Lecture 1

Question 1

State the definition of the Knudsen Number and explain it’s relevance.

Answer 1

Kn = lambda/L

lambda: mean free path
L = characteristic length of the problem

It represents the distance that the fluidic particles can travel without touching other particles.

Continuum hypothesis holds that Kn«1.

Question 2

How is the speed of sound defined in the framework of thermodynamics?

Answer 2

Fórmulas en la página 11
(Decir tanto la de la raíz como la del adiabatic exponent)

Question 3

Which effects have to be neglected when Euler-Equations are applied?

Answer 3

We need to neglect:

1. Viscous effects
2. Heat transfer or heat sources
3. Gravity
4. We consider compressible flow

Question 4

How is total enthalpy related to total energy?

Answer 4

H = E + p/pho = e + (1/2)v^2 + p/rho

Question 5

Which effects cannot take place in isentropic flows?

Answer 5

Isentropic equations are only valid for small changes. Therefore, they cannot be applied in shocks.

Question 6

Explain the concept of a “material derivative”.

Answer 6

Local derivative of the quantity + convective derivative of the quantity. This gives a very simple and compressed equation for representing that the process changes along streamline. The particles change their thermodynamic properties with the advance of the flow.

Equation in page 21

Question 7

Why are the balance laws for momentum and total energy balance laws but not conservation laws (in a strict sense)?

Answer 7

Because they account for external sources and sinks (forces and heat transfer) that can add or remove momentum and energy from a system.
Strict conservation laws applay only to quantities that remain constant within a closed system without external interactions.

Question 8

State the thermal and the caloric EoS for a perfect gas

Answer 8

Thermal EoS: p = p(rho,T). Basically, p=rhoRT
Caloric EoS: e = e(pho,T). basically, e=p/((gamma-1)*pho)

Question 9

What 2 conditions need to be satisfied in an insentropic process?

Answer 9

1. Reversible (lossless)
2. Adiabatic
   –> Entropy is constant

Question 10

Fundamental relation of thermodynamics?

Answer 10

dU = T*dS - pdV

dU: Change in Internal Energy

Question 11

Formula por calculating the adiabatic exponent?

Answer 11

gamma = pho*c^2/p

Question 12

Equation(s) for an isentropic process?

Answer 12

p*v^(gamma) = const
s = const

Remember that v: specific volume

Question 13

Relations cp, cv, gamma and R

Answer 13

1. gamma = cp/cv
2. R = cp - cv