Understanding Fluids

Fluids are materials that can flow and take the shape of their container, including both liquids and gases. Unlike solids, the molecules in fluids can move freely past each other.

Key Properties

• Density (\( \rho \)): Measures how much mass is packed into a given volume. It's calculated as \( \rho = \frac{m}{V} \).
• Pressure (\( P \)): The force exerted per unit area. In fluids, pressure increases with depth due to the weight of the fluid above.

Fluid Statics

When fluids are at rest, the pressure at a certain depth depends on the fluid's density and gravity:

\[ P = P_0 + \rho g h \] where \(P_0\) is surface pressure, \(g\) is acceleration due to gravity, and \(h\) is the depth.

Buoyancy

Archimedes' principle states that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.

Real-World Connections

Ships float because the buoyant force from water balances their weight. Submarines adjust their buoyancy by controlling the amount of water in ballast tanks.