Chapter 17: Hydrostatics

Fluid

Any matter that flows, including liquids, gases, and some solids.

Density (ρ)

The mass per unit volume of a substance, given by $\rho =\frac{m}{V}$. SI unit: kg/m³.

Specific Gravity

The ratio of the density of a substance to the density of pure water.

Pressure (P)

The force per unit area exerted by a fluid, measured in pascals (Pa).

Pressure at Depth

Formula

$P=P_0+\rho gd$

Key Points

• Pressure increases with depth.
• Shape and volume of the container do not affect the pressure at a given depth.

Pascal's Principle

Definition

An external pressure applied to an enclosed fluid is transmitted equally in all directions.

Applications

Hydraulic systems use Pascal's principle to amplify force.

Formula for Hydraulic Systems

$\frac{F_2}{F_1}=\frac{A_2}{A_1}$

Archimedes’ Principle

Definition

A fluid exerts an upward buoyant force on an object submerged in it, equal to the weight of the displaced fluid.

Formula

$F_{\text{buoyant}}={\rho }_{\text{fluid}}g{V}_{\text{displaced}}$

Questions for Students

1. Define fluid, density, and specific gravity.
2. State Pascal's principle and explain its application in hydraulic systems.
3. Use the formula for pressure at depth to calculate the pressure 10 meters below the surface of water.
4. Explain Archimedes’ principle with an example.
5. Describe why an object floats, sinks, or remains neutrally buoyant in a fluid.