Which equation expresses the total pressure at depth h in a fluid with density ρ and surface pressure P0?

• A. P = P0 - ρ g h
• B. P = P0 × ρ g h
• C. P = P0 + ρ g h
• D. P = P0 / (ρ g h)

Answer: (C)

Pressure in a fluid increases with depth because the weight of the fluid above adds to the surface pressure. At the surface you have P0, and going down a depth h you must support the hydrostatic column of fluid whose pressure is ρ g h. Add these together to get the total pressure at that depth: P = P0 + ρ g h. This matches the fact that deeper means more pressure, and ρ g h has the correct units for pressure (kg/m^3 × m/s^2 × m = N/m^2). Subtracting the hydrostatic term would imply pressure drops with depth, and multiplying or dividing by ρ g h would mis-match units and physical meaning, so the additive form is the correct relation.