# Torque on a square screw full with water

1. Mar 7, 2012

### Gh778

Hi,

I would like to calculate the torque on a color square screw full with water like the drawing show. All grey screws don't move or turn, only color screws can turn (and so move up or down). Color screws are square (see top view for that). There is water between color screw and grey scew (gaskets are not visible ! ;) ), so like that the only faces can put forces are external and internal faces.

The problem for me, I see at each corner a small torque (because the altitude is not the same) but I don't find where this torque is cancel by another part of the screw. Can you help me ?

Maybe you need some others views, don't hesitate to tell.

Thanks :)

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2. Mar 8, 2012

### Gh778

This is like I see forces but maybe the weight is not full at bottom ? I'm drawing only a corner like that it's better for see where is another torque.

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3. Mar 9, 2012

### Gh778

I have cut 3D circular thread (first drawing) with 2 rectangular cuboids for obtain square thread (second and third drawings). Like that I'm sure the square thread can turn in the circular thread.

If you look at the square thread you can see a torque when the thread is in water due to external/internal surfaces. This torque is cancel by another torque with up/down surface. But it's easy to cancel this last torque if you put this square thread in a circular thread. So, another torque must cancel all torque but I don't find where. Maybe you can ?

Thanks

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4. Mar 9, 2012

### Hassan2

I' not sure I have understood the problem, but if you consider that the forces due to hydraulic pressure is normal to the surface ( which I'm sure you do), the problem is solved.

I think you can simplify the problem to a simple slab in the water. Wouldn't it be the same problem?

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5. Mar 9, 2012

### Gh778

Hi Hassan2 ;)

Yes, forces are normal to the surface, can you explain more I don't understand how ext and int surfaces give no torque ?

Up and down surfaces can be canceled so we rest with ext and int surfaces. Really, look at the drawings, you'll see a torque due to the corner. I don't think this 3D shape can be resume with a 2D shape.

thanks

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6. Mar 9, 2012

### Hassan2

The hydraulic force on any differential( infinitesimal)surface in any direction is equal to the force on the projection of the differential surface on the plane perpendicular to that direction.

Any differential surface at any point on the screw has a projection on the plane of the axis and r ( r being the vector from the axis to the point)being the distance from the axis). There is another differential surface on the other side of the plane the same projection on the plane, thus exerting equal forces in opposite directions.

This is true for any arbitrary shape.

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7. Mar 9, 2012

### Hassan2

About the torque on the screw in the figure, The force on the upper and lower sides are not equal. the torque the net is canceled by the net corner force.

8. Mar 9, 2012

### Gh778

I'm ok with #6 message

#7: Yes a torque up/down cancel another ext/int, ok. But like it's a thread we can put it between 2 circular threads (show first drawing) and cancel up and down surfaces (for example with thin thickness of air with gaskets). We have only the external/internal torque. I don't know if you understand me ? Don't forget I cancel the up and down surface pressure easily and without energy.

9. Mar 9, 2012

### Hassan2

In one of your figures, I see the words " up" and "down". My up and down surfaces are both sides of the thread separated by the thickness. The are not equal because they are like two parallel surfaces at different depth.

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10. Mar 9, 2012

### Gh778

The problem is, there are 2 thickness: up thickness and proof thickness. See the drawing below. Imagine air gap for up and down surfaces like that we sure there is no torque from these surfaces and we sure this cost nothing in energy if we turn in circular threads. But external and internal have a torque, for me, sure ;)

Drawing: look at "Z" axe

It's not a problem to cancel the forces on these surfaces if we put small air gap (with gaskets) and put in a "sandwich" in 2 fixed circular threads. This cost nothing (in theory) about energy.

I add a drawing with a square thread in a "sandwich" of circular threads. Air gap at up and down surfaces.

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11. Mar 9, 2012

### Hassan2

Thanks for the explanations and the figure. I think I understands the problem now. In this simplified problem, no water touches the up and down and also internal surfaces. The problem becomes interesting and challenging now. Think of the proofs ( gaskets, fillers,..); They experience the same but opposite forces. If the gaskets are free, they transfer the force to the internal surfaces of the screw and cancel the forces on the screw. If there are rind connected like "another" screw, the forces cause a torque which tends to rotate the opposite direction the screw tends to rotate. Again no net torque.

Added: Sorry in case of a rigid proof, my description may be incorrect.

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12. Mar 9, 2012

### Gh778

Thanks to you for your help ;) it's friendly

It's more difficult to think with the internal face without water because gaskets will be great with important surface. Or maybe I don't understand your explanations. Tell me ?

For my experience (no water at down and up surfaces but water at internal and external surfaces), the air gap could be like 1µm so the surface of the gasket is very small and this can't cancel the torque I see on internal/external surfaces. The weight can't be changed because internal/external surfaces are verticals.

13. Mar 9, 2012

### Hassan2

Yes, but with water touching the internal faces too, again there is a net torque on the screw as you said before. But again the gaskets cancel the torque. If the gaskets thickness is much less than the screw thread, much of the forces on the thread is canceled by the forces on other side of the thread the remaining is canceled by the gaskets. If the thickness ratio is not small, again the number of gaskets must be large.

My problem now is with the case of the rigid gaskets fixed to the water container ( pipe). I have no explanation for this yet.

by the way, what software do you use for draw such figures?

14. Mar 9, 2012

### Hassan2

You said that the gap is filled with air? it must be pressurized air, the same pressure as the water pressure. If so, it tells you where the cancelling force come from!

15. Mar 9, 2012

### Gh778

An air gap with air at pressure 1 bar for example, this air will apply the same force all along up and down surfaces, it's easy to do, and this cancel the pressure of water like that we can forget these surfaces (they have the same surface) and think with only external and internal surfaces.

I use Maxwell (electromagnetic simulator) but I think you can do with Blender (free) but I don't know how.

it's evidence that the external surface apply much torque than internal surface but need some calculations for be net.

When you think about that you imagine a square thread in a sandwich of 2 circular threads ? I don't understand.

I don't understand what case you think. Don't forget the square thread will be turn, and this said it will move up (or down) and if water is not everywhere around, the water can (it depend of the torque) move down and we can lost energy like that.

Could you send a drawing even with pen ? I don't understand.

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16. Mar 9, 2012

### Hassan2

Read post #14 please. There must be a pressure on the up and down forces otherwise water fills the narrow gaps. This pressure doesn't answer the question? As if the screw was in the water without any gasket.

17. Mar 9, 2012

### Gh778

Not like you think, the gasket is only there for prevent water to fill the air gap, you can think with P=0 bar in the air gap. Sure water will put forces on surface of the gasket [because we have X bars in one side due to the water, and this change with altitude, and 0 bar in other side (air gap)] but the surface of the gasket can be so low that we can considered the torque = 0 on the gasket. In this case, I put thr square thread in a sandwich of 2 circular threads, it's very important, the gaskets don't have up and down surfaces, they have only external and internal surfaces but so small...

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18. Mar 9, 2012

### Hassan2

First of all, the problem is the same for any sort of screw thread, square of helical or even arbitrary shapes and asymmetric teeth. I think the problem is becoming more clear and more simple. Imagine the three scenarios:

1. No gasket at all, all surfaces are in touch with water. In this case the problem is solved and we agreed on it.

2. gasket fills the spaces fully and rigidly as if the whole is one object. again , the problem is solved. No mater if the object has tooth or blades. I guess you still have problem with this but it is solved for me. Narrow or thick doesn't matter.

3. The gasket is there but it is not stuck to to the surfaces.Water will enter in between and it becomes case 1 or a combination of 1 and 2.

I have an analysis in my mind and if I can convey it to you, you would have no problem with the small thickness of the gasket. I try it here:

The net torque on the screw due to screw surface only, depends on the ratio of the filler( gasket) thickness to the screw thread thickness. When the ratio is small, this means most of the force on the screw surfaces is canceled with their opposite forces on the other side where the water has the same depth. In fact at any point on the screw surface, if you can connect a line throw the screw thread to the other side with the same height, WITHOUT passing through the gasket, the force on that point is canceled. If the ratio is small, more points of the surface are like that. If the ratio is not small but the thickness is small, this means we have almost as much gasket surface as thread surface ( external surface). The total torques are not negligible.

I have made a poor drawing to show how a portion of the forces cancel each other. In the figure, the black arrows canceled by the forces on the other side of the thread. The red ones are not because the gasket/gap is between them.

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19. Mar 9, 2012

### Gh778

Ok but I would like to understand this particular problem in details ;)

I put two 3D drawings:

1/ a zoom of the bottom of the thread (yellow), we can see the difference of altitude of the thread and this show there is a torque with external/internal surfaces,
2/a zoom of the thread in sandwich with anothers fixed thread. I put the gasket extremely thin 1µm between yellow and grey threads. This don't cost energy. And inside (the volume create by gaskets which is between up/down surface and grey surface) there is no water only air.

I have questions:

a/ are you agreed with the torque with only 2 surfaces external/internal (don't think at another surfaces) ?
b/ Why do you think the torque is proportional with the thin of the torque ? The thickness of the square thread don't change with the thickness of the gasket.
c/ orange color of your drawing is gasket for you ? Because for me not at all. See for that the zoom.

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20. Mar 9, 2012

### Gh778

I have draw new thread like that no problem with part of the axe Z.
Maybe it's more easy to see where I see a torque ?

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