Fluids, Density, and Pressure

A fluid is any state of matter that flows and yields to shearing (sideways) forces rather than resisting them. Both liquids and gases are fluids:

• Liquids: Definite volume, nearly incompressible, atoms in close contact but free to slide.
• Gases: Variable volume, highly compressible, large separation between atoms.

Density and Specific Gravity

Average density ($\rho$) is defined as mass per unit volume:

In heterogeneous materials where density varies throughout the volume, local density at a point is defined by taking the limit:

• SI Unit: $\text{kg/m}^3$ ($1 \text{ g/cm}^3 = 1000 \text{ kg/m}^3$).
• Water Standard: $\rho_{\text{water}} = 1000 \text{ kg/m}^3$ at $4.0^\circ\text{C}$.

Specific Gravity is a dimensionless ratio comparing a material's density to the density of water at $4.0^\circ\text{C}$:

Pressure

Average pressure ($p$) is the perpendicular force per unit area:

For non-uniform forces or infinitesimal surfaces, local pressure at a point is given by:

• SI Unit: Pascal ($1 \text{ Pa} = 1 \text{ N/m}^2$).
• Standard Atmosphere: $1 \text{ atm} = 1.013 \cdot 10^5 \text{ Pa} = 101.3 \text{ kPa}$.

Pressure is a scalar quantity that acts equally in all directions at a point within a fluid; the force exerted by pressure always acts perpendicularly to any surface it contacts.