Pressure compensation piston

[msuple2]

I have a thin walled cylinder that is filled with oil at atmospheric pressure. This cylinder will be subjected to an overburdening external pressure of 22ksi. Under these circumstances the cylinder will crush.
To prevent crush I have added a piston with cross-sectional area of "X." When acted upon by the external 22ksi, the piston moves, decreasing the internal volume of the cylinder, effectively increasing the internal pressure to 22ksi and preventing crush. I need to determine the maximum stroke length of the piston in order to achieve equilibrium at 22ksi external pressure.

Thank you.

 

[btrueblood]

Then you need to know the bulk modulus of your oil (or its inverse, the compressibility), so you can calculate the volumetric change of the oil vs. applied pressure.

Knowing that value would also let you find the increase in pressure of an un-compensated cylinder undergoing elastic deformation (i.e. whether or not the filled cylinder would actually crush).

 

[msuple2]

How would I apply that?

 

[btrueblood]

from wikipedia,

The bulk modulus K can be formally defined by the equation

K = -V dP/dV (note the definition usually includes the term "isothermal", i.e. at a constant temperature)

So, if you wanted to know the volume displaced due to a pressure change, you would calculate

dV = V*Pd/K

from the link below, a typical bulk modulus for mineral oil is 2.5x10^5 psi

http://www.engineeringtoolbox.com/bulk-modulus-elasticity-d_585.html

For the 2nd problem, you find the displacement of the cylinder due to external pressure, and calculate the internal volume change, and then use the above equation to compute the pressure change due to that displacement. Link the two equations to find the combined stiffness of the filled cylinder, or just iterate to find the actual displacement and actual internal pressure.