Fluid properties are the building blocks of fluid mechanics. Density, specific weight, and specific gravity help us understand how fluids behave under different conditions. These properties are crucial for solving real-world engineering problems.

Ideal fluids simplify analysis, but real fluids are more complex. Viscosity, a key property, affects flow behavior and energy dissipation. Temperature and pressure also impact fluid properties, influencing density and viscosity in both liquids and gases.

Fluid Properties

Density and specific properties

• Density ($\rho$) represents the mass per unit volume of a fluid
  • Formula: $\rho = \frac{m}{V}$
  • Units: $\frac{kg}{m^3}$ (SI), $\frac{slug}{ft^3}$ (English)
  • Examples: Water at 4°C has a density of 1000 $\frac{kg}{m^3}$, air at standard conditions has a density of 1.225 $\frac{kg}{m^3}$
• Specific weight ($\gamma$) represents the weight per unit volume of a fluid
  • Formula: $\gamma = \rho g$
  • Units: $\frac{N}{m^3}$ (SI), $\frac{lb}{ft^3}$ (English)
  • Relationship with density: $\gamma = \rho g$, where $g$ is the acceleration due to gravity
  • Examples: Water at 4°C has a specific weight of 9810 $\frac{N}{m^3}$, mercury has a specific weight of 133,100 $\frac{N}{m^3}$
• Specific gravity (SG) represents the ratio of a substance's density to the density of a reference substance (usually water at 4°C)
  • Formula: $SG = \frac{\rho_{substance}}{\rho_{reference}}$
  • Dimensionless quantity
  • Examples: The specific gravity of oil is typically around 0.8, while the specific gravity of glycerin is about 1.26

Ideal vs real fluids

• Ideal fluids have simplified properties that make them easier to analyze
  • Incompressible (constant density) regardless of pressure changes
  • Inviscid (no viscosity) meaning they have no resistance to shear stress
  • No thermal conductivity, so heat transfer within the fluid is not considered
  • Examples: Potential flow around an airfoil, inviscid flow through a nozzle
• Real fluids have properties that more closely represent actual fluids encountered in engineering applications
  • Compressible (density changes with pressure) especially relevant for gases
  • Viscous (has viscosity) which causes resistance to flow and energy dissipation
  • Has thermal conductivity, allowing heat transfer within the fluid
  • Examples: Air flow over an aircraft wing, water flow through a pipe, oil lubricating a bearing

Viscosity in fluid mechanics

• Viscosity ($\mu$) measures a fluid's resistance to deformation under shear stress
  • Dynamic (absolute) viscosity represents the ratio of shear stress to velocity gradient
    • Formula: $\tau = \mu \frac{du}{dy}$
    • Units: $Pa \cdot s$ (SI), $\frac{lb \cdot s}{ft^2}$ (English)
    • Examples: Water at 20°C has a dynamic viscosity of 1.002 mPa·s, while honey at room temperature has a dynamic viscosity of about 10,000 mPa·s
  • Kinematic viscosity ($\nu$) represents the ratio of dynamic viscosity to density
    • Formula: $\nu = \frac{\mu}{\rho}$
    • Units: $\frac{m^2}{s}$ (SI), $\frac{ft^2}{s}$ (English)
    • Example: The kinematic viscosity of air at standard conditions is about 1.46 × 10⁻⁵ $\frac{m^2}{s}$
• Viscosity plays a crucial role in various aspects of fluid mechanics
  • Affects boundary layer formation near solid surfaces
  • Influences flow regime (laminar vs. turbulent) through the Reynolds number
  • Determines pressure drop in pipes and ducts (Hagen-Poiseuille equation)
  • Impacts heat transfer in fluids (Prandtl number)

Temperature and pressure effects

• Temperature effects on fluid properties
  • Density
    1. Liquids: Density decreases with increasing temperature due to thermal expansion
    2. Gases: Density decreases with increasing temperature according to the ideal gas law ($\rho = \frac{P}{RT}$)
  • Viscosity
    1. Liquids: Viscosity decreases with increasing temperature as molecular cohesion weakens
    2. Gases: Viscosity increases with increasing temperature due to increased molecular agitation
• Pressure effects on fluid properties
  • Density
    1. Liquids: Slight increase in density with increasing pressure due to their nearly incompressible nature
    2. Gases: Density increases with increasing pressure according to the ideal gas law ($\rho = \frac{P}{RT}$)
  • Viscosity
    1. Liquids: Negligible effect on viscosity since liquid molecules are already closely packed
    2. Gases: Viscosity is independent of pressure for most engineering applications