Pressure at Depth in a Fluid (P = Pa + ρgh)
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P = Pa + ρgh
What each symbol means
| Symbol | What it stands for |
|---|---|
| P | Absolute pressure at depth h (Pa) |
| g | Acceleration due to gravity (m/s²) |
| h | Depth below the free surface (m) |
| Pa | Atmospheric pressure at the surface (Pa), ≈ 1.013 × 10⁵ Pa |
| ρ | Density of the fluid (kg/m³) |
When to use this
Assumes incompressible fluid with uniform density. Pressure depends only on vertical depth, not on container shape or cross-sectional area (hydrostatic paradox). Gauge pressure = P − Pa = ρgh. At same horizontal level, pressure is the same everywhere in a connected fluid.