A smooth vertical cylindrical column of diameter 2 m and height 6 m is placed on top of the seabed in water 5 m deep (see Figure 1). If the peak tidal current has a horizontal velocity profile with depth of: () = ( 0.32 ) 1/7 where is a vertical coordinate that is directed positive upwards from the mean free surface, is the depth-average velocity and is the water depth, how large can the depth-average current speed be until the column will become unstable (due to rotation)? You may assume the column is made of concrete (submerged density 1250 kg/m3 and density in air of 2277 kg/m3 ) and placed on a rigid bed such that rotation of the column would occur about point 'O' in Figure 1. You may take the water density to be 1027 kg/m3 and the viscosity to be 1.010-6m2 /s