Definitions of basic fluid properties

These are the basic physical properties used to describe a fluid.

• Specific weight (weight density), $w$ or $\gamma$: weight per unit volume, $\gamma = \rho g$. Unit N/m³. Water: 9810 N/m³.
• Specific gravity, $S$: ratio of the density (or specific weight) of a fluid to that of a standard fluid (water at 4 °C for liquids, air for gases). $S = \rho/\rho_w$; no unit. Mercury: 13.6.
• Specific mass (mass density), $\rho$: mass per unit volume, $\rho = m/V$. Unit kg/m³. Water: 1000 kg/m³.
• Specific volume, $v$: volume per unit mass, $v = 1/\rho$. Unit m³/kg. Mostly used for gases.
• Viscosity: the property by which a fluid resists the relative motion (shear) between its layers. By Newton's law, $\tau = \mu \dfrac{du}{dy}$, where $\mu$ is the dynamic viscosity (N·s/m² or Pa·s). Kinematic viscosity $\nu = \mu/\rho$ (m²/s).
• Surface tension, $\sigma$: the tensile force per unit length acting on the free surface of a liquid, caused by cohesion between liquid molecules. Unit N/m. Water–air at 20 °C: about 0.073 N/m.
• Capillarity: rise or fall of a liquid in a thin tube due to surface tension, adhesion and cohesion. Rise $h = \dfrac{4\sigma \cos\theta}{\rho g d}$. Water rises (adhesion > cohesion); mercury falls.
• Compressibility: the reciprocal of bulk modulus; it measures the fractional change in volume per unit change of pressure, $\beta = \dfrac{1}{K} = -\dfrac{dV/V}{dp}$. Unit m²/N. Liquids have very low compressibility, so they are treated as incompressible.