Deflection of inflatted tubes 2

[Jonathan R]

Hi,

I have carried out an experiment on 2 hoses. Hose A, a typical garden hose of 15mm OD 10mm ID (thick walled) and hose B a polyester woven lay flat fire type hose of 52mm OD 49mm ID (thin walled). When inflated to 4 bar pressure hose A didn't straighten and was only seen to bulge in the circumferential direction, however, hose B didn't bulge and immediately straightened. Can anyone explain to me as to why one hose straightened and the other didnt. I understand that hose A because it bulged experienced significant circumferential strain but I don't understand how this resulted in it not straightening, I assumed that once pressursied both hoses would straighten.

 

[Compositepro]

Two explanations.

The diameter of the hose has a large influence on the amount of force trying to straighten the hose.

The construction of the hoses are different. A garden hose likely has +/-45 degree reinforcement to allow greater flexibility, but this does allow the hose to stretch. In bending the neutral axis is in the center of the hose so axial pressure on each side of the hose somewhat balance. A fire hose has mainly 0/90 degree reinforcement, so the neutral axis in bending is the hose wall on the outside of the bend because the fibers do not stretch. The axial fibers on the inside of the bend go into compression and buckle. So axial forces due to pressure are all trying to straighten the hose. If a fire hose were made with +/-45 reinforcement the hose would stretch when pulled without internal pressure, like a bungee cord does. Then it would shrink suddenly when pressurized. This would be dangerous. There are actuators that are built this way, which are sometimes used like "muscles".

 

[Jonathan R]

Thanks for the reply, ok so i understand what you are saying however i also tested a plain pvc no renforced tube, thick walled,same outer diameter as the woven fire hose and it also didnt straighten. Would this be down to the pvc rube being simply to haevy at 5 bar to straighten or due to it being thick walled? Im consfused becasue in this case there is no reinforcment.

Thanks

 

[Compositepro]

In an non-reinforced hose, the neutral axis is in the center.

 

[prex]

I think that the tendency of a hose to straighten up when pressurized is not due to strain effects in the wall, but to the increase in volume when straightened: this tends to lower the pressure, hence the potential energy decreases. In this of course we assume the hose is closed at the end, as dynamic effects at the outlet are completely different.
Now as to why the behaviour is different for different hoses, this has to do with all the parameters involved: the straightening force is relatively low, a lower ID tends to lower this force, the smoother bending of a plastic thick walled pipe reduces the change in volume, thus the straightening force, and perhaps more parameters are also involved.

prex
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[Jonathan R]

Prex,

That sounds like a more plausable theory. Thanks

 

[Lnewqban]

Seen from another point of view:
Pressure tries to fill the cavity up as much as possible: that only happens when volume/surface ratio of the recipient is maximum.
In the case of the cross section, that translates to area/perimeter ratio, which is max only for a circle.

Looking at the rolled garden hose from the side:
Internal areas above and below the neutral line are different.
Because pressure = force / area, force = pressure x area
Then the internal force exerted by pressure is greater over the surface away from the center of the turn.
If you study an arc section, the two vector forces at the ends of the arc are not parallel to each other, those push more or less away from each other.

That unbalance of internal forces naturally tends to reach a balance, as far as the resisting rigidity of the hose allows it.
That par of forces creates a moment that tends to straighten that arc section and then the roll or curve of the whole hose (kind of what happens on a bending beam loaded with distributed weight, but in reverse).

Copied from

https://en.m.wikipedia.org/wiki/Pascal's_law

"Pascal's law (also Pascal's principle or the principle of transmission of fluid-pressure) is a principle in fluid mechanics that states that a pressure change occurring anywhere in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere. The law was established by French mathematician Blaise Pascal."

Because internal pressure is uniformly applied to the walls, each infinitesimal superficial area is loaded with similar circumferential stress and radial stress: hence, each little portion of the cylindrical surface should have the same deformation in each direction (circumferential and radial).

The principle has been used in Bourdon-tube type manometers:

http://www.instrumentationtoday.com/bourdon-tube/2011/09/

"Engineering is achieving function while avoiding failure." - Henry Petroski

 

[Jonathan R]

Thanks everyone. Made writing this report a whole lost easier!!

 

[Compositepro]

These last few posts help to explain why any tube with internal pressure tends to straighten. However, the original questions were why are there differences between hoses and why does a thick-walled tube not evidence much straightening.

 

[prex]

I don't think that a perfect torus (or a perfectly round pipe bend) has a tendency to straighten up under pressure: this is because the volume of the torus is exactly the same as the straight pipe of the same axial length and diameter. Of course I do not account here for geometric irregularities and for the fact that straightening a rigid pipe would change its shape.
The above means also that internal pressure forces are internally balanced in a torus and also in a cut torus. And in fact Bourdon manometers have the curved tube with an elliptical or otherwise flattened section.
So I'll have to insist: IMO it's the change in volume that drives the straightening effect.

prex
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[Jonathan R]

Hmm, you siad its the change in volume that drives the straightening effect but surely the change in volume reduces the prospect of the pipe straightening and when the volume increases the force descreases. Surely its the chabge in volume that reduxes the prospect or the pipe straightening, no?

 

[Denial]

Interesting topic, and one that I have observed hundreds of times but thought about zero times.[ ] I think Prex is right that the straightening tendency is associated with an increase in volume.[ ] But he is also right that the volume of a length of torus of circular cross-section is the same as the volume of the same length of a circular cylinder.[ ] (Think Pappus's Centroid Theorem.)[ ] So where does the volume change come from?[ ]

My money's on it coming from a change in the hose's cross-section's shape.[ ] When the hose is toroidal various "second order" effects tend to cause its cross-section to flatten slightly:[ ] it becomes elliptical, with the ellipse's major semi-axis perpendicular to the plane of the toroidal bending.[ ] Under internal pressure the ellipse wants to revert to a circle, in order to lessen the pressure by increasing the internal volume.[ ] This has the "side effect" of changing the second moment of inertia of the cross-section, thereby "stiffening it up" against whatever it is that is making it want to adopt a slightly toroidal longitudinal shape.

 

[gruntguru]

Hose A (soft material with cross-ply reinforcing) is more flexible than hose B. (rigid material with axial and radial plies?).

The pressure is not creating the straightening - it is forcing hose B to a cylindrical shape where its own axial rigidity keeps it straight.

je suis charlie

 

[moon161]

It has to come down to a net force in some way.