Deflection of hose when internally pressurised

[ronniejooney]

Hi,

I have carried out an experiment on 2 hoses. Hose A, a typical garden hose of 15mm OD 10mm ID and hose B a polyester woven lay flat fire type hose of 52mm OD 49mm ID. 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. Thanks

 

[anorlunda]

This is just a guess, but I think that they assume the shape that minimizes surface area.

The flat hose gets round and straight. There is no spring force to make it want too roll up again.

The typical garden hose is already very close to the minimum area shape before pressurization . So the tendency to straighten is slight and it has to fight the springy nature of the hose. If you put more pressure in, it might tend to straighten more.

Fun question

 

[JBA]

It has to due with the longitudinal pressure force on the end of the sealed hose that is trying to straighten the hose and the difference in the diameters of the 2 hoses. The longitudinal force is proportional to the ratio of x-section areas of the hoses.
As a result, the ratio of the fire hose force to the garden hose force = 49^2 / 10^2 = 24/1 or 24 times the force on the garden hose.

 

[ronniejooney]

It has to due with the longitudinal pressure force on the end of the sealed hose that is trying to straighten the hose and the difference in the diameters of the 2 hoses. The longitudinal force is proportional to the ratio of x-section areas of the hoses.
As a result, the ratio of the fire hose force to the garden hose force = 49^2 / 10^2 = 24/1 or 24 times the force on the garden hose.

JBA I also tested a rubber hose pipe with almost the same diameter and it didn't straighten either, therefore would it not be due to the material properties of the rubber/garden hose compared to the polyester woven hose as the pressure would also be the same. ?

 

[Chestermiller]

JBA I also tested a rubber hose pipe with almost the same diameter and it didn't straighten either, therefore would it not be due to the material properties of the rubber/garden hose compared to the polyester woven hose as the pressure would also be the same. ?

I agree that the difference is due to the material properties. Hoses are typically fiber reinforced plied laminates. The orientation of the plies is very important in determining the response to pressurization. Hare you cut up the hoses and examined the ply layup?

 

[ronniejooney]

I agree that the difference is due to the material properties. Hoses are typically fiber reinforced plied laminates. The orientation of the plies is very important in determining the response to pressurization. Hare you cut up the hoses and examined the ply layup?

I haven't no, as the garden hose is just PVC however the woven hose is longitudinally woven. but I am thinking now that the pressure will be concentrated on the area of least resistance. In the case of the garden hose pipe this would be in the hoop/circumferential direction, therefore this is why it bulged and didnt straighten as the longitudinal pressure wasn't high enough to force it to straighten. For the lay flat polyester woven hose due to being sufficiently stiff in the circumferential/hoop direction to stop bulging the pressure was highest in the longitudinal direction therefore causing it to straighten. This would fit with the thin walled assumption that for a thin walled hose (the woven polyester) that the longitudinal stress is twice the hoop/circumferential.

I'm not entirely sure however what I have assumed is correct.

 

[Chestermiller]

I haven't no, as the garden hose is just PVC however the woven hose is longitudinally woven. but I am thinking now that the pressure will be concentrated on the area of least resistance. In the case of the garden hose pipe this would be in the hoop/circumferential direction, therefore this is why it bulged and didnt straighten as the longitudinal pressure wasn't high enough to force it to straighten. For the lay flat polyester woven hose due to being sufficiently stiff in the circumferential/hoop direction to stop bulging the pressure was highest in the longitudinal direction therefore causing it to straighten. This would fit with the thin walled assumption that for a thin walled hose (the woven polyester) that the longitudinal stress is twice the hoop/circumferential.

I'm not entirely sure however what I have assumed is correct.

Well, irrespective of the material properties, it is correct to say that the longitudinal stress is twice the hoop stress.

 

[ronniejooney]

Well, irrespective of the material properties, it is correct to say that the longitudinal stress is twice the hoop stress.

This assumption can only be applied to the woven hose though and not the others as they are thick walled and this is where its becomes confusing...

 

[JBA]

Small correction on the stress ratio. For thin wall vessels the longitudinal stress (pr/2t) is 1/2 that of the circumferential (hoop) stress (pr/t); but, as stated, for thick wall vessels it is more complicated.

 

[JBA]

Apart from my first post regarding the longitudinal load issue I agree that hose materials and construction are also a factor. One thought that comes to mind is that most thinner wall hoses tend to flatten as they bend as opposed to heavy walled composite hoses that tend to retain their circular shape; as a result, it would appear that the very act of the pressure reshaping the cross section from an oval or flat shape would tend to have its own straightening effect on the curved section of the thinner wall hose.

 

[Chris_R]

To complicate the problem a bit:
If a hose of the lay flat, thin walled variety is pressurized and run straight off of a cliff, at what cliff height will the hose kink instead of bending gradually down to meet the lower ground level? Given information is the internal pressure, and the hose inner and out diameter.

 

[JBA]

That is an interesting question but because the internal hose pressure at the kink is clearly a factor then the answer is going variable depending upon whether you are discussing a hose with a closed bottom end vs one with an open end or with a restricting flow orifice at its discharge end. vs the downpipe flow issue due to the gravitational flow of the water in the vertical hanging portion of the hose.

 

[Chris_R]

That is an interesting question but because the internal hose pressure at the kink is clearly a factor then the answer is going variable depending upon whether you are discussing a hose with a closed bottom end vs one with an open end or with a restricting flow orifice at its discharge end. vs the downpipe flow issue due to the gravitational flow of the water in the vertical hanging portion of the hose.

The higher end is attached to a pump providing a given flow rate. The other end is attached to a boiler with a given back pressure.

 

[JBA]

Unfortunately, I was only expounding on the factors that would affect the result. I don't have a clue as to actual get a solution; but I think I have an inkling as to the rounding issue. In the flat regions, x-section strips of the hose can be treated essentially as beams with a distributed pressure load bending moment stress applied; whereas, the curved end regions of those flats are the rigidly connected ends of those beams which are transforming from their curved configurations due to the tension exerted by curving of the flat segments until the bending/hoop stress is fully normalized throughout the circumference of the hose segment.

Following my above discussion a sort web search for "stresses on elliptic pressure vessels" revealed the below extended paper on that subject for those with interest and time.
http://www.ewp.rpi.edu/hartford/~ernesto/F2006/EP/Aids/Papers/Blake/Wang/seminar_final.pdf

Of course that is only one half of the route to a solution to how that transition translates into a perpendicular longitudinal straightening of successive hose segments. As to the source of that effect, I am considering the possibility that it might the result of a longitudinal pressure load that propagates through successive flattened sections along the hose until it reaches the circular hose region attached round connector at the end of the hose.

Unfortunately, if both of those are true we are still left with issue of the interaction between the rounding force and resistance to that imposed by weight of hose tending to maintain a hose section in its bent flattened condition or essentially the effective section modulus of the flattened regions of the hose x-section segments.

Interestingly, another factor in this issue is whether the section of the hose downstream of a flattened section is water filled or empty because the pressure affecting a flattened section is then either going to be from both ends of the flattened section or from only one.

At his point my mental speculator is just about exhausted from the above efforts so any and all responses to the above are welcomed.

 

[Baluncore]

For thin wall vessels the longitudinal stress (pr/2t) is 1/2 that of the circumferential (hoop) stress (pr/t);

That makes me more comfortable, because pipes that burst due to pressure tend to do so by splitting along their length, and the split tends to open first along the inside surface of the pipe.

Not mentioned yet is the length to diameter ratio of the hoses used in the experiment. The straightening effect needs to be measured as a bend angle per length of hose measured in hose diameters. Temperature and material properties are going to be important in any experiment.

My experience is mainly with moving and laying out a traveling irrigator hose twice each day. I use a 200m length of 2” ID lay-flat hose, (polyester fibre reinforced PVC), and up to 400m of 2” ID black HDPE for distribution. HDPE is called poly-pipe here.

The poly-pipe has a thick wall, (without fibre reinforcing), and needs to lay in large radius curves. It is not really important what pressure is in poly-pipe, it stays where you put it as the weight of water and the thick wall seem to be more important than internal pressure. Warming in the sun seems to give it flexibility, so it can be straightened or bent more easily. It will remember the new shape when it cools again.

On the other hand, the lay-flat hose has a much thinner PVC wall that is reinforced with woven polyester fibres. The 'lay' of the polyester fibres in the lay-flat hose wall are in both directions but not at 90° to each other. The tensile fibres wrap around the hose more than they move along so as to allow for the hoop stress being about twice the axial stress. I believe the helix angle is about 26½° from the circumference so the fibres appear to cross at 53°. Another advantage is that by not crossing fibres at 90° it needs less moving spools of continuous fibre on the machine that fabricates the woven hose. The diagonally crossed fibres also permit the hose to make curved bends under pressure. Because the tensile fibres travel in short pitch helical paths, each fibre travels equally on the inside and the outside of the curve, while the PVC allows a small amount of shear and stretch between adjacent fibres. The lay-flat hose employs two materials, one to carry tension and the other, more elastic, to provide water proofing. That composite structure is important to the properties and economy of lay-flat hose.

The key difference is that in lay-flat hose, there is shear between fibres that is not available in the thicker homogeneous wall poly-pipe, where only one material does both the tension and the waterproofing jobs.

 

[JBA]

ronniejooney, What is the weight, lbs / ft (or equivalent units) for your lay flat hose?