A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The figure (not drawn to scale) shows the arrangement of differential manometer attached to the duct.  

When the water flows, the differential manometer shows a deflection of 8cm of mercury (Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively. Consider the acceleration due to gravity, g = 9.81 m/s². Assuming frictionless flow, the flow rate (in m³/s, round off to 3 decimal places) through the duct is __________.