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
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Density (ρ \rho ρ ) represents the mass per unit volume of a fluid
Formula: ρ = m V \rho = \frac{m}{V} ρ = V m
Units: k g m 3 \frac{kg}{m^3} m 3 k g (SI), s l u g f t 3 \frac{slug}{ft^3} f t 3 s l ug (English)
Examples: Water at 4°C has a density of 1000 k g m 3 \frac{kg}{m^3} m 3 k g , air at standard conditions has a density of 1.225 k g m 3 \frac{kg}{m^3} m 3 k g
Specific weight (γ \gamma γ ) represents the weight per unit volume of a fluid
Formula: γ = ρ g \gamma = \rho g γ = ρ g
Units: N m 3 \frac{N}{m^3} m 3 N (SI), l b f t 3 \frac{lb}{ft^3} f t 3 l b (English)
Relationship with density: γ = ρ g \gamma = \rho g γ = ρ g , where g g g is the acceleration due to gravity
Examples: Water at 4°C has a specific weight of 9810 N m 3 \frac{N}{m^3} m 3 N , mercury has a specific weight of 133,100 N m 3 \frac{N}{m^3} m 3 N
Specific gravity (SG) represents the ratio of a substance's density to the density of a reference substance (usually water at 4°C)
Formula: S G = ρ s u b s t a n c e ρ r e f e r e n c e SG = \frac{\rho_{substance}}{\rho_{reference}} SG = ρ re f ere n ce ρ s u b s t an ce
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 (μ \mu μ ) measures a fluid's resistance to deformation under shear stress
Dynamic (absolute) viscosity represents the ratio of shear stress to velocity gradient
Formula: τ = μ d u d y \tau = \mu \frac{du}{dy} τ = μ d y d u
Units: P a ⋅ s Pa \cdot s P a ⋅ s (SI), l b ⋅ s f t 2 \frac{lb \cdot s}{ft^2} f t 2 l b ⋅ s (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 (ν \nu ν ) represents the ratio of dynamic viscosity to density
Formula: ν = μ ρ \nu = \frac{\mu}{\rho} ν = ρ μ
Units: m 2 s \frac{m^2}{s} s m 2 (SI), f t 2 s \frac{ft^2}{s} s f t 2 (English)
Example: The kinematic viscosity of air at standard conditions is about 1.46 × 10⁻⁵ m 2 s \frac{m^2}{s} s m 2
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
Liquids: Density decreases with increasing temperature due to thermal expansion
Gases: Density decreases with increasing temperature according to the ideal gas law (ρ = P R T \rho = \frac{P}{RT} ρ = RT P )
Viscosity
Liquids: Viscosity decreases with increasing temperature as molecular cohesion weakens
Gases: Viscosity increases with increasing temperature due to increased molecular agitation
Pressure effects on fluid properties
Density
Liquids: Slight increase in density with increasing pressure due to their nearly incompressible nature
Gases: Density increases with increasing pressure according to the ideal gas law (ρ = P R T \rho = \frac{P}{RT} ρ = RT P )
Viscosity
Liquids: Negligible effect on viscosity since liquid molecules are already closely packed
Gases: Viscosity is independent of pressure for most engineering applications