Fluid Pressure

Definition

Fluid pressure $p$ is the force per unit area exerted by a fluid at depth $h$: $p = wh$ where $w$ is the weight-density of the fluid.

• How to read: “The pressure p equals w times h.”
• Meaning: Hydrostatic pressure at depth $h$ equals weight-density times depth—force per unit area from the fluid column above.

Why It Matters

Accurate calculation of fluid pressure is a literal life-and-death requirement in engineering; failure to account for depth-dependent pressure leads to the catastrophic collapse of hulls and storage tanks.

Core Concepts

• Depth Dependence: Pressure increases linearly with depth due to the weight of the fluid column above.
• Pascal’s Principle: Fluid pressure is exerted equally in all directions at a given depth.
• Scalar Quantity: Pressure is a scalar, meaning it has magnitude but no specific direction until it acts on a surface.

Connected Concepts

• Fluid Forces
• Physics
• Bernoulli’s Principle