Problem $05\mathrm{.}055-$ Water discharged from the bottom of a pressurized tank

A pressurized tank of water has a $10-cm-$diameter orifice at the bottom, where water discharges to the atmosphere. The water level is $2\mathrm{.}5$ m above the outlet. The tank air pressure above the water level is $250$ kPa $($absolute$),$ while the atmospheric pressure is $100$ kPa $.$ Neglecting frictional effects, determine the initial discharge rate of water from the tank. $($Round the final answer to three decimal places.$)$

The initial discharge rate of water from the tank is determined to be $\frac{m^3}{s}$