Module 1
Mass per unit volume: ρ = m / V. Units: kg·m⁻³. Water (25°C) ≈ 1000 kg/m³, Air (25°C) ≈ 1.184 kg/m³.
Specific weight γ = ρ g (N/m³).
Specific gravity SG = ρ_fluid / ρ_water (dimensionless).
Viscosity is internal resistance to shear. Dynamic μ relates shear stress to velocity gradient: τ = μ du/dy. Kinematic ν = μ/ρ. Liquids: μ ↓ with T; gases: μ ↑ with T.
Bulk modulus K = −V dP/dV. Liquids have high K (low compressibility), gases low K. Speed of sound: a = √(K/ρ).
Vapor pressure is the pressure at which liquid vaporizes. High vapor pressure → easier evaporation; important for cavitation in pumps and propellers.
Surface tension σ causes liquids to minimize surface area; capillary rise formula:
h = (2 σ cos θ) / (ρ g r)θ = contact angle, r = tube radius.
- Shear-Thinning: Paint, blood, ketchup τ = k (du/dy)n, n < 1
- Shear-Thickening: Cornflour mixture (oobleck) τ = k (du/dy)n, n > 1
- Bingham Plastic: Toothpaste τ = τ₀ + μₚ (du/dy)
- Thixotropic: Gels, yogurt μ = μ(t)
- Rheopectic: Gypsum paste
| Category | Newtonian Fluids | Non-Newtonian Fluids |
|---|---|---|
| Nature / Behavior | Viscosity remains constant, independent of shear rate. | Viscosity changes with shear rate or time. |
| Mathematical Model | τ = μ (du/dy) | τ = k (du/dy)n or τ = τ₀ + μₚ (du/dy) |
| Shear Stress vs Shear Rate | Linear relationship | Non-linear relationship |
| Viscosity Dependence | Depends only on temperature | Depends on shear rate, time, and molecular structure |
| Flow Curve | Straight line | Curved / non-linear |
| Examples | Water, air, kerosene, alcohol, mercury | Honey, ketchup, blood, toothpaste, paints, oobleck |
| Types | — (No types; simple behavior) | Pseudoplastic, Dilatant, Bingham Plastic, Thixotropic, Rheopectic |
| Applications | Aerodynamics, lubrication, pipelines, hydraulic systems | Food processing, cosmetics, drilling mud, biomedical fluids, paints |
| Industries Used | Aviation, aerospace, chemical plants, HVAC | FMCG, oil & gas, biomedical, pharmaceuticals, construction |
| Behavior Under Force | Predictable, easy to model | Complex, may require rheometers for analysis |
| Temperature Sensitivity | Moderate | High (strong dependence on structure) |
Steady: ∂(property)/∂t = 0
Unsteady flow properties vary with time. ∂(property)/∂t ≠ 0
Example (Unsteady): Pump start-up flow
Uniform: Velocity same at every point.
∂u/∂x = 0
Example: Long straight pipe flow
Non-uniform: Velocity varies along path.
∂u/∂x ≠ 0
Example: Flow through a nozzle
Laminar: Smooth, orderly motion of fluid layers.E.g., Honey or oil flow (Re < 2000)
Turbulent:Chaotic, mixing flow. E.g., Water from a fast-open tap (Re > 4000)
or, ∇·V = 0
Example: High-speed air flow.
Incompressible: Constant density, dρ/dt ≠ 0
Example: Water at low speeds.
Rotational: Vortex near drain
∇ × V = 0
Irrotational: Potential flow over airfoils
V = V(x, y) 2D: Flow over a flat plate
V = V(x, y, z) 3D: Turbulent flow in real world
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Silver mist suffused the deck of the ship.
As I went on, still gaining velocity, the palpitation of night and day merged into one continuous greyness; the sky took on a wonderful deepness of blue, a splendid luminous color like that of early twilight; the jerking sun became a streak of fire, a brilliant arch, in space; the moon a fainter fluctuating band; and I could see nothing of the stars, save now and then a brighter circle flickering in the blue.
Andorson
The spectacle before us was indeed sublime.
Apparently we had reached a great height in the atmosphere, for the sky was a dead black, and the stars had ceased to twinkle. By the same illusion which lifts the horizon of the sea to the level of the spectator on a hillside, the sable cloud beneath was dished out, and the car seemed to float in the middle of an immense dark sphere, whose upper half was strewn with silver. Looking down into the dark gulf below.
Kevin D. Roberts - CEO