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I'm conducting some experiments to test for the pressure exerted by a thermally expanding cylinder inside a tube. The cylinder is placed snugly inside the tube, usually with zero to a few 0.001s clearance. The cylinder has a higher coefficient of friction than the tube, therefore we expect pressure to be exerted onto the inside surface area. I've tried using

\begin{equation}

P=E\frac{\Delta R}{R}

\end{equation}

where E is the elastic modulus of the cylinder and $\Delta$ R is the constrained length (also considering the expansion of the outer tube). And R is the radius of the cylinder. Am I right in assuming the expansion is radial?

Now enter a new variable. The tube is lined with a soft fabric that will absorb some of the pressure as deflection. How can I calculate the pressure on the surface of the fabric liner caused by the thermally expanding cylinder? Is there a way to include both compressibilities (elastic modulii) into one equation? Help!

Thanks!!