The Colebrook equation (Eq. 8.37) for computing the turbulent friction factor is implicit in \(f\). An explicit expression [31] that gives reasonable accuracy is

\[f_{0}=0.25\left[\log \left(\frac{e / D}{3.7}+\frac{5.74}{R e^{0.9}}\right)\right]^{-2}\]

Compare the accuracy of this expression for \(f\) with Eq. 8.37 by computing the percentage discrepancy as a function of \(\operatorname{Re}\) and \(e / D\), for \(R e=10^{4}\) to \(10^{8}\), and \(e / D=0,0.0001,0.001,0.01\), and 0.05. What is the maximum discrepancy for these \(\operatorname{Re}\) and \(e / D\) values? Plot \(f\) against \(R e\) with \(e / D\) as a parameter.

Data From  (Eq. 8.37)

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