A viscous fluid flows slowly by gravity down a \(2 \mathrm{~cm}\) diameter galvanized iron pipe. The pressures at the higher and lower locations are \(120 \mathrm{kPa}\) and \(130 \mathrm{kPa}\), respectively. The horizontal distance between the two locations is \(6 \mathrm{~m}\), and the pipe has a slope of \(2 \mathrm{~m}\) rise per \(10 \mathrm{~m}\) of run (horizontal distance). For a fluid with a kinematic viscosity of \(4 \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s}\) and a density of \(880 \mathrm{~kg} / \mathrm{m}^{3}\).

a. Determine the flow rate (in \(\mathrm{m}^{3} / \mathrm{s}\) ).

b. What is the Reynolds number of this flow?

c. What is the friction factor and head loss for flow through this pipe?

\[f=\frac{64}{R e_{d}} \quad h_{L}=f\left(\frac{\bar{v}^{2}}{2 g}\right)\left(\frac{L}{d}\right)\]