An oil of density $870 \mathrm{~kg} / \mathrm{m}^{3}$ and viscosity $0.036 \: \mathrm{Pa.s}$ flows through a straight pipe of $10 \: \mathrm{cm }$ diameter and $1.5 \: \mathrm{km}$ length at the flow rate of $250$ liters per minute under the steady and incompressible flow conditions. To control the flow rate of oil, a valve is fixed at the middle of the pipe causing no change in the total length of the pipe. The total head loss measured across the two ends of the pipe is $11.60 \: \mathrm{m}$. Using gravitational acceleration as $10 \mathrm{~m} / \mathrm{s}^{2}$, the minor head loss contributed by the presence of the valve in $\mathrm{m}$ (rounded off to $2$ decimal places) is $\_\_\_\_\_\_$
