What is the hydrostatic force on a flat vertical wall of area A submerged to centroid depth h_c?

What is the hydrostatic force on a flat vertical wall of area A submerged to centroid depth h_c?

• A. F = ρ g h_c
• B. F = ρ g h A
• C. F = ρ g h_c^2 A
• D. F = ρ g h_c A^2

Answer: (A)

The key idea is that hydrostatic force on a submerged vertical plane surface comes from the fluid pressure that varies with depth. For a flat vertical wall, the pressure distribution is triangular, and the total force equals the pressure at the surface of the centroid depth multiplied by the area of the wall. Since the pressure at the centroid depth is p = ρ g h_c, the resultant force is F = p × A = ρ g h_c A. The given option that only has ρ g h_c gives a pressure, not a force, because it misses the area term. So the correct relationship for the force on the wall is F = ρ g h_c A. The discrepancy in the provided choices likely reflects a missing factor of A in that option.

The key idea is that hydrostatic force on a submerged vertical plane surface comes from the fluid pressure that varies with depth. For a flat vertical wall, the pressure distribution is triangular, and the total force equals the pressure at the surface of the centroid depth multiplied by the area of the wall. Since the pressure at the centroid depth is p = ρ g h_c, the resultant force is F = p × A = ρ g h_c A. The given option that only has ρ g h_c gives a pressure, not a force, because it misses the area term. So the correct relationship for the force on the wall is F = ρ g h_c A. The discrepancy in the provided choices likely reflects a missing factor of A in that option.