Friction Factor, f, can be estimated using following relations -
Colebrook-White (Modified)
\displaystyle \frac{1}{\sqrt{f}}= -2*Log_{10}\left[ \frac{\epsilon}{3.7}+\frac{2.825}{\left(Re*\sqrt{f}\right)}\right]
IGT Improved
\displaystyle \frac{1}{\sqrt{f}}=2.3095*Re^{0.1}
Chen
\displaystyle \frac{1}{\sqrt{f}}=-2\log_{10}\left(\frac{\epsilon}{3.7065} - \frac{5.0452}{Re}*\log_{10}C\right)
where,
\displaystyle C=\frac{\epsilon^{1.1096}}{2.8257}+\frac{7.149}{Re^{0.8961}}
Gouder - Sonnad
\displaystyle \frac{1}{\sqrt{f}}=0.8686*\ln\left[\frac{0.4587*Re}{{C-0.31}^{C/(C+1)}}\right]
where,
\displaystyle C = 0.124*Re*\epsilon+\ln\left(0.4587*Re\right)
Renouard
\displaystyle \frac{1}{\sqrt{f}}=0.21*{Re}^{-0.2}, Re < 4000
\displaystyle \frac{1}{\sqrt{f}}=2.4112*{Re}^{0.09}, 4000 < Re < 4e6
\displaystyle \frac{1}{\sqrt{f}}=2.1822*{Re}^{0.1}, Re > 4e6