Fluid mechanics - Additional liquid capacity due to compression

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Discussion Overview

The discussion revolves around the effects of compressibility in a cylindrical tube filled with liquid under pressure. Participants explore the relationship between the deformation of the tube and the liquid, particularly focusing on how much additional liquid capacity can be accommodated due to these compressibility effects. The scope includes theoretical considerations and homework-related inquiries.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant describes the tube as a pressure vessel and notes that the internal pressure creates hoop stress in the wall, which significantly affects the volume change.
  • Another participant emphasizes the importance of understanding hoop stress and mentions that the compression of the fluid may be the least significant factor in the overall volume change.
  • A participant requests assistance with the homework problem, indicating a need for further clarification on the topic.
  • Another response asserts that participants should engage with the material and formulate questions rather than seeking direct answers, highlighting the need for a foundational understanding of the subject.

Areas of Agreement / Disagreement

Participants express differing views on the significance of fluid compression versus structural deformation of the tube. There is no consensus on the relative importance of these factors in determining the additional liquid capacity.

Contextual Notes

Participants have not fully resolved the mathematical relationships or assumptions regarding the compressibility of the liquid and the deformation of the tube. The discussion lacks detailed definitions and specific parameters that could clarify the problem further.

Who May Find This Useful

This discussion may be useful for students studying fluid mechanics, particularly those interested in the effects of pressure on materials and the behavior of fluids in confined spaces.

amora
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A cylindrical tube (diameter = D, width = L) is completely filled with a liquid (density = ρ). A pump pressurizes the system with a pressure P. Consequently, 1) the solid tube is compressed and deformed according to Hooke's law (σ = ε.E), and 2) the liquid is compressed and deformed, following the modulus of elasticity (k).
The question is: what additional percentage of liquid will the tube accommodate as a result of the compressibility effect?

Tips:
Start by:
m = ρV
dm = ρdV + Vdρ
dm/m = ρdV/m + Vdρ/m
Apply Hooke's law to the first term and the modulus of compressibility to the second term.

Mentor note: Moved to homework forum from technical forum so no template.
 
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Welcome to PF.

The cylinder is a pressure vessel. The pressure inside the cylinder places the wall material in tension, to a greater degree than the internal pressure thins the wall. The hoop stress in the wall causes the most significant change, increasing the volume by the greatest amount. The next significant factor will be the increased length of the cylinder. Compression of the fluid will probably be least important.

Is this a homework assignment ?
 
Yes, it is
 
please help
 
We do not do your work for you.
You must read about the subject and ask questions when you get stuck.

The cylinder needs a wall thickness.
Now you need to understand hoop stress.

Assume the ends of the cylinder are flat and do not bend.
The ends are pushed apart by the internal pressure, which stretches the cylinder.
 

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