Fluid Mechanics L4 - Properties of Fluids and Viscosity

Properties

Describe how a fluid (liquid or gas) behaves; chracteristics of a system

Intensive properties

Independent of mass

• T, P, ρ

Extensive properties

Dependent on mass

• mass, volume, momentum, size

Define fluid and what we treat it as

Collection of molecules sometimes widely spaced apart but we treat it as continuous and homogeneous matter (a continuum)

What does continuum idealization allow us to assume?

Properties vary continually in space with no jump discontinuities

Continuum idealization is valid as long as

The system is large relative to the space between molecules

Density formula

ρ = m/V

Ideal Gas Law

Pv = RT

What is density like in gases vs liquids

• Highly variable in gases (Ideal Gas Law)

• Nearly constant in liquids (assumed incompressible)

Density of water

1000 kg/m³

Specific volume formula

v = V/m = 1/ρ

Differential volume element

ρ = δm/δV

Specific gravity meaning and units

Relative density to water; dimensionless

Specific gravity formula

SG = ρ/ρH₂O

Specific weight

The weight per unit volume of a substance

Specific weight formula

γ = ρg

Total energy formula

E or e = u +ke + pe

Internal energy symbol

U or u
Group thermal energy with internal energy

What is microscopic energy due to molecular activity

Internal energy

Kinetic energy

Energy as a result of motion

Kinetic energy formula

ke = v²/2

Velocity symbol

v

Potential energy

Elevation

Potential energy equation

pe = gz
(z = elevation)

Enthalpy

Internal energy and flow energy (energy needed to move fluid)

Enthalpy equation

h = u + Pv = u + P/ρ

Viscosity

Measure of a fluid’s internal resistance to flow

Dynamic or absolute viscosity symbol

µ

Dynamic or absolute viscosity formula

µ = m/Lt

Kinematic velocity symbol

v (nu)

Kinematic velocity formula

v = µ/ρ

Drag force

Force a flowing fluid exerts on a body in the flow direction, depends on viscosity

Shear thickening fluids (dilatant)

Apparent viscosity increases with the rate of deformation

• starch, sand

Shear thinning fluids (pseudoelastic)

Apparent viscosity decreases as it is sheared harder

• paints

Bingham plastics

Acts as a solid past a specific shear stress

• toothpaste