Hydrostatic Pressure

A fluid at rest exerts pressure that increases with depth. This hydrostatic pressure arises from the weight of fluid above a given point:

$P = \rho g h$

where:

• $\rho$ is fluid density (kg/m³)
• $g = 9.81\,\text{m/s}^2$ is gravitational acceleration
• $h$ is depth below the free surface (m)

Total Absolute Pressure at Depth

Adding atmospheric pressure gives the total (absolute) pressure at depth $h$:

$P_{\text{total}} = P_{\text{atm}} + \rho g h$

where $P_{\text{atm}} = 101\,325\,\text{Pa}$.

Hydrostatic Force on a Horizontal Surface

The hydrostatic force on a horizontal flat surface of area $A$ at depth $h$ is simply:

$F = P \cdot A = \rho g h A$

Examples

Your Task

Implement:

• hydrostatic_pressure(rho, h) — gauge pressure at depth $h$ (Pa)
• total_pressure(rho, h) — absolute pressure at depth $h$ (Pa)
• hydrostatic_force(rho, h, A) — force on a horizontal surface (N)