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Hooman Fatoorehchi Assistant Professor School of Chemical Engineering University of Tehran, Tehran, Iran  Fluid Mechanics I The Moody diagram that gives the Darcy-Weisbach friction factor. 
You can download a high-quality PDF file version of this diagram by clicking HERE. The Darcy-Weisbach friction factor for single-phase turbulent flow in rough pipes: $\frac{1}{\sqrt{f}}=-2 \log_{10}\left( \frac{150.39}{Re^{0.98865}}-\frac{152.66}{Re}+\frac{\epsilon}{3.71 D} \right) $ Reference: DOI= 10.1016/j.nucengdes.2011.07.042 Remark: In the advanced Bernoulli equation (the one from Bird's textbook), the friction factor is Fanning's friction factor. The Darcy or the Darcy-Weisbach Friction Factor $f=4\frac{\tau_w}{\frac{\rho V^2}{2}}=8\frac{\tau_w}{\rho V^2} $, where $\tau_w$ is the shear stress value at the inner wall (of the pipe). Minor (non-frictional) Losses:
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