I will have to look at my older copy of Brannan's book but in reviewing my references and going through some other sources I have, Q is not included in the exponent. The equation I gave above is all I have.
I have done some comparisons of the two formulas and pleckner's version looks more reasonable to me. Using the C. Brannan formula tells me that in a 10" line 25 USgpm, which would have a velocity of 0.10 ft/s, will fill the pipe. This feels very wrong to me. Pleckner's formula would give a flow of 3225 USgpm flowing at 13.2 ft/s and my gut feeling tells me this would fill the pipe. It wouldn't be the first time I have suspected a formula from the Brannan book.