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 define how its molecules pack together, how gravity acts on its mass, and how it compares to standard reference fluids.

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 ( $\rho$ )

Calculates the mass of a fluid per unit volume.

\rho = \frac{m}{V}

Variables

Symbol	Description	Unit
	Fluid density	-
$m$	Mass of the fluid	-
$V$	Volume of the fluid	-

Note

Typical Reference Values for Density:

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 ( $\gamma$ )

Relates fluid weight to volume or density using local gravitational acceleration.

\gamma = \rho g

Variables

Symbol	Description	Unit
	Specific weight	-
	Fluid density	-
$g$	Acceleration due to gravity	-

Note

Typical Reference Value for Specific Weight of Water:

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 ( $v$ )

Calculates the volume occupied per unit mass of fluid.

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

Variables

Symbol	Description	Unit
$v$	Specific volume	-
$V$	Volume of the fluid	-
$m$	Mass of the fluid	-
	Fluid density	-

Specific Gravity ( $S G$ )

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 ( $S G$ )

Determines the ratio of the fluid's density/specific weight compared to water (for liquids) or air (for gases).

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

Variables

Symbol	Description	Unit
$S G$	Specific gravity (dimensionless)	-
	Density of the fluid	$k g / m^{3}$
	Density of water at 4°C (1000 kg/m^3)	$k g / m^{3}$
	Specific weight of the fluid	$N / m^{3}$
	Specific weight of water at 4°C (9.81 kN/m^3)	$N / m^{3}$

Note

Typical Specific Gravity (SG) Values:

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

Viscosity

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 ( $μ \mu$ )

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 ( $μ \mu$ )

Relates the internal shear stress in a fluid to its rate of shear deformation.

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

Variables

Symbol	Description	Unit
	Shear stress	-
	Dynamic (absolute) viscosity	-
	Velocity gradient (rate of shear strain)	$s^{- 1}$

Note

Viscosity Units Conversion:

Standard SI unit: $\text{Pa}\cdot\text{s}$ or $\text{N}\cdot\text{s/m}^2$ .
CGS unit: Poise ( $\text{P}$ ), where $1\text{ P} = 0.1\text{ Pa}\cdot\text{s} = 0.1\text{ N}\cdot\text{s/m}^2$ .
Centipoise ( $\text{cP}$ ), where $1\text{ cP} = 10^{-3}\text{ Pa}\cdot\text{s}$ . (Water at 20°C has $\mu \approx 1.0\text{ cP}$ ).

Kinematic Viscosity ( $ν \nu$ )

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 ( $ν \nu$ )

Calculates the ratio of dynamic viscosity to density, representing the rate of momentum diffusion.

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

Variables

Symbol	Description	Unit
	Kinematic viscosity	-
	Dynamic viscosity	-
	Fluid density	-

Note

Kinematic Viscosity Units Conversion:

Standard SI unit: $\text{m}^2/\text{s}$ .
CGS unit: Stoke ( $\text{St}$ ), where $1\text{ St} = 10^{-4}\text{ m}^2/\text{s}$ .
Centistoke ( $\text{cSt}$ ), where $1\text{ cSt} = 10^{-6}\text{ m}^2/\text{s}$ .

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

)

What this teaches

This simulation illustrates fundamental fluid properties: surface tension and dynamic viscosity. Capillary rise shows how surface tension causes fluids to climb inside narrow tubes, while the shear stress visualization demonstrates how viscosity resists fluid deformation under a moving plate.

Try this

Select Water and decrease the Tube Diameter to 0.5mm. Observe the high capillary rise. Then switch to Oil to see the effect of lower surface tension and different specific weight.
Set Plate Velocity to 1.0 m/s. Switch between Water, Oil, and Honey. Notice the dramatic increase in Shear Stress required to move the plate through Honey due to its much higher dynamic viscosity.

Specific Weight (

\\gamma

)

9810 N/m³

Surface Tension (

\\sigma

)

0.0728 N/m

Dynamic Viscosity (

\\mu

)

0.001 Pa·s

Surface Tension and Capillarity

Surface tension and capillarity are 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.

Note

Surface Tension Units:

Standard units: $\text{N/m}$ or $\text{J/m}^2$ .

Pressure in Droplets, Bubbles, and Jets

Surface tension creates a pressure difference ( $\Delta P$ ) between the inside and outside of a curved interface, with the internal pressure always being higher. The magnitude of this pressure difference depends on the shape of the interface and the number of surface boundaries.

Internal Pressure in a Liquid Droplet

Calculates the pressure difference inside a spherical liquid droplet with a single surface boundary.

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

Variables

Symbol	Description	Unit
	Pressure difference (internal pressure minus external pressure)	-
	Surface tension	N/m
$R$	Radius of the droplet	m

Internal Pressure in a Soap Bubble

Calculates the pressure difference inside a spherical soap bubble, which has two surface boundaries (inner and outer).

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

Variables

Symbol	Description	Unit
	Pressure difference (internal pressure minus external pressure)	-
	Surface tension	N/m
$R$	Radius of the bubble	m

Internal Pressure in a Liquid Jet

Calculates the pressure difference inside a cylindrical liquid jet.

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

Variables

Symbol	Description	Unit
	Pressure difference (internal pressure minus external pressure)	-
	Surface tension	N/m
$R$	Radius of the cylindrical jet	m

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

Determines the vertical height of capillary rise or depression in a tube due to surface tension.

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

Variables

Symbol	Description	Unit
$h$	Capillary height (rise if positive, depression if negative)	m
	Surface tension	N/m
	Contact angle (wetting angle)	-
	Specific weight of the liquid	$N / m^{3}$
$d$	Internal diameter of the tube	m

Note

Capillary Characteristics & Wetting Angles:

Highly Wetting (e.g., Water & Clean Glass): $\theta \approx 0^\circ \implies \cos\theta \approx 1$ (results in capillary rise, $h > 0$ ).
Non-Wetting (e.g., Mercury & Glass): $\theta > 90^\circ$ (typically $\theta \approx 130^\circ$ to $140^\circ$ ), causing $\cos\theta$ to be negative (results in capillary depression, $h < 0$ ).

Vapor Pressure

Vapor pressure is the pressure exerted by a fluid's vapor in phase equilibrium with its liquid.

Vapor Pressure ( $P_{v}$ )

The pressure exerted by a fluid's 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.

Note

Characteristics of Vapor Pressure:

Vapor pressure is strongly dependent on temperature; it increases as temperature rises.
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

Compressibility describes 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

Relates the change in pressure to the corresponding fractional volumetric or density change.

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

Variables

Symbol	Description	Unit
$E_{v}$	Bulk modulus of elasticity	-
$d P$	Change in pressure	-
$d V$	Change in volume	$m^{3}$
$V$	Original volume	$m^{3}$
	Change in density	$k g / m^{3}$
	Original density	$k g / m^{3}$

Note

Understanding Bulk Modulus:

A large $E_v$ implies the fluid is relatively incompressible. For example, water has an $E_v$ of approximately $2.2\text{ GPa}$ , meaning a massive pressure increase is required to cause a small change in volume.
A small $E_v$ implies the fluid is highly compressible (such as gases).
The negative sign in the volume formulation compensates for the volume decrease ( $-dV$ ) resulting from a pressure increase ( $+dP$ ), ensuring $E_v$ is positive.

Ideal Gas Law

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

Ideal Gas Law (Equation of State)

The governing equation of state relating absolute pressure, temperature, and density for an ideal gas.

P = \rho R T

Variables

Symbol	Description	Unit
$P$	Absolute pressure	-
	Density	$k g / m^{3}$
$R$		-
$T$	Absolute temperature	K

Compressibility of Gases

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), whereas Kinematic Viscosity ( $\nu$ ) is dynamic viscosity divided by density ( $\nu = \mu / \rho$ ).
Newtonian Fluids have constant dynamic viscosity regardless of shear rate, whereas Non-Newtonian Fluids have viscosity that changes with shear rate.
Surface Tension ( $\sigma$ ) creates a pressure difference across a curved interface ( $\Delta P = 2\sigma/R$ for droplet, $4\sigma/R$ for bubble, $\sigma/R$ for jet), causing capillary rise/depression.
Vapor Pressure ( $P_v$ ) is the pressure at which a liquid boils at a given temperature; drop in pressure below this point triggers cavitation.
Bulk Modulus ( $E_v$ ) measures a fluid's resistance to compression (large for liquids, indicating incompressibility; small for gases).

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Concept Overview

Mass and Weight Properties

Density (ρ\rhoρ)

Density (ρ\rhoρ)

Note

Specific Weight (γ\gammaγ)

Specific Weight (γ\gammaγ)

Note

Specific Volume (vvv)

Specific Volume (vvv)

Specific Gravity (SGSGSG)

Specific Gravity (SGSGSG)

Note

Viscosity

Dynamic (Absolute) Viscosity (μ\muμ)

Dynamic (Absolute) Viscosity (μ\muμ)

Note

Kinematic Viscosity (ν\nuν)

Kinematic Viscosity (ν\nuν)

Note

Note

Fluid Properties Explorer

Fluid Properties Explorer

Capillary Rise (Surface Tension)

Shear Stress (Dynamic Viscosity)

What this teaches

Try this

Surface Tension and Capillarity

Surface Tension (σ\sigmaσ)

Note

Pressure in Droplets, Bubbles, and Jets

Internal Pressure in a Liquid Droplet

Internal Pressure in a Soap Bubble

Internal Pressure in a Liquid Jet

Capillary Rise/Depression (hhh)

Capillary Rise/Depression

Note

Vapor Pressure

Vapor Pressure (PvP_vPv​)

Note

Compressibility

Bulk Modulus of Elasticity (EvE_vEv​)

Bulk Modulus of Elasticity

Note

Ideal Gas Law

Ideal Gas Law (Equation of State)

Compressibility of Gases

Density ( $\rho$ )

Density ( $\rho$ )

Specific Weight ( $\gamma$ )

Specific Weight ( $\gamma$ )

Specific Volume ( $v$ )

Specific Volume ( $v$ )

Specific Gravity ( $S G$ )

Specific Gravity ( $S G$ )

Dynamic (Absolute) Viscosity ( $μ \mu$ )

Dynamic (Absolute) Viscosity ( $μ \mu$ )

Kinematic Viscosity ( $ν \nu$ )

Kinematic Viscosity ( $ν \nu$ )

Surface Tension ( $\sigma$ )

Capillary Rise/Depression ( $h$ )

Vapor Pressure ( $P_{v}$ )

Bulk Modulus of Elasticity ( $E_{v}$ )