Basic Fluid Properties

What you’ll learn

Fluids, which include both liquids and gases, are fundamental in fluid mechanics, where their behavior is analyzed based on key properties that influence motion, pressure, and flow dynamics. These properties determine how fluids respond to external forces and interact with their surroundings in various engineering applications.

Density

Density is the ratio of mass of fluid and its volume. It represents how much matter is packed into a given space and is one of the most fundamental fluid properties.

$\rho=\frac{M}{V}}$

Where:
$\rho$ =density
$M$ =mass
$V$ =volume

Typical Values

Fluid	Density ( $kg/m^3$ ) at $20^o C$
Water	998
Air	1.2
Mercury	13560
Glycerin	1260

Example

The glycerin has a mass of 1200 kg and a volume of 0.952 cu.m. Find its density?

$\rho=\frac{M}{V}$

$\rho=\frac{1200}{0.952}$

$\rho=12.366\:kN/m^3$

Specific Volume

Specific volume occupied by a unit mass of fluid. It is the reciprocal of density and is particularly useful in thermodynamic analysis.

$V=\frac{1}{\rho}$

where:
$V$ =specific volume $(m^3/kg)$
V=volume $(m^3)$
m=mass(kg)
$\rho$ =density $(kg/m^3)$

Specific Weight

Specific weight (also called unit weight) is the weight of fluid per unit volume. It represents the gravitational force exerted by a fluid per unit volume.

Where:
$\gamma$ = specific weight
W = weight (N)
V = volume $(m^3)$
$\rho$ = density $(kg/m^3)$
g = gravity acceleration

Example

Specific Gravity of an oil is 0.82. Determine its specific weight

Specific Gravity

Specific gravity (relative density) is the ratio of the density of a substance to the density of a reference substance.

$s=\frac{\rho_f}{\rho}=\frac{\gamma_f}{\gamma_w}$

where:
$\rho_f$ =density of the fluid
$\rho_w$ =density of the water
$\gamma_f$ =specific weight of the fluid
$\gamma_w$ =specific weight of the water

Bulk Modulus of Elasticity

Bulk modulus of elasticity measures a fluid’s resistance to compression. It quantifies how much pressure is required to produce a given fractional change in volume.

Example

A liquid compressed in a cylinder has a volume of 1000 cu.m at $\frac{2MN}{m^2}$ and a volume of $990\: cm^3$ at $\frac{3 \:MN}{m^2}$ . What is its bulk modulus of elasticity?

Compressibility

Compressibility is the reciprocal of the bulk modulus. It measures how much a material decreases in volume when subjected to pressure.

$\beta=\frac{1}{K}$

Types of Compressibility

Isothermal Compressibility

Volume change at constant temperature

Adiabatic Compressibility

Volumes changed without heat transfer

Example

If the Bulk Modulus of Water is 2.2 GPa. What is its coefficient of Compressibility?

Viscosity

Viscosity is defined as the fluid’s resistance to flow. It represents internal friction between fluid layers moving at different velocities.

Types of Viscosity

Dynamic Viscosity

Units: poise or 0.1 Pa-s

where:
$\tau$ =shear stress (Pa)
$\mu$ =dynamic viscosity $(Pa\dot s)$
$du/dy$ =velocity gradient ( $s^-1$ )

Kinematic Velocity

$v=\frac{\mu}{\rho}$

where:
$\nu$ =kinematic viscosity
$\mu$ =dynamic viscosity
$\rho$ =density

Surface Tension

The force responsible for the tension that acts along its surface and arises from the attractive forces between the liquid’s molecules. The strength of this force per unit length is known as surface tension.

Capillary Action

is when liquid rise or fall through narrow spaces without external forces.

References

J. D. Anderson Modern Compressible Flow with Historical Perspective, 3rd ed. New York: McGraw-Hill, 2003.

F L U I D M E C H A N I C S FUNDAMENTALS AND APPLICATIONS Third Edition. (n.d.). https://engineeringbookslibrary.wordpress.com/wp-content/uploads/2019/03/fluid-mechanics-fundamentals-and-applications-3rd-edition-cengel-and-cimbala-2014.pdf

CH2: HYDROSTATIC PRESSURE