A large rectangular plate of area A=0.40m2 is completely submerged in a freshwater lake so that the center of the plate is at a depth h=3.0m below the surface.
Case 1: The plate is oriented horizontally (facing upward).
Case 2: The same plate is oriented vertically (facing sideways toward the shoreline) with its center still at the same depth h.
Assume the water is at rest and has density ρ=1000kgm−3. Neglect atmospheric pressure, because it acts on both sides of the plate in both cases.
(a) Determine the gauge pressure exerted by the water at the center of the plate.
(b) Calculate the magnitude of the net force exerted by the water on the plate for Case 1.
(c) Without repeating the full calculation, determine the magnitude of the net force on the plate for Case 2. State and justify any assumption you make.
(d) Briefly explain, using microscopic reasoning, why the force magnitudes obtained in parts (b) and (c) are the same or different.