GD Midterm 1 Review - Section 1

Question 1

Define a system.

Answer 1

A fixed set of identifiable particles of constant mass; the
same set of particles is followed throughout the analysis.

Section 1, Page 1

Question 2

Define Control Volume.

Answer 2

In fluid dynamics, a control volume is an arbitrarily chosen region in space through which fluid can flow. It is defined by its boundary—known as the control surface—which may be fixed or moving.

Lecture Notes Definition: A region of space which may or may not be moving (often taken to be fixed in space) and through which fluid may flow. Therefore, the identity of the particles in the control volume may vary from instant to instant

Section 1, Page 1

Question 3

Describe the Reynolds Transport Theorem.

Answer 3

Reynolds’ Transport Theorem relates the time rate of change of an extensive property following a system to the local change within the control volume and the flux of that property across the control surface.

Section 1, Page 1 & ChatGPT

Question 4

What are the sign conventions for the heat transfer rate \dot{Q} and the work rate \dot{W}?

Answer 4

\dot{Q} > 0 for heat transfer into the system.
\dot{W} > 0 for work done by the system.

Section 1, Page 4

Question 5

True or False
Surface forces can only be identified at the boundaries of the control volume.

Answer 5

True.

Section 1, Page 3

Question 6

True or False
Body forces can only be identified at the boundaries of the control volume.

Answer 6

False.

Body forces are distributed throughout the control volume.

Question 7

What’s the difference between a calorically and thermally perfect gas?

Answer 7

A calorically perfect gas is one in which the specific heats (at constant pressure and constant volume) are assumed to be constant over the range of temperatures considered. This assumption leads to a linear relationship between internal energy or enthalpy and temperature.

In contrast, a thermally perfect gas still obeys the ideal gas law (PV = RT), but its specific heats are allowed to vary with temperature. As a result, the internal energy and enthalpy are not linear functions of temperature, reflecting a more realistic behavior of gases, especially at high temperatures.

Question 8

Define a “static” property.

Answer 8

The static thermodynamic properties are those properties measured when moving along with the flow at the local fluid velocity.

Question 9

What is the difference between adiabatic and isentropic flow?

Answer 9

Adiabatic involves no heat transfer (\dot{Q} = 0).

Isentropic flow is both adiabatic and reversible.

Question 10

True or False
The stagnation temperature in a steady, adiabatic flow is constant.

Answer 10

True.

Section 1, Page 13

Question 11

Rules of Choking:
If dG < 0 –> ____________.

Answer 11

No limiting pattern, no choking.

Question 12

Rules of Choking:
If dG > 0 –> _________.

Answer 12

No further changes in flow properties are possible after M = 1.

Question 13

Rules of Choking:
If dG > 0 and M = 1 is reached _________________.

Answer 13

Changes in flow can only occur if dG becomes negative precisely when M = 1.

Question 14

What are some of the techniques for the numerical solution near the critical point?

Answer 14

M = 1, dG = 0

1. Linearized governing eqns near M = 1.
2. Maintain consent property derivatives near M = 1.
3. LHopital’s Rule
4. Use different set of driving potentials.
5. Solve unsteady 1D flow eqns to steady state.