- Practice · 4+4 marks
Fluid properties and flow description methods
Short answer
A fluid deforms continuously under shear. Newtonian fluids have constant viscosity (e.g., water); non-Newtonian viscosity varies with shear rate (e.g., blood). Temperature rise decreases liquid viscosity but increases gas viscosity. Lagrangian tracks individual particles; Eulerian observes fixed points. A system is a fixed mass; a control volume is a fixed region allowing mass flow across its surface.
(a) Define a fluid. Differentiate between a Newtonian and a non-Newtonian fluid with examples, and state how temperature affects the viscosity of liquids and gases. (b) Differentiate between the Lagrangian and Eulerian methods of describing fluid motion, and between a system and a control volume.
(a) Fluid, Newtonian and non-Newtonian fluids
A fluid is a substance that deforms continuously under the action of a shear stress, however small. Liquids and gases are fluids.
A Newtonian fluid obeys Newton's law of viscosity: shear stress is directly proportional to the rate of shear strain (velocity gradient).
| Basis | Newtonian fluid | Non-Newtonian fluid |
|---|---|---|
| vs | Straight line through origin | Curved line, or has a yield stress |
| Viscosity | Constant at given temperature | Changes with shear rate (apparent viscosity) |
| Examples | Water, air, kerosene, mercury | Blood, paint, toothpaste, polymer solutions |
| Types | Single type | Pseudoplastic, dilatant, Bingham plastic |
Effect of temperature:
- Liquids: viscosity decreases as temperature rises, because cohesive forces between molecules weaken.
- Gases: viscosity increases as temperature rises, because molecular momentum exchange between layers increases.
(b) Lagrangian and Eulerian methods
| Basis | Lagrangian | Eulerian |
|---|---|---|
| Idea | Follow an individual fluid particle along its path | Observe a fixed point in space as the fluid passes |
| Variables | Position and velocity as functions of time for each particle | Velocity, pressure as functions of |
| Acceleration | Directly | Needs material derivative (local + convective) |
| Use | Particle tracking, sprays, dispersion | Most fluid mechanics, velocity fields |
Fluid mechanics mostly uses the Eulerian method because it is easier to handle mathematically.
| Basis | System | Control volume |
|---|---|---|
| Definition | Fixed identifiable mass of fluid | Fixed region in space chosen for analysis |
| Boundary | Moves and deforms with the fluid | Fixed (usually); called control surface |
| Mass crossing boundary | None | Mass can cross the surface |
| Used with | Lagrangian view | Eulerian view, Reynolds transport theorem |
✓ Answer checked by Claude Opus 5.5 (high effort)
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