8.45 Repeat Prob. 8.44, but incorporate the fact that the friction factor can be computed with the von Karman equation, \frac{1}{\sqrt{f}} = 4 \log_{10}(Re\sqrt{f}) - 0.4 where Re = the Reynolds number Re = \frac{\rho VD}{\mu}
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The Swamee and Jain formula for the friction factor is $$f=\frac{0.25}{\left[\log \left(\varepsilon / 3.7 D+5.74 / \mathrm{Re}^{0.9}\right)\right]^{2}}$$ Compare this equation for $\varepsilon / D=0.00001,0.0001,0.001,$ and 0.01 and Reynolds numbers of $10^{4}, 10^{5}, 10^{6},$ and $10^{7}$ with the Moody chart and decide whether it is an acceptable replacement for the Colebrook formula.
The Haaland formula for the friction factor is $$f=\frac{0.3086}{\left\{\log \left[6.9 / \mathrm{Rc}+(\varepsilon / 3.7 D)^{1.11}\right]\right\}^{2}}$$ Compare this equation for $f$ for $\varepsilon / D=0.00001,0.0001,0.001$ and 0.01 and Reynolds numbers of $10^{4}, 10^{5}, 10^{6},$ and $10^{7}$ with the Moody chart and decide whether it is an acceptable replacement for the Colebrook formula.
Equating the expressions for hL from Darcy's equation and Hagen-Poiseuille equation as follows 32Ģ·Lv / Ģ³DĀ² = f (L/D) (vĀ²/2g) show that for laminar flow, the friction factor can be expressed as: f = 64 / NR
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