Properties of Fluids

Properties of Fluids

Fundamental properties of fluids including density, specific weight, specific gravity, viscosity, surface tension, and compressibility.

Concept Overview

Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. A fluid is defined as a substance that deforms continuously under the application of a shear stress, no matter how small the stress may be. Understanding the fundamental properties of fluids is essential for analyzing fluid behavior at rest (hydrostatics) and in motion (fluid dynamics).

Mass and Weight Properties

The fundamental relationships between the mass, volume, and weight of a fluid.

Fundamental Density Properties

Density ( $\rho$ )

Mass per unit volume of a substance. It is a measure of how tightly matter is packed together. Density is a crucial property for determining the buoyant force and the kinetic energy of a moving fluid.

Density ($\rho$)

The fundamental relationships between the mass, volume, and weight of a fluid.

\rho = \frac{m}{V}

Water (at 4°C): \rho \approx 1000 \text{ kg/m}^3 or 1.94 \text{ slugs/ft}^3
Air (at STP): \rho \approx 1.2 \text{ kg/m}^3

Specific Weight ( $\gamma$ )

Weight per unit volume of a substance. It relates the density of a fluid to the local acceleration due to gravity, making it extremely useful in hydrostatic pressure calculations.

Specific Weight ($\gamma$)

\gamma = \rho g

Water: \gamma \approx 9.81 \text{ kN/m}^3 or 62.4 \text{ lb/ft}^3

Specific Volume ( $v$ )

Volume per unit mass of a substance. It is the reciprocal of density.

Specific Volume ($v$)

v = \frac{V}{m} = \frac{1}{\rho}

Units: m^3/\text{kg} or \text{ft}^3/\text{slug}

Specific Gravity ( $SG$ )

The ratio of the density (or specific weight) of a fluid to the density (or specific weight) of a standard fluid (typically water at 4°C for liquids, and air at standard temperature and pressure for gases). It is a dimensionless quantity.

Specific Gravity ($SG$)

SG = \frac{\rho_{fluid}}{\rho_{water}} = \frac{\gamma_{fluid}}{\gamma_{water}}

Mercury: SG \approx 13.6
Oil: SG \approx 0.8 \text{ to } 0.9

Viscosity

The internal resistance of a fluid to shear forces and continuous deformation.

Concept Overview

Viscosity is a property that represents the internal resistance of a fluid to motion or the "fluidity". It determines the fluid's flow characteristics and is the primary source of energy loss in fluid flow due to friction.

Dynamic (Absolute) Viscosity ( $\mu$ )

The constant of proportionality in Newton's Law of Viscosity, which states that shear stress is directly proportional to the rate of shear strain (velocity gradient) for Newtonian fluids.

Dynamic (Absolute) Viscosity ($\mu$)

The internal resistance of a fluid to shear forces and continuous deformation.

\tau = \mu \frac{du}{dy}

\tau = Shear stress (Pa or N/m^2)
du/dy = Velocity gradient or rate of shear strain (s^{-1})
Units: Pa\cdot s or N\cdot s/m^2 (SI), Poise (P) where 1 \text{ P} = 0.1 \text{ Pa}\cdot s.

Kinematic Viscosity ( $\nu$ )

The ratio of dynamic viscosity to density. It appears frequently in fluid dynamics equations (e.g., Reynolds number) because it represents the ratio of viscous forces to inertial forces.

Kinematic Viscosity ($\nu$)

\nu = \frac{\mu}{\rho}

Units: m^2/s (SI), Stoke (St) where 1 \text{ St} = 10^{-4} \text{ m}^2/s.

Note

Newtonian vs. Non-Newtonian Fluids:

Newtonian Fluids: Shear stress is linearly proportional to the rate of shear strain (e.g., water, air, gasoline). The dynamic viscosity \mu is constant for a given temperature and pressure.
Non-Newtonian Fluids: The relationship between shear stress and strain rate is non-linear (e.g., blood, toothpaste, ketchup, cornstarch suspensions). Their apparent viscosity changes with the applied shear rate.

Fluid Properties Explorer

Interact with fluid properties like surface tension and dynamic viscosity across different fluid types.

Fluid Properties Explorer

Fluid Type

Tube Diameter ($d$)2.0 mm

Plate Velocity ($U$)0.50 m/s

Capillary Rise (Surface Tension)

Observe how tube diameter and fluid type affect rise.

14.8 mm

Calculated Rise ($h$)

Shear Stress (Dynamic Viscosity)

Drag a plate over a 5mm gap of fluid.

MOVING PLATE

0.100 Pa

Shear Stress ($\tau$)

Specific Weight ($\gamma$)

9810 N/m³

Surface Tension ($\sigma$)

0.0728 N/m

Dynamic Viscosity ($\mu$)

0.001 Pa·s

Surface Tension and Capillarity

Phenomena arising from unbalanced cohesive forces at fluid interfaces.

Surface Tension ( $\sigma$ )

The intensity of the molecular attraction per unit length along any line in the surface. It is caused by cohesive forces between fluid molecules. In the bulk of the liquid, molecules are pulled equally in all directions, but at the surface, there is a net inward pull, creating a "skin" effect.

Units: N/m or J/m^2

Pressure in Droplets and Bubbles

Surface tension creates a pressure difference (\Delta P) between the inside and outside of a curved interface. The inside pressure is always higher.

Liquid Droplet: (Has one surface)

Pressure in Droplets and Bubbles

Phenomena arising from unbalanced cohesive forces at fluid interfaces.

\Delta P = \frac{2\sigma}{R}

Soap Bubble: (Has two surfaces, inner and outer, so the force is doubled)

\Delta P = \frac{4\sigma}{R}

Liquid Jet: (Cylindrical shape)

\Delta P = \frac{\sigma}{R}

Capillary Rise/Depression ( $h$ )

The rise or fall of a liquid in a small diameter tube inserted into the liquid. It is caused by the interplay between cohesive forces (within the liquid) and adhesive forces (between the liquid and the tube wall).

Capillary Rise/Depression ($h$)

h = \frac{4\sigma \cos\theta}{\gamma d}

\theta = Contact angle (0° for pure water/clean glass - highly wetting; >90° for mercury/glass - non-wetting)
d = Tube inside diameter
\gamma = Specific weight of the liquid

Vapor Pressure

The pressure exerted by a fluid's vapor in phase equilibrium with its liquid.

Vapor Pressure ( $P_v$ )

The pressure exerted by its vapor in phase equilibrium with its liquid at a given temperature. If the local absolute pressure in a fluid system drops below the vapor pressure, the liquid locally boils, leading to a potentially destructive phenomenon called cavitation.

Strongly dependent on temperature: as temperature increases, vapor pressure increases.
Water at 20°C: P_v \approx 2.34 \text{ kPa}
Water at 100°C: P_v \approx 101.325 \text{ kPa} (1 \text{ atm})

Compressibility

The change in volume or density of a fluid in response to a change in pressure.

Bulk Modulus of Elasticity ( $E_v$ )

A measure of a fluid's resistance to compression. It relates the change in pressure to the fractional change in volume or density.

Bulk Modulus of Elasticity ($E_v$)

The change in volume or density of a fluid in response to a change in pressure.

E_v = - \frac{dP}{dV/V} = \frac{dP}{d\rho/\rho}

Large E_v implies the fluid is relatively incompressible. For example, water has an E_v of about 2.2 GPa, meaning it requires a massive pressure increase to slightly reduce its volume.
Small E_v implies the fluid is highly compressible (like gases).
The negative sign in the volume formulation accounts for the fact that an increase in pressure (+dP) results in a decrease in volume (-dV), ensuring E_v is a positive value.

Ideal Gas Law

The equation of state relating pressure, temperature, and density for gases.

Equation of State

For gases under normal conditions, the relationship between absolute pressure, absolute temperature, and density is given by the Ideal Gas Law.

Equation of State

The equation of state relating pressure, temperature, and density for gases.

P = \rho R T

Variables

Symbol	Description	Unit
$P$	Absolute pressure	Pa
$\rho$	Density	kg/m$^3$
$R$	Specific gas constant (J/kg$\cdot$K) - For air, $R \approx 287$ J/kg$\cdot$K	-
$T$	Absolute temperature	Kelvin, K

Compressibility of Gases

How the bulk modulus changes depending on the thermodynamic process.

Isothermal vs. Isentropic

The bulk modulus of a gas depends on the thermodynamic process of compression.

Isothermal Process (Constant Temperature): $E_v = P$
Isentropic Process (Adiabatic and Reversible): $E_v = k P$

Where

k

is the specific heat ratio (

c_p/c_v

). For air,

k \approx 1.4

Key Takeaways

Density (\rho) is mass per unit volume. For water, it is approximately 1000 \text{ kg/m}^3.
Specific Weight (\gamma) is weight per unit volume, which factors in gravity (\gamma = \rho g).
Specific Gravity (SG) is a dimensionless ratio comparing a fluid's density to a standard reference (usually water for liquids).
Dynamic Viscosity (\mu) relates shear stress to the rate of shear strain (velocity gradient).
Kinematic Viscosity (\nu) is dynamic viscosity divided by density (\nu = \mu / \rho).
For Newtonian Fluids, dynamic viscosity is constant regardless of shear rate.
Surface Tension (\sigma) creates a pressure difference across a curved interface, where pressure inside a droplet or bubble is higher than outside.
A Soap Bubble has two surfaces, resulting in double the pressure difference compared to a standard droplet.
Capillary Action depends on surface tension, contact angle, tube diameter, and fluid specific weight. A contact angle over 90° (like mercury) leads to capillary depression.
Vapor Pressure is the pressure at which a liquid boils. It is highly temperature-dependent and crucial for predicting cavitation in pumps and pipes.
Bulk Modulus (E_v) measures a fluid's resistance to compression.
A very large E_v value, typical of liquids like water, indicates the fluid is practically incompressible.
Gases have small E_v values, making them highly compressible under pressure changes.
Density vs Specific Weight: Density is mass-based; Specific Weight is force/weight-based. They are strictly related by local gravitational acceleration (g).
Viscosity: Temperature dependent. For liquids, viscosity decreases with an increase in temperature (due to reduced cohesive forces). For gases, viscosity increases with temperature (due to increased molecular momentum exchange).
Surface Tension: Causes droplets to form spheres to minimize surface area and causes liquids to rise or fall in capillary tubes depending on the wetting angle.
Compressibility: Water and most liquids are generally treated as incompressible (E_v is very large), whereas gases are compressible.
Units: Always strictly convert values to standard SI units (kg, m, s, Pa) before entering them into formulas to prevent scale errors.

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Concept Overview

Mass and Weight Properties

Fundamental Density Properties

Density (ρ\rhoρ)

Density ($\rho$)

Specific Weight (γ\gammaγ)

Specific Weight ($\gamma$)

Specific Volume (vvv)

Specific Volume ($v$)

Specific Gravity (SGSGSG)

Specific Gravity ($SG$)

Viscosity

Concept Overview

Dynamic (Absolute) Viscosity (μ\muμ)

Dynamic (Absolute) Viscosity ($\mu$)

Kinematic Viscosity (ν\nuν)

Kinematic Viscosity ($\nu$)

Note

Fluid Properties Explorer

Fluid Properties Explorer

Capillary Rise (Surface Tension)

Shear Stress (Dynamic Viscosity)

Surface Tension and Capillarity

Surface Tension (σ\sigmaσ)

Pressure in Droplets and Bubbles

Pressure in Droplets and Bubbles

Capillary Rise/Depression (hhh)

Capillary Rise/Depression ($h$)

Vapor Pressure

Vapor Pressure (PvP_vPv​)

Compressibility

Bulk Modulus of Elasticity (EvE_vEv​)

Bulk Modulus of Elasticity ($E_v$)

Ideal Gas Law

Equation of State

Equation of State

Compressibility of Gases

Isothermal vs. Isentropic

Density ( $\rho$ )

Specific Weight ( $\gamma$ )

Specific Volume ( $v$ )

Specific Gravity ( $SG$ )

Dynamic (Absolute) Viscosity ( $\mu$ )

Kinematic Viscosity ( $\nu$ )

Surface Tension ( $\sigma$ )

Capillary Rise/Depression ( $h$ )

Vapor Pressure ( $P_v$ )

Bulk Modulus of Elasticity ( $E_v$ )