# Shrink Tape Applying Pressure

*Most recent answer: 10/12/2017*

- Drew (age 30)

Charlotte, North Carolina

That's a nice physics problem. The tension force in the tape is the same as the dF/dL where F is the free energy and L is the length. You say T=(8.5 lbs/inch)*W where W is tape width, presumably assuming that the tape is not allowed to contract.

The pressure is dF/dV where V is volume. Now we have to make a physical assumption. Can the material squish out the ends of the cylinder? If so, squeezing it won't put it under extra pressure.If it's held in so it can't squish out, than dV=WdA where A is the cross-section area. A=L^{2}/4π. So dV=(WL/2π)dL.

The material is probably highly incompressible, so you get the maximum T. The added pressure is then dF/dV=(2π/WL)dF/dL=(2π/L)*8.5 lbs/inch. That's about 54 lbs/inch*L. If you measure L in inches, that gives pressure in convenient pounds per square inch. A 10" tape would give 5.4 psi.

Mike W.

*(published on 10/12/2017)*