A thin $1\mathrm{.}2$ m wide, right$-$angle gate with negligible mass is free to pivot about a frictionless hinge at point O $,$ as shown in Figure $3.$ The horizontal portion of the gate covers a $0\mathrm{.}3$ m diameter drainpipe, which contains air at atmospheric pressure. Determine the minimum water depth, h $,$ at which the gate will pivot to allow water to flow into the pipe.

Figure. $3$