(Solved): Problem 2. A thin 3-meter-wide, right-angle gate with negligible mass is free to pivot about a fri ...

Problem 2. A thin 3-meter-wide, right-angle gate with negligible mass is free to pivot about a frictionless hinge at point $$\mathrm{O}$$, as shown in Fig. 1(b). The horizontal portion of the gate covers a 1-m-diameter drain pipe that 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. The specific weight of water at $$20^{?}\mathrm{C}$$ is $$9790\mathrm{N}/{\mathrm{m}}^3$$. Figure 1: Diagrams corresponding to (a) problem 1, and (b) problem 2.