Updated on 04/05/26 by Mananjay Mahato
- Properties and Classification of Fluid:
- Ideal & real fluids
- Newton’s law of viscosity
- Newtonian and Non Newtonian fluids
- compressible and incompressible fluids
Newton’s Law of Viscosity
- This law states that the shear stress (τ) on a fluid element layer is directly proportional to the rate of shear strain (or velocity gradient).
- τ = μ (du/dy)
- τ: Shear stress (N/m² or Pascal).
- μ: Constant of proportionality, known as Dynamic Viscosity (Units: Pa·s or Poise; 1 Pa·s = 10 Poise).
- du/dy: Velocity gradient or rate of shear strain (s⁻¹).
Classification of Fluids (Based on Viscosity)
- Fluids are primarily classified based on how they respond to shear stress.
- A. Ideal Fluid
- Incompressible and has zero viscosity (no friction).
- Does not exist in reality; it is a mathematical concept used for simplified analysis.
- Surface tension is zero.
- B. Real Fluid
- Possesses viscosity, surface tension, and compressibility.
- All fluids found in nature are real fluids.
- C. Newtonian Fluids
- Follow Newton’s Law of Viscosity.
- The viscosity (μ) remains constant regardless of the shear strain rate.
- Examples: Water, Air, Kerosene, Mercury, Alcohol.
- D. Non-Newtonian Fluids
- Do not follow Newton’s Law of Viscosity.
- The relationship between shear stress and velocity gradient is non-linear.
- Examples: Blood, Paint, Toothpaste, Polymer solutions.
| Type | Characteristic | Examples |
| Pseudoplastic | Viscosity decreases with stress (Shear-thinning) | Blood, Milk, Paper pulp |
| Dilatant | Viscosity increases with stress (Shear-thickening) | Starch in water, Quick sand |
| Bingham Plastic | Requires a “yield stress” before it starts to flow | Toothpaste, Sewage sludge |
| Thixotropic | Viscosity decreases with time under constant stress | Lipstick, Enamel paints |
Compressibility and Incompressibility
- Compressibility (β)
- It is the measure of the change in volume (or density) of a fluid due to a change in external pressure. It is the reciprocal of the Bulk Modulus (K).
- β = 1/K
- Incompressible Fluid: A fluid where the density (ρ) does not change with pressure. Liquids are generally considered incompressible for most engineering calculations.
- Compressible Fluid: A fluid where the density changes significantly with pressure. Gases (Air, Steam) are highly compressible.
- Kinematic Viscosity (ν): The ratio of dynamic viscosity to density (ν = μ / ρ). Units: m²/s or Stokes.
- Effect of Temperature:
- In Liquids, viscosity decreases as temperature increases (due to weakened cohesive forces).
- In Gases, viscosity increases as temperature increases (due to increased molecular momentum transfer).
- No-slip condition: At a solid boundary, the velocity of the fluid is zero relative to the boundary.
- Ideal Plastic: A fluid that reaches a certain yield stress and then behaves like a Newtonian fluid (constant du/dy).