Lec1 to 38

Continuum Hypothesis

We neither want Sampling large volume nor small volume.Moderate vol or optimum vol is required. When volume is small we will have molecular uncertainity- Discontinuous and fluctuatng nature of density will be observed .When volume is large we will have macroscopic uncertainity - Spatial variations(different spaces has difff values) will be observed in density.

Rarefied gases means gases at very low pressure.Very few molecules at large vol.

For use of calculus also continuum hypothesis is required.

These are valid when deltax tends to 0 and that also describes the continuum hypothesis.

Two approaches for describing fluid flow.

Lagrangian and Eulerian Descriptions

Lagrangian - We are folllowing the particle.(One particle)

Eulerian- Particular location.(several particles)

Recall Road example-Detecting air pollution.

Eulerian-detectors at specific positions on roads

Lagrangian-detectors on vehicles itself.

Lagrangian Approach-Seeding is done . Solid neutral particles are added with the same density as fluid.Laser and laser light sheet is used . Camera is used .Images or Snaps are taken in a very short interval of time.

The word field is related to Eulerian description.

Lagrangian comes before eulerian in Naturality and syllabus.

Substantial Derivative

These are the examples where only the first term (local component) is used. In the first example no motion so vx vy vz are zero. And in the 2nd term their gradients are zero as pipe has constant cross section area.

in +x direction.

Take care of sign conventions.

Flow Patterns