I want to calculate the signal propagation speed in a real life coaxial cable. I have the data sheet which tells me its impedance and capacitance per unit length.
For long parallel wires carrying currents in opposite directions (i.e. transmission lines), we can use $$Z=\sqrt{\frac{L}{C}}$$ (where $Z$ is characteristic impedance, $L$ is inductance/unit length, $C$ is capacitance/unit length) to get $L$ given $Z$ and $C$. Then the signal speed is simply $$c=\frac{1}{\sqrt{LC}}$$ (see e.g. Griffith's, fourth edition, problem 7.62)
and boom, problem solved. How can I carry out a similar calculation for long, coaxial wires?