Hydrostatic pressure at the bottom of a vertical column of liquid is described by which equation?

Hydrostatic pressure at the bottom of a vertical column of liquid is described by which equation?

• A. P = m g h
• B. P = ρ h / g
• C. P = h / (ρ g)
• D. P = ρ g h

Answer: (D)

Hydrostatic pressure in a liquid increases with depth because the weight of the fluid above pushes down. At depth h, the pressure is the weight of the column per unit area: P = (mass per unit area) × g. The mass per unit area is density times height, ρ h, so P = ρ g h. This is often written as P = γ h, where γ = ρ g is the specific weight. To see why the other forms don’t fit: P = m g h would have units of energy (N·m), not pressure. P = ρ h / g and P = h / (ρ g) mix in density and gravity incorrectly and yield incorrect units for pressure. For a quick check, with water (ρ ≈ 1000 kg/m^3) at 10 m depth (g ≈ 9.81 m/s^2), P ≈ 1000 × 9.81 × 10 ≈ 98,100 Pa.

Hydrostatic pressure in a liquid increases with depth because the weight of the fluid above pushes down. At depth h, the pressure is the weight of the column per unit area: P = (mass per unit area) × g. The mass per unit area is density times height, ρ h, so P = ρ g h. This is often written as P = γ h, where γ = ρ g is the specific weight.

To see why the other forms don’t fit: P = m g h would have units of energy (N·m), not pressure. P = ρ h / g and P = h / (ρ g) mix in density and gravity incorrectly and yield incorrect units for pressure.

For a quick check, with water (ρ ≈ 1000 kg/m^3) at 10 m depth (g ≈ 9.81 m/s^2), P ≈ 1000 × 9.81 × 10 ≈ 98,100 Pa.