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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.

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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