A cylindrical tank with a diameter of $500 \mathrm{~mm}$ contains water (density $=1 \mathrm{~g} \cdot \mathrm{cm}^{-3}$ ) upto a height $h$. A $5 \mathrm{~mm}$ diameter round nozzle, whose center is $1 \mathrm{~cm}$ above the base of the tank, has its exit open to the atmosphere as shown in the schematic below. The pressure above the water level in the tank is maintained at $2$ bar (absolute). Neglect all frictional and entry/exit losses. Use acceleration due to gravity as $10 \mathrm{~m} \cdot \mathrm{s}^{-2}$ and atmospheric pressure as $1$ bar. The absolute value of initial $\frac{d h}{d t}$ (in $\mathrm{mm} \cdot \mathrm{s}^{-1}$ ) when $h=51 \mathrm{~cm}$ is equal to___________(rounded off to two decimal places).
