Pressure of Fluids

Pressure is the normal force exerted by a fluid per unit area, measured in pascals. Unlike force, which is a vector with specific direction, pressure is a scalar quantity with no directional component. Pressure always acts perpendicular to any surface in contact with the fluid because fluids cannot withstand shearing forces.

A needle concentrates force over a much smaller area than a finger, creating significantly higher pressure. The same force applied to 1 mm² produces 100 times greater pressure than when applied to 1 cm². This demonstrates how pressure, not force alone, determines whether a surface is penetrated or deformed.

Pressure at depth h equals atmospheric pressure plus the pressure from the fluid's weight above that point. This weight-based pressure is calculated as the product of fluid density, gravitational acceleration, and depth. In a swimming pool with constant density, pressure increases gradually with depth due to the water column above.

Water density remains approximately constant, so pressure changes predictably with depth. Air density, however, changes significantly just above Earth's surface, causing variation of atmospheric pressure to follow a different pattern. This fundamental difference affects how pressure behaves in the atmosphere versus in liquid bodies.

A perpendicular force compresses or expands the fluid, triggering a reaction force that develops at each point inside the fluid in the outward direction. This reaction force balances the applied force on the molecules at the boundary, maintaining equilibrium. This behavior is fundamental to understanding how fluids respond to external pressure.

Fluids cannot withstand or exert shearing forces, so they can only resist forces applied perpendicular to their surfaces. In a static fluid enclosed in a tank, forces on the walls and on any object within the fluid are always exerted perpendicular to the inner surface. This perpendicular orientation is a defining characteristic of fluid pressure.

When force is applied parallel to a fluid's surface, molecules flow freely to accommodate the horizontal force with minimal resistance. In contrast, perpendicular forces compress or expand the fluid, creating reaction forces. This difference reflects the fundamental property that fluids lack significant resistance to shearing forces but respond strongly to normal forces.