How to determine length of coax to get a certain delay?
Velocity factor is the proportion of c (speed of light) that a signal travels at in a cable: -

VF = \$\dfrac{1}{c\sqrt{LC}}\$

Where L and C are the distributed inductance and capacitance per metre length of the cable. Little "c" is the speed of light.

You can use \$\epsilon_R\$ as well because \$\mu_R\$ can be assumed to be unity: -

VF = \$\dfrac{1}{\sqrt{\epsilon_R}}\$

So (with the assumption that VF = 1) if you have a piece of coax that is 7.5m long and you feed it with a 10 MHz sinewave, the delay (phase shift) will be 90 degrees. If it's 15m long then the delay will be 180 degrees. A 30m length will look like the same phase as the original sinewave expect it will be lagging by one full wavelength.

If VF = 0.6667 (for example) the signal takes longer to travel a fixed distance than the speed of light hence, to obtain a 90 degree phase shift at 10MHz requires a length of cable that is 0.667 x 7.5m = 5m.

If all you can find is the characteristic impedance and capacitance per unit length you can also calculate VF like this: -

VF = \$\dfrac{1}{C\cdot Z_0}\$ because \$Z_0 = \sqrt{\dfrac{L}{C}}\$