Part 5

Question 1

What is compressible flow?

Answer 1

Flow where density changes significantly with pressure and temperature variations

This occurs at high speeds, unlike incompressible flow where density is assumed constant.

Question 2

What is the conservation of mass equation for compressible flow?

Answer 2

𝑚˙=𝜌𝑎𝑢=constant

This indicates that mass flow rate remains constant along a streamline.

Question 3

What does the equation 𝜌1𝑎1𝑢1=𝜌2𝑎2𝑢2 represent?

Answer 3

Continuity equation for mass conservation between two stations

Assumes density changes in compressible flow.

Question 4

What is a perfect gas?

Answer 4

Theoretical gas composed of randomly moving point particles interacting through elastic collisions

Ideal gas behavior is often assumed in thermodynamic analyses.

Question 5

What is the equation of state for a perfect gas?

Answer 5

𝑝=𝜌𝑅𝑇

Where 𝑝 is pressure, 𝜌 is density, 𝑅 is the specific gas constant, and 𝑇 is temperature.

Question 6

What is specific internal energy?

Answer 6

Total energy of all molecules in a volume divided by mass

It includes translational, rotational, vibrational, and electronic energies.

Question 7

What is the relationship between specific internal energy and specific enthalpy?

Answer 7

ℎ=𝑒+𝑝𝑣

Where ℎ is specific enthalpy, 𝑒 is specific internal energy, 𝑝 is pressure, and 𝑣 is specific volume.

Question 8

What does the First Law of Thermodynamics state?

Answer 8

Energy cannot be created or destroyed, only transformed

This relates to changes in heat and work within a system.

Question 9

What is an adiabatic process?

Answer 9

Process where no heat is added or removed from the system

Important for analyzing thermodynamic cycles.

Question 10

What is an isentropic process?

Answer 10

A process that is both reversible and adiabatic

Entropy remains constant during this process.

Question 11

What does the Second Law of Thermodynamics state?

Answer 11

Processes occur in a direction that increases total entropy

Entropy generation indicates irreversibility in thermodynamic processes.

Question 12

What is compressibility?

Answer 12

Measure of the relative volume change of a fluid in response to pressure change

More significant in gases than in liquids or solids.

Question 13

What is the Reynolds number?

Answer 13

Non-dimensional quantity that quantifies viscous effects in fluid flow

Defined as 𝑅𝑒=𝜌𝑈∞𝐿/𝜇 or 𝑈∞𝐿/𝜈.

Question 14

What is the Mach number?

Answer 14

Ratio of local flow velocity to local speed of sound

Defined as 𝑀=𝑉/𝑎.

Question 15

What is inviscid flow?

Answer 15

Flow with negligible viscosity

Simplifies analysis and equations in fluid dynamics.

Question 16

What is a boundary layer?

Answer 16

Region near a surface where velocity gradients and viscous effects are significant

Influences drag and flow characteristics over bodies.

Question 17

What are the isentropic relationships?

Answer 17

Equations relating state variables in an adiabatic and reversible process

Given by 𝑝2/𝑝1=(𝜌2/𝜌1)𝛾=(𝑇2/𝑇1)𝛾/(𝛾−1).

Question 18

Fill in the blank: The equation for a perfect gas is _______.

Answer 18

𝑝=𝜌𝑅𝑇

Question 19

Fill in the blank: The First Law of Thermodynamics can be expressed as _______.

Answer 19

𝛿𝑒=𝛿𝑞−𝛿𝑤

Question 20

True or False: A process can be isentropic if it is not reversible.

Answer 20

False

Question 21

What is the conservation of mass in compressible flow?

Answer 21

𝑚˙1=𝑚˙2=constant

Where 𝑚˙=𝜌𝑎𝑢 and 𝜌1𝑎1𝑢1=𝜌2𝑎2𝑢2=constant

Question 22

In a 1D and bounded system, what does the conservation of mass indicate?

Answer 22

The mass flow rate along a streamline is constant

For compressible flows, 𝜌1≠𝜌2.

Question 23

What is the steady flow energy equation assuming isentropic flow?

Answer 23

ℎ1+𝑢212=ℎ2+𝑢222=ℎ0=constant

ℎ0 is the total enthalpy, 𝑢 is the velocity, and ℎ is the specific enthalpy.

Question 24

What conditions must be assumed for the steady flow energy equation to be valid?

Answer 24

Isentropic, adiabatic, and inviscid

Viscous effects result in heat generation.

Question 25

How does the steady flow energy equation relate to Bernoulli's equation?

Answer 25

It is akin to Bernoulli's equation but works over a larger range of flow speeds ## Footnote More accurate when the flow is compressible (i.e. 𝑀>0.3).

Question 26

What is the limitation of the steady flow energy equation?

Answer 26

It does not provide a direct link to the pressure field ## Footnote Isentropic relations are often used to link state variables.

Question 27

How can the steady flow energy equation be modified for an ideal gas?

Answer 27

𝑐𝑝𝑇1+𝑢212=𝑐𝑝𝑇2+𝑢222=ℎ0=constant ## Footnote Enthalpy is modeled as a function of temperature.

Question 28

What key concepts were introduced regarding compressible flow?

Answer 28

Fundamentals of compressible flow and adaptations of conservation laws for higher speeds ## Footnote Future lectures will explore shockwave physics and characteristics.

Question 29

True or False: The conservation of energy applies only to incompressible flows.

Answer 29

False ## Footnote It applies to compressible flows as well.

Question 30

What are the flight regimes based on Mach number?

Answer 30

* Subsonic (𝑀⪅0.7) * Transonic (0.7⪅𝑀<1) * Supersonic (1<𝑀<5) * Hypersonic (𝑀≥5) ## Footnote Each regime is characterized by specific flow behaviors and compressibility effects.

Question 31

Define subsonic flight.

Answer 31

Subsonic flight occurs when the aircraft is moving at speeds below the local speed of sound. ## Footnote There are two types: incompressible (𝑀⪅0.3) and compressible (0.3⪅𝑀⪅0.7).

Question 32

What is transonic flight?

Answer 32

Transonic flight occurs when an aircraft is flying at speeds close to the speed of sound (0.7⪅𝑀<1) with regions of subsonic and supersonic flow. ## Footnote The critical freestream Mach number varies based on wing geometry.

Question 33

What characterizes supersonic flight?

Answer 33

In supersonic flight, the aircraft flies at speeds approximately within 1<𝑀<5, with a flow that is entirely supersonic. ## Footnote Shock waves are a key aerodynamic feature in this regime.

Question 34

Define hypersonic flight.

Answer 34

Hypersonic flight occurs at speeds greater than 𝑀≥5, where shock waves form very close to the aircraft surface. ## Footnote At these speeds, significant energy is imparted to the flow, affecting air chemistry.

Question 35

What happens to sound disturbances from a stationary source?

Answer 35

Sound disturbances propagate away from the stationary source at the speed of sound, forming a spherical wavefront. ## Footnote The propagation can be visualized in a two-dimensional plane.

Question 36

How do disturbances propagate from a subsonic source?

Answer 36

Disturbances travel in front of a subsonic source, with waves packed closer together ahead, resulting in higher frequency sound. ## Footnote This effect is known as the Doppler effect.

Question 37

What is a Mach wave?

Answer 37

A Mach wave is formed when a source travels at the speed of sound (𝑀=1), leading to constructive interference of sound disturbances. ## Footnote This phenomenon results in a sonic boom.

Question 38

What occurs when a source travels at supersonic speeds?

Answer 38

Sound propagation occurs in the wake of the object, and observers ahead do not hear sound until the Mach wave reaches them, resulting in a sonic boom. ## Footnote The region between Mach waves is known as the Mach cone.

Question 39

What are shock waves?

Answer 39

Shock waves are regions in flow where fluid properties change abruptly and rapidly, acting as flow discontinuities. ## Footnote They form when an object travels at supersonic speeds, preventing air from moving out of the way.

Question 40

Define bow shocks.

Answer 40

Bow shocks are generated in front of objects traveling beyond the speed of sound and are detached from the object. ## Footnote They can cause energy losses and increased temperatures.

Question 41

What are normal shock waves?

Answer 41

Normal shock waves form at 90 degrees to the freestream and can be either internal or external. ## Footnote They introduce design challenges in transonic flight, affecting control surfaces.

Question 42

What are oblique shock waves?

Answer 42

Oblique shock waves develop at an angle relative to the freestream and are preferred in supersonic flight due to less pronounced energy loss. ## Footnote They are also used to control flow in supersonic engine inlets.

Question 43

How do flow properties change across shock waves?

Answer 43

Upstream properties (pressure, temperature, density) increase across shock waves, while velocity and Mach number decrease. ## Footnote For normal shocks, the downstream Mach number is always subsonic.

Question 44

What is the pressure ratio across a normal shock wave?

Answer 44

The pressure ratio is defined as 𝑝2/𝑝1, indicating the relative change in pressure across the shock wave. ## Footnote The pressure increases significantly, especially at higher freestream velocities.

Question 45

What happens to properties across a normal shock wave?

Answer 45

All properties increase across a normal shock wave.

Question 46

Which quantity grows more rapidly across a normal shock wave?

Answer 46

Pressure.

Question 47

At a freestream velocity of 𝑀1≈4, by what factor is the downstream flow compressed?

Answer 47

Around 20.

Question 48

What is the asymptotic value of the density ratio when 𝑀1≈5?

Answer 48

Just above 5.

Question 49

What is the total pressure?

Answer 49

The pressure that would be measured if the flow is brought to rest without any losses.

Question 50

What does total pressure combine?

Answer 50

Static pressure and dynamic pressure (kinetic energy).

Question 51

What is another term for total pressure?

Answer 51

Stagnation pressure.

Question 52

What does the total pressure ratio (𝑝0,2/𝑝0,1) represent?

Answer 52

The ratio between the total pressure downstream and upstream from the normal shock wave.

Question 53

What does the subscript 0 indicate in total pressure notation?

Answer 53

Total conditions.

Question 54

How do the Mach number and total pressure ratio behave in the supersonic flight regime?

Answer 54

They decrease exponentially with the upstream Mach number.

Question 55

What is the asymptotic value of the downstream Mach number (𝑀2) as flow becomes hypersonic?

Answer 55

Approximately equal to 𝑀2≈0.4.

Question 56

What percentage of the upstream total pressure is lost at 𝑀1≈5?

Answer 56

Approximately 95%.

Question 57

Fill in the blank: The total pressure is often referred to as _______.

Answer 57

Stagnation pressure.

Question 58

True or False: The density ratio increases rapidly at first and then tends towards a constant value.

Answer 58

True.