(Solved): 6. (30 pts.) A container is attached to the bottom of a pool of \( 20^{\circ} \mathrm{C} \) Glyceri ...

6. (30 pts.) A container is attached to the bottom of a pool of \( 20^{\circ} \mathrm{C} \) Glycerin as show above, A hatch, \( 2 \mathrm{~m} \) in diameter, is located in a \( 25^{\circ} \) inclined wall and hinged on one edge. The top of the container is located a depth of \( 8 \mathrm{~m} \) below the surface of the Glycerin. Initially, the container holds Methane gas at a temperature of \( -50{ }^{\circ} \mathrm{C} \) and a density of \( 0.75 \mathrm{~kg} / \mathrm{m}^{3} \). The Methane is then heated until the hatch opens. Assume the Methane acts like an incompressible, ideal gas. Neglect the weight of the hatch and friction in the hinge. The atmospheric pressure is \( 101 \mathrm{kPa} \). (a) Determine the magnitude of the resultant force due to the pressure of the Glycerin on the hatch. (b) Determine the location with respect to the hinge where the resultant force acts on the hatch. (c) Draw a complete Free Body Diagram of the hatch. (d) Determine the minimum Methane pressure within the structure that will open the hatch. (e) Determine the absolute temperature of the Methane when the hatch opened. Problem 6.