A rough pipe of $0.5$ m diameter, $300$ m length and roughness height of $0.25$ mm, carries water (kinematic viscosity $= 0.9 \times 10^{-6} \: m^2/s$) with velocity of $3$ m/s. Friction factor $(f)$ for laminar flow is given by $f=64/R_e$, and for turbulent flow it is given by $\frac{1}{\sqrt{f}} = 2 \log_{10} \Big( \frac{r}{k} \Big) + 1.74$, where, $R_e$ = Reynolds number, r=radius of pipe, k=roughness height and $g=9.81 \: m/s^2$. The head loss (in m, up to three decimal places) in the pipe due to friction is _______