Clean water is passed through a bed of uniform spherical sand at a filtration velocity of $0.002 \mathrm{~m} / \mathrm{sec}$. The sand grains are $0.4 \mathrm{~mm}$ in diameter and have a specific gravity of 2.65. Bed depth is $0.67 \mathrm{~m}$ and porosity $(\eta)$ is $0.35$. Given, water density $=998.2 \mathrm{~kg} / \mathrm{m}^{3}$; water dynamic viscosity $=1.002 \times 10^{-3}$ Pa.s. Friction factor $(f)$ is given as: $f=1.75+\{150 \times(1-\eta) /(\operatorname{Re})\}$ where Re is Reynolds number. The headloss (in $\mathrm{m}$, rounded off to three decimal places) calculated using the Carmen-Kozney equation is _____________.
