How does hydrostatic pressure vary with depth in a fluid?

How does hydrostatic pressure vary with depth in a fluid?

• A. Pressure is independent of depth.
• B. Pressure increases linearly with depth, P = ρ g h.
• C. Pressure decreases with depth.
• D. Pressure varies with area.

Answer: (B)

Hydrostatic pressure in a fluid increases with depth because the amount of fluid above a point grows as you go deeper, adding more weight that pushes down. If the fluid has constant density, the pressure rises linearly with depth: P = P0 + ρ g h. In open conditions, P0 is the atmospheric pressure at the surface, so the depth dependence is essentially P ≈ ρ g h. This means deeper points experience higher pressure in direct proportion to how deep they are. The pressure at a given depth is the same across a horizontal plane, independent of the container’s cross-sectional area, which relates to total force but not to pressure itself.

Hydrostatic pressure in a fluid increases with depth because the amount of fluid above a point grows as you go deeper, adding more weight that pushes down. If the fluid has constant density, the pressure rises linearly with depth: P = P0 + ρ g h. In open conditions, P0 is the atmospheric pressure at the surface, so the depth dependence is essentially P ≈ ρ g h. This means deeper points experience higher pressure in direct proportion to how deep they are. The pressure at a given depth is the same across a horizontal plane, independent of the container’s cross-sectional area, which relates to total force but not to pressure itself.