Governing Equations (Week 1 and 2)

Question 1

Explain the difference between continuum flow and low density/free molecule flow

Answer 1

Continuum: mean free path of molecules is order of magnitude smaller than scale of body

Fluid appears as a continuum to the aircraft; characterise fluid by continually varying properties.

Low-density: mean free path of molecules is of same order as scale of body (not necessary to account for the molecular motion)

Question 2

Whats the difference between compressible and incompressible flow?

Answer 2

Compressable - density constant

Incompressible - density variable, depends on co-ordinates and time

Question 3

Whats the difference between the eulers frame of reference and the Lagrangian frame of reference for a control volume?

Answer 3

Euler: Finite control volume fixed in space with the fluid moving through it

Langrangian: Finite control volume moving with fluid such that the fluid particles stay the same within control volume.

Question 4

What is the divergence of a vector field?

Answer 4

For each point in space how much more flows into the vicinity of that point than out of it (indicates sources and sinks)

Question 5

What is the physical principle of the continuity equation?

Answer 5

Mass can neither be created nor destroyed

Question 6

What does the Knudsen number show?

Answer 6

Dimensionless number defined as the ratio of the molecular mean free path length to a representative physical length scale

Question 7

What is the Gauss Divergence theorem?

Answer 7

Relates the flux of a vector field through a close surface to the divergence of the field in the volume enclosed.

Question 8

What is the physical principle for the momentum equation?

Answer 8

Force = time rate of change of momentum

Question 9

What is the physical principle for the energy equation?

Answer 9

Energy can neither be created nor destroyed; it can only change in form.