Water flows through a smooth circular pipe under turbulent conditions. In the viscous sub-layer, the velocity varies linearly with the distance from the wall. The Fanning friction factor is defined as, $f=\frac{\tau _{w}}{\rho \bar{u}^{2}/2}$ where $\tau _{w}$ is the shear stress at the wall of the pipe, $\rho$ is the density of the fluid and $\bar{u}$ is the average velocity in the pipe. Water (density=$1000\:kg\:m^{-3}$, viscosity = $1 \times 10^{-3}\:kg\:m^{-1}\:s^{-1}$) flow as at an average velocity of $1\:m\:s^{-1}$ through the pipe. For this flow condition, the friction factor $f$ is $0.005$. At a distance of $0.05\:mm$ from the wall of the pipe (in the viscous sub-layer), the velocity (in $m\:s^{-1}$, rounded off to the third decimal place ), is _____________

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