Week 2 - Fluids and Fluid Properties

What is a fluid?

A substance that deforms continuously (or flows) under the action of shearing forces (no matter how small)

3 Examples of fluids

Liquids (Water), Gas (Air), Multiphase (Slurries)

Fluid mechanics is the branch of applied mechanics that’s concerned with ... and ... of fluids

Statics (Fluids at rest), Dynamics (Fluid is moving)

What’s the equation for Shear Stress (𝜏)?

Force (N) / Area (m²) = Shear stress (𝜏) (N/m² or Pa)

What is Viscosity?

Viscosity is the resistance of fluids to flow (shear forces)

What is Newtons law of Viscosity / shear stress equation?

𝝉 = 𝝁 * ⅆ𝒖/ⅆ𝒚

Shear stress ( Pa or N/M²) 𝝉 = 𝝁 Dynamic viscosity (Pa · s) x (ⅆ𝒖 (change in velocity) / ⅆ𝒚 (change in distance))

What is a Newtonian fluid?

Fluids that HAVE a constant dynamic viscosity value.

(Shear stress is linearly related to the velocity gradient)

What is a Non-Newtonian fluid?

Fluids that DON’T have a constant dynamic viscosity value.

Therefore the viscosity changes when you apply varied shear forces.

What is a Plastic Fluid?

A Non-Newtonian fluid that behaves like a solid until a certain minimum shear stress (called the yield stress) is exceeded after which it flows like a liquid

What is a Pseudo-Plastic?

Dynamic viscosity decreases ↓ as the rate of shear increases ↑

(e.g. milk and cement)

what is a Dilatant Substance?

Dynamic viscosity increases ↑ as rate of shear increases ↑

(e.g. quicksand)

What happens when a fluid is at rest?

NO shearing forces acting

So all forces in the fluid must be perpendicular to the planes upon which the act

What is deformation caused by?

Shearing Forces that act tangentially (in the direction) to the surfaces to which they are applied.

What is a fluid in motion?

A fluid whose particles are moving relative to a reference point. Shear stresses are developed when the fluid is in motion.

For fluids the … is proportional to the … so …

rate of strain is proportional to the applied stress so a fluid continues to flow as long as the force is applied.

For solids the … is a function of the … provided that the … is not exceeded

strain is a function of the applied stress provided that the elastic limit is not exceeded

What is the equation for density ?

ρ (kg/m³) = m (kg) / V (m³)

density = mass / volume

What are the equations for specific weight

γ (N/m³) = W (N) / V (M³)

γ (N/m³) = M (kg) * g (9.81m/s²) / V (m³)

γ (N/m³) = ρ (kg/m³) * g (9.81m/s²)

W - Weight

V - Volume

g - Gravity

ρ - Density

What defines relative density / specific gravity (SG) ?

Ratio of the mass density of a substance to some standard mass density

For solids and liquids what is the standard mass density chosen as

The maximum density of water ( which occurs at 4℃)

What is the equation for specific gravity or relative density?

SG = ρ (of the substance) / ρ (water at 4℃)

What is the coefficient of dynamic viscosity (μ)?

shear force per unit area required to drag one layer of fluid with unit velocity (u) past another layer a unit distance (s) away.

What is the equation for dynamic viscosity?

μ = 𝝉 / (dv/dy) = 𝝉 Shear stress ( Pa or N/M²) / (ⅆv (change in velocity) / ⅆ𝒚 (change in distance))

μ = (Force/Area) / (Velocity/Distance)

μ = (Force x Time) / Area

OR

Mass / (Length x Time)

What is kinematic Viscosity (ν)?

Ratio of dynamic viscosity (μ) to mass density (ρ)

What is the equation of Kinematic Viscosity?

v = μ/ρ

m²/s = Pa·s/ (kg/m³)