Pressure in Tube, Bulk Modulus

[nathangrand]

A straight tube, 1m long, of radius 10mm and wall thickness, is closed at both ends. It is found that when the pressure inside is increased from 10^5 Pa to 10^6 Pa the tube lengthens by 100um. What is the bulk modulus of the material of the tube?

Well know that P = -Bdv/V and also that for a thin tube of radius r and thickness t<<r under pressure P the hoop stress is rP/t and the stress in the axial direction is rp/2t

I can work out the fractional change in volume etc but really stuck with the question! Please HELP!

 

[jbsteele]

The bulk modulus of the material of the tube can be calculated using the following equation: Bulk Modulus = -(Pressure x Change in Volume) / (Original Volume x Change in Pressure) Therefore, the Bulk Modulus of the material of the tube is: Bulk Modulus = -(10^5 Pa x 0.0001 m^3) / (1 m^3 x 10^6 Pa) = -0.1 GPa