(Solved): A fluid flow through pipes and tubes has great application in many areas of engineering. The resist ...

A fluid flow through pipes and tubes has great application in many areas of engineering. The resistance to flow is parameterized by a dimensionless number called the friction factor (f). For turbulent flow, the Colebrook equation is applicable $$0=\frac{1}{\sqrt{f}}+2.0\log \left(\frac{?}{3.7D}+\frac{2.51}{Re\sqrt{f}}\right)\text{ and }Re=\frac{?VD}{?}$$ where $$?=$$ the roughness $$(\mathrm{m}),\mathrm{D}=$$ diameter $$(\mathrm{m})$$, and $$\mathrm{Re}=$$ the Reynolds number Determine the friction factor $$\mathrm{f}$$ for air flow through a smooth, thin tube. For this case, $$?=1.23\mathrm{kg}/{\mathrm{m}}^3,?=1.79\times 10^{?5}\mathrm{N}?\mathrm{s}/{\mathrm{m}}^2,\mathrm{D}=0.005\mathrm{m},\mathrm{V}=40\mathrm{m}/\mathrm{s}$$ and $$?=0.0015\mathrm{mm}$$. Note that friction factors range from about $$0.008$$ to $$0.08$$. a) Use the bisect function with 3 iterations b) Use the False position with 3 iterations c) Use the Newton-Raphson method with initial guess $$\left(x_0=0.008\right)$$ and 3 iterations d) Use the Newton-Raphson method with initial guess $$\left(x_0=0.08\right)$$ and 3 iterations