Turbulent Pipe Flow
n is the exponent in the empirical power-law equation of a turbulent flow in a pipe. (See equations 8.22, 8.23 & 8.24. In chapter 8.5)
a is close to 1 for highly turbulent flow.
From empirical data, the exponent, n, in the power law is a function of the Reynolds number for a fully developed, smooth pipe flow: n = -1.7 + 1.8 log(ReU) = -1.7 + 1.8 log(UD/n), where U is the centerline velocity.