Fluid Mechanics: Properties of Fluids

Fluid Definition

• A fluid continuously deforms under shear stress, regardless of its size
• Shear stress is the tangential force divided by the surface area

Shear Stress and Solids

• Solids deform under shear stress but cease to deform when stress is removed

Dimensions of Physical Quantities

• Dimensions measure the type of quantity (length, time, mass)
• Units express the magnitude of a physical quantity (meters, seconds, kilograms)

Primary Dimensions

• Mass (M), Length (L), Time (t), Temperature (T)

SI Units

• Mass: kilogram (kg)
• Length: meter (m)
• Time: second (s)
• Temperature: Kelvin (K)

BG Units

• Mass: pound-mass (lbm)
• Length: foot (ft)
• Time: second (s)
• Temperature: Rankine (R)

Density

• Density $(\rho)$ is mass per unit volume: $\rho = \frac{m}{V}$
• SI Units for density: $kg/m^3$
• BG Units for density: $lbm/ft^3$

Specific Volume

• Specific volume $(v)$ is volume per unit mass: $v = \frac{V}{m} = \frac{1}{\rho}$
• SI Units for specific volume: $m^3/kg$
• BG Units for specific volume: $ft^3/lbm$

Specific Weight

• Specific weight $(\gamma)$ is weight per unit volume: $\gamma = \frac{W}{V} = \rho g$
• SI Units for specific weight: $N/m^3$
• BG Units for specific weight: $lbf/ft^3$

Specific Gravity

• Specific gravity (SG) is the density ratio relative to a reference substance:
• $SG = \frac{\rho}{\rho_{H_2O}}$ for liquids
• $SG = \frac{\rho}{\rho_{air}}$ for gases
• $\rho_{H_2O}$ is the density of water at 4°C
• $\rho_{air}$ is the density of air at standard conditions
• Specific gravity is dimensionless.

Vapor Pressure

• Vapor pressure is the pressure exerted by a vapor in equilibrium with its condensed phases at a given temperature.
• Vapor pressure indicates a liquid's evaporation rate.

Surface Tension

• Surface tension is the tendency of liquid surfaces to minimize their area.
• Measured in dynes/cm or N/m.

Viscosity

• Viscosity measures a fluid's resistance to flow, indicating internal friction.
• High viscosity fluids resist motion more than low viscosity fluids.
• Shear stress is defined as: $\tau = \mu \frac{du}{dy}$
• Where $\tau$ is shear stress, $\mu$ is dynamic viscosity, and $\frac{du}{dy}$ is the velocity gradient
• SI Units for viscosity: $Pa \cdot s$
• BG Units for viscosity: $lbf \cdot s/ft^2$

Kinematic Viscosity

• Calculated via: $\nu = \frac{\mu}{\rho}$
• $\nu$ is kinematic viscosity, $\mu$ is dynamic viscosity, and $\rho$ is density.
• SI Units for kinematic viscosity: $m^2/s$
• BG Units for kinematic viscosity: $ft^2/s$