We saw in Section 8.7 that instead of the implicit Colebrook equation (Eq. 8.37) for computing the turbulent friction factor \(f\), an explicit expression that gives reasonable accuracy is \[\frac{1}{\sqrt{f}}=-1.8 \log \left[\left(\frac{e / D}{3.7}\right)^{1.11}+\frac{6.9}{R e}\right]\] 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 \(R e\) and \(e / D\) values? Plot \(f\) against \(R e\) with \(e / D\) as a parameter.