property with a great view, when that view is because it sits on a cliff face on the outside bend of the river.
posted by Xoebe at 12:49 PM on May 9, 2011
(1) Spin a closed length of pipe filled with water around an axis. Measure the force applied to keep the pipe rotating at a steady state.
Spin a pipe of the same dimension as in (1) filled with water, but with a small hole at the end of the pipe permitting water to flow out. Does the force change?
You have to be careful not to impart energy through the flow of water - pressurized water (by pump or gravity) will impart energy to the pipe. Sprinklers work because of this.
(2) Take a hoop of pipe, closed, filled with water. Stand the hoop up so that the diameter is perpendicular to the ground. Spin the hoop along the axis perpendicular to the ground, the axis running through the center of the hoop.
Do the same thing again, but this time, pump the water so that it is moving.
Will the inertia in the moving water in the hoop act like precession in a gyroscope and force you to impart more energy to keep the hoop moving? This would be becuase of friction at the point of rotation.
(3) Same as 2, but instead of the axis of rotation being through the center of the hoop, move the axis off to one side, outside the hoop, so that the entire hoop is rotating around the axis. Will this affect the precessive inertia of the moving water in the hoop?
You could simulate this without the water. Spin a metal hoop like a wheel, and rotate the spinning wheel around the axes described above. The spinning of the wheel would be like the water without the enclosing pipe.
Note that I am assuming the water in the pipe is to actually have rotational inertia around an axis perpendicular the pipe as stated in the OP's question. Water running through a non rotating pipe doesn't have rotational inertia. Although water running through a pipe that bends incurs rotational inertia in turbulent flow. Analyzing fluid flow in pipe involves some really heavy duty math, if you are interested in what's going on in the fluid itself. I don't do that kind of math.
Here's something to think about. A river that has a bend in it will erode the bank on the outside of the bend and deposit silt on the inside of the bend, do to flow variations caused by the bend itself. This partly is how oxbow lakes form. Don't buy property with a great view, when that view is because it sits on a cliff face on the outside bend of the river.
posted by Xoebe at 12:49 PM on May 9, 2011
Response by poster: Guys I think you for all your responses, it is clear that this question NEEDS DIAGRAMS.
I hope this diagram clarifies sufficiently, and please ask if there are any remaining ambiguities.
I know that the diagram doesn't show HOW the water is made to flow through continuously... I don't know yet either... but I hope we can still analyze it theoretically.
posted by gluino at 10:18 PM on May 11, 2011
I hope this diagram clarifies sufficiently, and please ask if there are any remaining ambiguities.
I know that the diagram doesn't show HOW the water is made to flow through continuously... I don't know yet either... but I hope we can still analyze it theoretically.
posted by gluino at 10:18 PM on May 11, 2011
I hope this diagram clarifies sufficiently
It helps a little, but not fully. If the water magically disappeared at the outlet and reappeared at the inlet with the same momentum (portal style), I think it would have the same moment of inertia as a closed tube full of water. Otherwise, I'm wondering whether the path that the water takes into and out of the system (and the attendant accelerations) would have an effect as jamjam suggests.
Maybe your diagram should show a complete loop, with a pump? If both legs of the loop pass through the axis, the inertia should be constant. Of course, now that I've read that, I'm thinking that such a loop would have gyroscopic effects. Maybe if it was a figure of 8.
Can I ask what the application is?
posted by Popular Ethics at 10:42 AM on May 14, 2011
It helps a little, but not fully. If the water magically disappeared at the outlet and reappeared at the inlet with the same momentum (portal style), I think it would have the same moment of inertia as a closed tube full of water. Otherwise, I'm wondering whether the path that the water takes into and out of the system (and the attendant accelerations) would have an effect as jamjam suggests.
Maybe your diagram should show a complete loop, with a pump? If both legs of the loop pass through the axis, the inertia should be constant. Of course, now that I've read that, I'm thinking that such a loop would have gyroscopic effects. Maybe if it was a figure of 8.
Can I ask what the application is?
posted by Popular Ethics at 10:42 AM on May 14, 2011
I think I've just thought of a disproof:
Think of your tube of standing (no flow) liquid. As you spin the tube, the rotational acceleration will tend to "throw" the fluid outward, increasing the density from the axis towards the ends of the tube. When you introduce a flow, the momentum of the liquid will tend to resist this centripetal acceleration, so the density curve will be biassed towards the outlet end. The mass distribution, and thus the moment of inertia will be different in both cases.
The effect may be small depending on the relative speed of the flow, angular velocity of the pipe, and density of the fluid, but it will be there. A loop with flow going both ways across the axis may balance this effect.
posted by Popular Ethics at 11:02 AM on May 14, 2011
Think of your tube of standing (no flow) liquid. As you spin the tube, the rotational acceleration will tend to "throw" the fluid outward, increasing the density from the axis towards the ends of the tube. When you introduce a flow, the momentum of the liquid will tend to resist this centripetal acceleration, so the density curve will be biassed towards the outlet end. The mass distribution, and thus the moment of inertia will be different in both cases.
The effect may be small depending on the relative speed of the flow, angular velocity of the pipe, and density of the fluid, but it will be there. A loop with flow going both ways across the axis may balance this effect.
posted by Popular Ethics at 11:02 AM on May 14, 2011
This thread is closed to new comments.
That said, if you're asking the broader question - will moving water affect the forces seen by a rotating system, the answer is probably yes, but there is a lot missing from your question. Where are you drawing the boundaries to your system (is the water flowing in a self contained loop, or entering and leaving the control volume?) Does the measuring axis pass through the pipe centerline? Is the system at steady state, or undergoing a transient change in flow / pressure / volume?
posted by Popular Ethics at 11:45 PM on May 7, 2011