8.2 Fluids and Pressure

Defining Pressure

Pressure (P) is force per unit area applied perpendicular to a surface: P = F/A, measured in pascals (Pa = N/m²). Pressure is a scalar, not a vector — it acts equally in all directions at a point in a fluid. Increasing force or decreasing area increases pressure.

Pressure Varies with Depth

In a static fluid, pressure increases with depth because of the weight of fluid above: P = P₀ + ρgh, where P₀ is pressure at the surface, ρ is fluid density, g is gravity, and h is depth. This explains why deeper water exerts more pressure and why pressure is the same at all points at equal depth.

Pascal's Principle

Pascal's principle states that a pressure change applied to an enclosed, incompressible fluid is transmitted undiminished throughout the fluid. This is why hydraulic systems (like car lifts) can use a small force on a small piston to create a large force on a larger piston, since P = F/A is constant.

Key terms

Pressure formula

P = F/A, measured in pascals (Pa = N/m²).

Pressure and depth formula

P = P₀ + ρgh; pressure increases with depth due to the weight of fluid above.

Pascal's principle

A pressure change applied to an enclosed, incompressible fluid is transmitted undiminished throughout the fluid.

Is pressure a vector or scalar?

Scalar — it acts equally in all directions at a given point in a fluid.

Why hydraulic lifts work

A small force on a small-area piston creates the same pressure that produces a large force on a large-area piston (Pascal's principle).

Try an AP-style question

A hydraulic lift has a small piston of area 0.01 m² and a large piston of area 1 m². A 100 N force on the small piston can lift what weight?

1. 1,000 N
2. 10,000 N
3. 100 N
4. 1 N