B$.6$ A flushing tank has an L$-$shape gate at its bottom corner and hinged at $O$ as depicted in Fig. B$\mathrm{.}6.$ The vertical leaf of the gate is $600mm$ by $400mm$ and the horizontal leaf is $400mm$ by $400mm.$ Water is continuously filled into the tank. Determine the depth of water, $h,$ that will cause the gate to turn clockwise and to discharge the water.

$(20$ marks$)$