Relative end deflection of snaked pipe versus straight 1

[STH003]

Hi, I was wrestling with a thought experiment about the relative end displacements of a pipe with many bends in it versus a straight pipe (See attached) For ease of calcs lets just say that the total length of pipe for both types is ~100ft, and the cross sectional area of the pipe is 1 sq-ft, and the pressure is increased by 100 psf.

my question is will the relative displacement (in the y direction) of A and B be a fraction of that of the relative displacement of C and D? Also, is it safe to say that both systems have the same amount of work applied to them, therefore the internal strain energy for both is the same, meaning that the sum of the relative displacements of the points along the bent pipe is equal to the relative displacement of C and D?

Thanks for your help.

 

[BigInch]

The sum of all displacements in the Y direction will be equal, except for the bent pipe lengths that have growth components in the X direction.

The displacement in the Y direction of point B relative to point A will be [α] * [Δ]T * distance AB * sin([Θ]
The displacement in the X direction of point B relative to A will be [α] * [Δ]T * distance AB * cos([Θ])
The displacement in the Y direction of point C relative to D will be length CD * [α] * [Δ]T

The sum of linear growth will be the same, if linear length of the straightened bar AB = length CD, if [α] and [Δ]T are equal in both cases.

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http://www.youtube.com/watch?v=hpiIWMWWVco

http://virtualpipeline.spaces.liv

 

[STH003]

Great, this is what I thought.

Thanks for the explanation Biginch!

 

[ione]

STH003,

Are you dealing with steam? In that case an increased steam pressure would imply an increased temperature and it would be correct to speak about thermal dilatation (? ?T). Otherwise I think thermal dilation is not pertinent to the problem.

 

[STH003]

this was a question proposed in our office, and was more of a "what if" type of scenario to get our brains thinking. I guess it was more of an ideal gas type of question, with an increase in pressure.