Equation to fill the Headspace loop adequately.

I take a course for the 7697A Headspace sampler and I have a question regarding the equation used to make sure that the volume of gas in the HS vial was at least 3 times the volume of the loop. 

If I had a 1 mL loop, I need to flush it with at least 3 mL of vial's gas. If I used a 10 mL vial with 50% of gas space, my headspace volume is 5 mL. 

For example, if I pressurize the HS vial to 15 PSI and I am filling the loop until 10 PSI, how can I know how much volume of gas sample was flushing the loop before injection?

If I try the equation show above, I assume that the change in pressure is 5 PSI (15-10 = 5 PSI) and the initial pressure is (15 PSI + 14.7 PSI= 29.7 PSI).

(5 / 29.7) * 5 mL = 0.84 mL so it's not enough. right? 

Can someone help me with that? 

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