This document contains 51 short answer questions related to aerodynamics and compressible flow. The questions cover topics like gas dynamics, compressible versus incompressible flow, compressibility, types of compressibility, properties of perfect gases, adiabatic and isentropic processes, Mach number, flow regimes, continuity, momentum, and energy equations. Many questions also focus specifically on nozzle flow, including definitions of different types of nozzles, choking, expansion, under-expanded versus over-expanded nozzles, and nozzle efficiency.

1. INFANT JESUS COLLEGE OF ENGINEERING
Kamarajar Nagar, Keelavallanadu, Thoothukudi
AE 53- AERODYNAMICS II
SHORT ANSWERS
UNIT-I (ONE DIMENSIONAL COMPRESSIBLE FLOW)
1. What do you understand by the term Gas Dynamics?
 Gas dynamics is a science in fluid dynamics which deals with the study of motion
of gases and its effects on physical systems.
 Gas dynamics is a study of the kinetic theory of gases leading to the study of gas
diffusion, chemical thermodynamics.
 Some examples include nozzles flow, shock waves around jets, aerodynamic
heating on atmospheric reentry vehicles and flows of gas fuel within a jet engine.
2. Differentiate between compressible and incompressible flow?
S. No Compressible flow Incompressible flow
1 Compressible flow is a type of flow in
which the density of the fluid changes
from point to point in a fluid flow
Incompressible flow is a type of flow in
which the density of the fluid does not
change from point to point in a fluid flow
2 ρ ≠ constant ρ = constant
3. Define the term compressibility?
 The fractional change in the volume of the fluid element per unit change in
pressure is called as compressibility.
 It is also defined as the property of a substance to be reduced in volume by
application of pressure.
 It is the property of being able to occupy less space.
 Gases have high compressibility but liquids have low compressibility.
Where V is the volume and p is the pressure applied to the object

2. 4. Explain the different types of compressibility?
Compressibility can be classified into two types namely
1. Isothermal compressibility
2. Isentropic compressibility
5. What is isentropic and isothermal compressibility?
 If the temperature of the fluid element is held constant by some heat transferring
mechanism, then that compressibility is defined as isothermal compressibility
 If no heat is added or taken away from the fluid element and if the friction is
ignored, the compression of the fluid element takes place isentropically and that
compressibility is defined as isentropic compressibility
6. Distinguish between thermally perfect gas and calorically perfect gas?
S.No Thermally perfect gas Calorically perfect gas
1 A gas that follows the ideal equation
of state is said to be thermally perfect
If the specific heat capacity is a constant
value, the gas is calorically perfect
2 Gas that does not follow the ideal
equation of state is thermally
imperfect.
If the specific heat capacity changes with
temperature, the gas is said to be
calorically imperfect
3
7. What is meant by a perfect gas?
 The gas which obeys the equation of state is called as a perfect gas
P = ρRT
8. Define the adiabatic process?
 It is a process in which no heat is gained or lost by the system.
 It is a conversion that occurs without input or release of heat within a system.
9. Explain the reversible flow process?
 A process in which no dissipative phenomena occur that is where the effects of
viscosity, thermal conductivity and mass diffusion are absent.
 A process that can be reversed, and in so doing leaves no change in either the
system or surroundings.
 System and surroundings are returned to their original condition before the
process took place.

3. 10. What is meant by isentropic process?
 An isentropic flow is a flow that is both adiabatic and reversible.
 Process in which the entropy of the system remains constant.
 A change that takes place without any increase or decrease in entropy, such as a
process which is both reversible and adiabatic.
11. Differentiate adiabatic and non adiabatic flow?
S. No Adiabatic flow Non adiabatic flow
1 If the local total enthalpy and
temperature at point 1 is h01 and at point
it is h02, then for an adiabatic flow, h02 =
h01 and T02 = T01
If the local total enthalpy and temperature at
point 1 is h01 and at point it is h02, then for a
non adiabatic flow, h02 ≠ h01 and T02 ≠ T01
2
12. Differentiate isentropic and non isentropic flow?
S. No Isentropic flow Non isentropic flow
1 If the local static pressure and static
density at point 1 is P01 and ρ01 and at
point 2 is P02 and ρ02, then for an
isentropic flow, P01 = P02 ρ01 = ρ02
If the local static pressure and static density at
point 1 is P01 and ρ01 and at point 2 is P02 and
ρ02, then for a non isentropic flow, P01 ≠ P02
ρ01 ≠ ρ02
2

4. 13. What is Mach number? Write down the expression for it?
 Mach number is a dimensionless number representing the speed of an object
moving through air divided by the local speed of sound.
 Used to represent the speed of an object when it is traveling close to or above the
speed of sound.
𝑀 =
𝑉
𝑎
14. Classify the flow regimes in terms of Mach number?
Mach number Flow regimes
M < 0.3 Subsonic & incompressible
0.3 <M < 0.8 Subsonic & compressible
0.8 <M < 1.2 Transonic flow
1.2 <M < 5.0 Supersonic Flow
M > 3.0 Hypersonic Flow
15. Define characteristic Mach number and what is the maximum value of it?
Characteristic Mach number is defined as the ratio between the velocity of the object
and the critical velocity of sound
M∗
=
velocity of the object
critical velocity of sound
Maximum value for M∗
= √
γ+1
γ−1
For γ = 1.4, M∗
=2.45
16. Write steady state energy equation?
The adiabatic steady state energy equation can be written as
ℎ1 +
𝑉1
2
2
+ 𝑄 = ℎ2 +
𝑉2
2
2
+ 𝑊
Where h is the enthalpy
V is the velocity
Q is the heat added
W is the work done
17. Derive the relation
T0
T
= [1 + (
γ−1
2
) M2
]
h0 = h+
𝑉2
2
T0=T+
𝑉2
2𝐶𝑝
Sub for Cp, a2 and M
T0
T
= [1 + (
γ − 1
2
)M2
]

5. 18. What is meant by Barotropic fluids?
 The fluid in which the pressure depends only on the density and vice versa.
 A barotropic flow is a flow in which the pressure is a function of the density only
and vice versa.
19. What is the effect of Mach number on compressibility?
If the flow is incompressible, the value of the pressure coefficient is unity i.e.
Cp=1.0. But if the flow is compressible, the value of the pressure coefficient deviates
from unity i.e. Cp ≠ 1.0 and the magnitude of deviation increases with Mach number of
the flow.
𝑃0 − 𝑃
𝜌𝑉2
2
= 1 +
𝑀2
4
+
𝑀4
40
+ …… ….
20. Define Crocco number?
Crocco number is defined as the ratio between the velocity of the object and the
maximum velocity of the fluid. It is denoted by Cr
𝐶𝑟 =
velocity of the object
maximum velocity of the fluid
𝐶𝑟 =
𝐶
𝐶 𝑚𝑎𝑥
21. Write the one-dimensional energy equation for an adiabatic compressible steady flow?
The one-dimensional energy equation relates the enthalpy and the velocity of the
fluid element. So for an adiabatic compressible steady flow the energy equation can be
written as
ℎ0 = ℎ +
𝑉2
2
22. Define the principle of continuity equation?
 Continuity equation is based on the basic principle of law of conservation of mass
 It states that mass can neither be created nor be destroyed but can be transformed
from one form to another.
23. Give the forms of continuity equation?
Integral form
∂
∂t
∭ ρdѵ + ∬ ρVds= 0
Differential form
∇ρV +
∂ρ
∂t
= 0
24. What are the assumptions made while deriving Energy equation?
1. The flow is steady
2. The flow is adiabatic
3. The flow is inviscid

6. 25. Give the basic principle involved in momentum equation?
 Momentum equation is based on Newton’s second law
 It states that the force exerted on a body is directly proportional to the rate of
change of momentum on the body
F = ma
F =
d(mv)
dt
Where mv is the momentum
26. Write the momentum equation for one dimensional compressible flow?
Integral form
∭ ρfdѵ− ∬ Pds + Fvis = ∬ ρvds.V +
∂
∂t
∭ ρVdѵ
Differential form
∂
∂t
ρV + ∇ρv.V + ∇P − ρf− Fvis = 0
27. What is the basic principle behind energy equation?
 Energy equation is based on the basic principle of law of conservation of energy
 It states that energy can neither be created nor be destroyed but can be transformed
from one form to another.
28. Write internal energy equation for one dimensional high speed flow?
Integral form
∭ ρqdѵ + Qvis + ∭ ρfVdѵ− ∬ PVds + Wvis
= ∬ ρVds(e +
v2
2
) +
∂
∂t
∭ ρdѵ(e+
v2
2
)
Differential form
ρq+ Qvis + ρfv− ∇Pv + Wvis = ∇ρv(e +
v2
2
) +
∂ρ
∂t
(e +
v2
2
)
29. Write down the Bernoulli’s equation for compressible flow?
For compressible flows, the Bernoulli’s equation can be written as
P0 is the total pressure
ρ0 is the total density
30. What are the factors affecting the behavior of sound propagation
 A relationship between density and pressure.
 Motion of the medium itself. For example, sound moving through wind.
 Viscosity of the medium. It determines the rate at which sound is attenuated.

7. 31. How a sound wave is created?
 Sound is a mechanical wave that is an oscillation of pressure transmitted through
a solid, liquid, or gas composed of frequencies within the range of hearing by
vibrations.
 Sound is a sequence of waves of pressure that propagates through compressible
media such as air or water.
32. Give the properties of sound waves
 Frequency
 Wavelength
 Wave number
 Amplitude
 Sound pressure
 Sound intensity
 Speed of sound
 Direction
33. Write the expression for the velocity of sound in air at room temperature?
The general expression for the velocity of sound in air is
𝑎 = √𝛾𝑅𝑇
where 𝑎 is the velocity of sound
𝛾 is the specific heat constant
𝑅 is the gas constant
𝑇 is the temperature of the fluid
34. What are the properties of flow medium on which the velocity of sound through the
medium depends upon?
 Temperature
 Density of the medium.
 Compressibility
 Molecular composition.
 Heat capacity
35. Give the relationship between Mach number and characteristic Mach number?
The Mach number and characteristic Mach number can be related by
𝑀2
=
2
(
𝛾 + 1
𝑀∗2 ) − ( 𝛾 − 1)
Where M is the Mach number
M* is the characteristic Mach number
36. Show the relation between stagnation state and static state showing its parameters?

8. 37. Show the relation between stagnation state and critical state showing its parameters?
38. What is the purpose of a nozzle?
 A nozzle is a pipe of varying cross sectional area which is used to increase the
kinetic energy of the fluid by decreasing the pressure energy
 Used to control the direction flow and the rate of flow, speed, direction, mass,
shape, and the pressure of the fluid.
39. What are the different types of nozzles?
 Convergent nozzle
 Convergent-divergent nozzle
 Divergent nozzle

9. 40. What is the various pressure ratios involved in the evaluation of a nozzle?
 Throat pressure ratio
 Exit pressure ratio
 Back pressure ratio
41. Why is a convergent divergent nozzle required to expand a flow from stagnation
condition to supersonic velocity?
 The fluid at stagnation condition is increased to sonic speeds using a convergent
nozzle.
 To reach supersonic velocities, diverging section is used at the exit of a
converging nozzle.
 When the fluid leaves the converging nozzle at sonic velocity, and enters the
diverging section, there is a large decrease in density of the fluid which makes
acceleration in the divergent section possible, so to achieve mach numbers >1, we
must use a converging-diverging nozzle.
42. Explain the phenomenon of choking in a nozzle?
 Choked flow is a limiting condition which occurs when the mass flow rate will
not increase with a further decrease in the downstream pressure environment
while upstream pressure is fixed.
 Choked flow is a compressible flow effect.
 At choked flow the mass flow rate can be increased by increasing the upstream
pressure, or by decreasing the upstream temperature.
43. What is meant by ‘De Laval Nozzle’?
 De Laval Nozzle is a tube used to accelerate a hot, pressurized gas passing
through it to a supersonic speed, and upon expansion, to shape the exhaust flow so
that the heat energy propelling the flow is converted into directed kinetic energy.

10. 44. What are the assumptions of a gas in a De Laval Nozzle
 Gas is assumed to be an ideal gas.
 The gas flow is isentropic.
 The mass flow is constant.
 The gas flow is along a straight line from gas inlet to exhaust gas exit
 The gas flow behavior is compressible since the flow is at very high velocities.
45. Describe the shape of the nozzle required to increase the velocity from subsonic to
supersonic condition?
Convergent divergent nozzle
In the convergent portion, subsonic velocity is accelerated to sonic velocity and in
the throat section; velocity will be maintained constant at sonic speeds. In the divergent
portion, sonic velocity is accelerated to supersonic velocity because of the decrease in
pressure in the divergent section.
46. Explain how a subsonic nozzle can be supersonic diffuser?
A subsonic nozzle should have a convergent profile whose purpose is to convert a
subsonic flow to sonic flow.
A subsonic diffuser should have a divergent profile whose purpose is to convert a
supersonic flow to sonic flow.
47. How velocity of the flow varies in convergent and divergent ducts for subsonic and
supersonic condition?
 At subsonic speeds (Ma<1) a decrease in area increases the speed of flow.
 In supersonic flows (Ma>1) the effect of area changes are different. a supersonic
nozzle must be built with an increasing area in the flow direction.
 Divergent nozzles are used to produce supersonic flow in missiles and launch
vehicles.

11. 48. What is meant by expansion in nozzle? What are the types of nozzles based on
expansion?
The process of increasing the velocity of the fluid inside the nozzle from the
convergent part after the throat section is called as expansion in nozzle.
Based on expansion, the nozzle can be classified as
1. Under expanded nozzles
2. Over expanded nozzles
3. Correctly expanded nozzles
49. What is under-expanding nozzle flow?
When the exit pressure from the nozzle is greater than the back pressure,
expansion waves will be formed at the exit of the nozzle. Exit pressure will be reduced
when the fluid crosses the expansion wave to meet the required exit pressure.
50. What do you understand by an over expanded nozzle?
When the exit pressure from the nozzle is less than the back pressure, an oblique
shock wave will be formed at the exit of the nozzle. Exit pressure will be increased when
the fluid crosses the shock wave to meet the required exit pressure.
51. Define nozzle efficiency in terms of enthalpies?
The nozzle efficiency, ηn, is defined as the ratio of the actual enthalpy drop to the
isentropic enthalpy drop
Ƞ =
actual enthalpy drop
isentropic enthalpy drop
Ƞ =
h01 − h2
h01 − h2s
Where h01- stagnation enthalpy at the nozzle inlet
h2- enthalpy at the exit for actual nozzle
h2s- enthalpy at the exit for nozzle under isentropic conditions

12. 52. Write the Area Mach number relation?
Where A is the area at any section in the nozzle
A* is the throat area
M∞ is the freestreammach number
53. Draw the performance curve for a convergent nozzle
54. Draw the performance curve for a convergent-divergent nozzle

13. 55. Give the expression for the mass flow rate in a nozzle and what is its maximum value?
Mass flow rate is
𝑚√ 𝑅𝑇0
𝐴𝑃0√ 𝛾
= √
2
𝛾 − 1
[(
𝑃
𝑃0
)
2
𝛾
− (
𝑃
𝑃0
)
𝛾+1
𝛾
]
Maximum mass flow rate is
𝑚√ 𝑅𝑇0
𝐴𝑃0√ 𝛾
= (
2
𝛾 + 1
)
1
2
(
𝛾+1
𝛾−1
)
56. Sketch the supersonic process in a nozzle and a diffuser?

14. UNIT-II (NORMAL, OBLIQUE SHOCKS)
1. Define shock waves?
 A shock wave is a large-amplitude compression wave which carries energy and can
propagate through a medium.
 Shock waves are characterized by an abrupt, discontinuous change in the
characteristics of the medium.
 Across a shock there is a rapid rise in pressure, temperature and density of the flow.
2. What are the different types of shock waves?
 Normal shock wave
 Oblique shock wave
 Bow shock wave
3. Give some examples of shock waves
 Moving shock
 Detached shock
 Detonation wave
 Attached shock
 Recompression shock
4. Bring out any two important differences between shock waves and expansion waves in a
supersonic flow?
S.No Shock wave Expansion wave
1 A shock wave is a large-amplitude compression
wave which carries energy and can propagate
through a medium.
A pressure wave that decreases the
density of air as the air passes through
it.
2 Shock waves are characterized by an abrupt,
discontinuous change in the characteristics of
the medium.
Expansion waves occur when bodies
begin to narrow, making more space
available.
3 Across a shock there is a rapid rise in pressure,
temperature and density of the flow.
Across an expansion wave, air
velocity increases, temperature and
pressures are reduced.
5. Differentiate strong and weak shocks?
S.No Strong shocks Weak shocks
1 Shock wave across which the pressure jump
is very high is called as strong shocks
Shock wave across which the pressure
jump is less is called as strong shocks
2 There is a huge variation in the fluid
properties such as pressure, density,
velocity after the shock wave
variation in the fluid properties such as
pressure, density, velocity after the shock
wave will be less

15. 6. Define compression waves?
 A shock wave that compresses the medium through which it is transmitted.
 Pressure in the compression wave is higher than atmospheric pressure.
 A mechanical wave in which matter in the medium moves forward and backward
along the direction the wave travels
7. Give the differences between normal and oblique shocks?
S.No Normal shocks Oblique shocks
1 Shock waves which are formed
perpendicular to the flow field
Shock waves which are formed at an
angle to the flow field
2 One dimensional wave Two dimensional wave
3 It is a strong shock wave It is a weak shock wave
8. What is meant by this bow shock?
 Bow shock is a curved, stationary shock wave that is found in supersonic flow past
a finite body.
 It is a combination of a normal shock wave and an oblique shock wave.
 It is also called as a detached shock i.e. it is not attached to the tip of the body.
 A detached bow shock forms when the deflection angle is greater or lower Mach
number.
 The bow shock increases the drag in a vehicle traveling at a supersonic speed.
9. What are the various types of waves in a closed passage
1. Infinitesimal pressure waves (sound waves)
2. Non-steep pressure waves with finite amplitude
3. Steep pressure waves (shock wave)
4. Expansion waves.

16. 10. Explain the wave motion in incompressible flow model?
In an incompressible flow, velocity of the source of disturbance is very less
compared to the speed of sound ‘a’. Infinitesimal pressure waves are created which travel
at a velocity ‘a’ in all the directions. The displacement of the source of disturbance is
small compared to the distance travelled by the pressure waves.
11. How the pressure waves travel in a subsonic flow model? Explain?
In a subsonic flow model, the source of disturbance travels at half the speed of
sound, so pressure waves are generated at time t1,t2,t3, etc. the wave fronts move ahead of
the point source and the intensity is not symmetrical.
12. With a suitable sketch illustrate the propagation of waves from a sound source moving at
a speed of sound?
If the flow is sonic, the point source travels with the same velocity as that of the
wave, i.e. the velocity of the point source is sonic. The wave fronts always exists at the
present position of the point source and cannot move ahead of it

17. 13. Explain zone of action and zone of silence for a body moving at a speed of sound?
The region on the left of the wave front i.e. the region downstream of the source
of disturbance is called as zone of silence because the shock waves cannot reach this
zone. The region on the right of the wave front i.e. the region upstream of the source of
disturbance is called as zone of action because the shock waves will be created in this
zone.
14. Explain zone of action and zone of silence for a body moving at Supersonic speed?
The region inside the Mach cone where the source of disturbance is propagating is
called as the zone of action. The region outside the Mach cone where there is no
propagation is called as the zone of silence.
15. Explain why shocks cannot occur in subsonic flows?
In subsonic flows, the velocity of the object is less than the velocity of sound, and
the object will not have much pressure to compress the fluid, so shocks cannot occur in
subsonic flows .
16. What is meant by Supersonic flow?
 The flow of a fluid over a body at speeds greater than the speed of sound in the
fluid, i.e. the flow region above mach 1.2 is called as supersonic flow.
 The flow in which the shock waves start at the surface of the body.
 The term supersonic is used to define a speed that is over the speed of sound.
17. Explain why a supersonic airplane is not given a blunt nose?
When a blunt nose airplane is flying in air at supersonic speeds, bow shocks will
be formed in front of the nose which will reduce the velocity of the aircraft. So for this
reason, supersonic airplane is not given a blunt nose.
18. Explain the molecular behavior of air before and after a shock wave?
The flow consists of individual molecules which impact on the surface of the
object. When the flow impacts, there will be a change in the molecular energy and
momentum of the flow. The random motion of the molecules communicates this change
in energy to the upstream flow. So the presence of the object is felt by the flow and the
streamlines adjust itself due to the object.

18. 19. Write the continuity, momentum and energy equation for a normal shock wave?
a) Continuity equation
b) Momentum equation
c) Energy equation
20. Determine the pressure ratio across the wave when its Mach number is unity?
When the Mach number is 1, the strength of the shock wave will be equal to zero
and the shock is called as the shocks of vanishing strength.
𝑃2
𝑃1
= 1 +
2𝛾
𝛾 + 1
( 𝑀1
2
− 1)
When M=1,
𝑃2
𝑃1
= 1
𝑃2 − 𝑃1
𝑃1
= 0
21. Define the strength of a shock wave?
It is the ratio between the difference in downstream and upstream pressure to the
upstream pressure.
𝜉 =
𝑃𝑦 − 𝑃𝑥
𝑃𝑥
22. How the Mach number before and after a normal shock wave are related? (OR) Write the
shock relation of the perfect gas? (OR) State Prandtl relation in normal shock and bring
out its significance?
The Mach number before and after a normal shock wave can be related by Prandtl
equation which gives the relation between the velocities of the fluid before and after the
shock wave.
𝑢2 − 𝑢1 = 𝑎2
𝑀1
∗
𝑀2
∗
= 1
2211 uu  
2
222
2
111 upup  
22
2
2
2
2
1
1
u
h
u
h 

19. 23. Explain the shocks of vanishing strength?
 When the strength of the shock wave is equal to zero, that shock wave is called as
the shocks of vanishing strength
 This happens when the mach number of the flow becomes unity.
24. Write the Hugonoit equation and explain each terms involved in it?
Hugonoit equation states that the static pressure increases across the shock wave
which will compress the fluid and the object moving with the fluid
25. Draw a typical Rankine - Hugoniot curve and explain it?
The Rankine - Hugoniot curve shows the relation between pressure and density
ratios across the shock wave.
26. Explain the function of a Pitot-static tube in an aircraft?
 Pitot-static tube is a device which is used to increase the velocity of the fluid by
calculating the difference in pressure.
 It measures fluid velocity by converting the kinetic energy of the flow into
potential energy which takes place at the stagnation point.
 The static pressure is measured by comparing it to the flow's dynamic pressure
with a differential manometer.

20. 27. Define Pitot-static tube errors and mention its types?
1. Blocked Pitot tube
2. Blocked static port
3. Density error
4. Compressibility error
5. Fixed error
6. Variable error
28. What are the limitations of Pitot-static tube?
1. Don’t work well at low speeds because pressure difference is very small
2. At supersonic speeds, shock waves are formed in front of the tube
3. Ice will be formed at low speeds
29. What is Rayleigh correction formula for pressure measurements in supersonic flows?
Where P02 is the pressure at the entrance of the tube after the shock wave
P1 is the static pressure
30. State the importance of Rayleigh supersonic Pitot formula?
Rayleigh supersonic Pitot formula will give the correction factor to be applied to
the pitot static tube during pressure measurement, since the pressure measured exactly at
the tube is not the total pressure but it is the pressure after the shock wave. So this
formula has got its significance.
31. What is the need for a correction to the Pitot static tube readings in supersonic flow?
When a pitot static tube is immersed in a supersonic flow, shock waves will be
formed in front of the nose of the Pitot tube. The pressure measured after this ice formed
region will not be the correct total pressure of the air. So corrections should be done to
the pressure measurement in a Pitot tube.
32. Define Shock angle
The angle which the shock wave makes with the horizontal line is called as the
Shock angle. It is denoted by β.

21. 33. Flow deflection angle?
The angle by which the flow is deflected away from the horizontal is called as the
Flow deflection angle. It is denoted by θ.
34. Name some practical examples where the oblique shock wave occurs?
 Design of supersonic aircraft engine inlets, which are wedge-shaped to compress
air flow into the combustion chamber while minimizing thermodynamic losses.
 Oblique shock waves are used in engineering applications when compared with
normal shock waves.
35. Give the oblique shock relation in terms of flow angle and wave angle? (OR) Write the
relation between Shock angle and Flow deflection angle?
Where θ is the flow deflection angle
β is the shock angle
M is the Mach number
36. In the case of oblique shocks, what are the limiting values of shock angle?
 The weak limit of the oblique shock wave is the mach wave, i.e. the wave which
is nearer to the lower deflection angle.
 The strong limit of the oblique shock wave is the normal shock wave, i.e. the
wave which is nearer to the highest deflection angle.
37. What will happen if the upstream Mach number varies in an oblique shockwave?
 If the upstream Mach number is increased, wave angle decreases and the shock
becomes stronger due to the increase in the normal Mach number
 If the upstream Mach number is decreased, wave angle increases and the shock
becomes weaker
 If the upstream Mach number is decreased enough, shock wave will be detached
  








22cos
1sin
cot2tan 2
1
22
1



M
M

22. 38. Give the physical aspects in the flow pattern when the deflection angle is increased in an
oblique shock wave?
 If the deflection angle is increased, wave angle will be increased and the shock
becomes stronger
 If θ value exceeds the maximum value, the shock wave will become detached
from the object.
39. What is meant by attached and detached shocks?
When θ<θmax, an oblique shock wave will be formed in front of the object and it is
attached to the surface of the object. That is called as attached shocks. When θ>θmax, then
there is no solution for attached shocks and the shock wave will be detached from the
object, that shocks are called as detached shocks.
40. Define strong and weak shock solutions?
When θ<θmax, there are two possible solutions, for each value of θ and M, having
two different wave angles. The larger values of the wave angle are called as strong shock
solution and the smaller values of the wave angle are called as weak shock solution.
41. What is shock polar?
 The locus of all the points for θ values ranging from zero to maximum
representing all possible velocities behind the shock wave is called as shock polar.
 It is the graphical representation of oblique shock wave properties.

23. 42. Define sonic circle?
 The circle with radius M*=1 is called as the sonic circle
 Inside the sonic circle, the flow will be subsonic and outside the sonic circle, the
flow will be supersonic
43. Define Hodograph Plane?
The plane which uses velocity components as the coordinates of the system is
referred to as Hodograph Plane.
44. Draw the shock polar for different Mach numbers?
Shock polar for different Mach numbers will generate a family of curves. When
the Mach number increases from zero, the shock polar will be a curved line but when the
Mach number reaches infinity, shock polar will become a circle.

24. 45. What is meant by Mach wave
 Mach wave is a pressure wave traveling with the speed of sound caused by a
slight change of pressure added to a compressible flow.
 These weak waves can combine in supersonic flow to become a shock wave if
sufficient Mach waves are present at any location.
 Such a shock wave is called a Mach stem or Mach front.
 A Mach wave is the weak limit of an oblique shock wave.
46. Define mach angle?
The angle created by the mach cone with the horizontal line is called as mach
angle.
where M is the Mach number
𝛍 is the mach angle
47. Define Mach cone?
 The area bounded by the sides of the cone-shaped shock wave produced by a
sharp pointed object moving through the atmosphere at a speed greater than Mach
1 is called as Mach cone.
 It is the locus of the Mach lines.

25. 48. Differentiate between Mach wave and Shock wave?
S.No Mach wave Shock wave
1 Mach wave is a pressure wave traveling
with the speed of sound caused by a slight
change of pressure added to a
compressible flow.
A shock wave is a large-amplitude
compression wave which carries
energy and can propagate through a
medium.
2 A Mach wave is the weak limit of an
oblique shock wave.
Shock wave is the strong limit of an
oblique shock wave.
49. Under what conditions an attached shock wave to solid body like wedge is detached?
If the wedge angle δw is greater than the maximum wedge angle δmax, for a given
upstream mach number, the attached shock wave will become detached from the surface
of the wedge.
50. Draw the flow pattern of supersonic flow over a concave corner?
 For a concave corner, the wall must be deflected upwards through an angle of θ.
 The flow at the wall must be tangent to the wall, so that the streamlines are also
deflected through an angle of θ
 When a supersonic flow is deflected into itself, an oblique shock wave will occur
 Across this wave, Mach number decreases and all other flow properties increases.
51. Explain the flow over a wedge for symmetrical and unsymmetrical conditions?
If the wedge is symmetrical, the flow over the top and bottom surfaces is
symmetrical and so the flow pattern can be studied by one of its surfaces

26. If the wedge is unsymmetrical, the flow over the top and bottom surfaces will be
unsymmetrical and so the flow pattern should be studied separately because the flow
deflection angle is different
52. Explain the phenomenon of flow over a cone?
 A straight oblique shock wave emanates from the tip of the cone and the shock
wave will be weaker due to the three dimensional relieving effect of the cone.
 In a cone, the streamlines will be deflected only by 8° through the shock because
of the weaker shock wave.
53. List the assumptions in the flow over a cone?
1. The flow is axisymmetric with respect to the axis of the cone
2. The flow is steady and isentropic before and after the shock wave.

27. 54. How is flow over a cone different from flow over a wedge?
S.No Flow over a cone Flow over a wedge
1 Flow over a cone is three dimensional Flow over a wedge is two dimensional
2 Pressure over the surface of the cone is
less
Pressure over the surface of the wedge
is more
3 Streamlines above the cone surface is
curved
Streamlines above the cone surface is
straight
4
55. Define pressure turning angle?
The locus of all possible static pressures behind an oblique shock wave as a
function of deflection angle for any given upstream conditions is called as pressure
turning angle.
56. What is meant by shock tube?
 Shock tube is a device used to produce high speed flow with high temperatures by
traversing the normal shock waves which are generated by the rupture of the
diaphragm separating a high pressure gas from a low pressure gas.
 It is an instrument used to replicate and direct blast waves at a sensor or a model
in order to simulate actual explosions and their effects, usually on a smaller scale.
 Shock tubes can also be used to study aerodynamic flow under a wide range of
temperatures and pressures that are difficult to obtain in other types of testing
facilities.
57. What are the applications of shock tube?
 Shock tubes have been used in wind tunnel, allowing higher temperatures and
pressures therein replicating conditions in the turbine sections of jet engines.
 Used to investigate compressible flow phenomena
 Used to study gas phase combustion reactions.
 Used in biomedical research to study how biological specimens are affected by
blast waves.
 Used to measure dissociation energies and molecular relaxation rates.

28. UNIT-III (EXPANSION WAVES, RAYLEIGH AND FANNO FLOW)
1. What do you mean by expansion waves?
 A pressure wave that decreases the density of air as the air passes through it.
 In supersonic flow, expansion waves occur when bodies begin to narrow, making
more space available.
 In passing through an expansion wave, air velocity increases, while temperature
and pressures are reduced.
 It is the opposite of a compression wave. Also called a rarefaction wave.
2. Differentiate between shock wave and expansion wave?
S.No Shock wave Expansion wave
1 A shock wave is a large-amplitude
compression wave which carries energy and
can propagate through a medium.
A pressure wave that decreases the
density of air as the air passes through it.
2 Shock waves are characterized by an abrupt,
discontinuous change in the characteristics of
the medium.
Expansion waves occur when bodies
begin to narrow, making more space
available.
3 Across a shock there is a rapid rise in
pressure, temperature and density of the flow.
Across an expansion wave, air velocity
increases, temperature and pressures are
reduced.
3. Give the properties of air before and after an expansion wave?
Before the expansion wave
 Pressure is higher
 Temperature is higher
 Density is higher
 Mach number is lower
After the expansion wave
 Pressure is lower
 Temperature is lower
 Density is lower
 Mach number is higher

29. 4. Explain the supersonic flow over a convex corner? (OR) With a neat sketch, illustrate
Prandtl Meyer expansion round a convex corner?
 For a convex corner, the wall must be deflected downwards through an angle of θ.
 The flow at the wall must be tangent to the wall, so that the streamlines are also
deflected through an angle of θ
 When a supersonic flow is deflected away from itself, expansion wave will occur
 Across this wave, Mach number increases and all other flow properties decreases.
5. Distinguish between compression waves and mach lines?
S.No Compression waves Mach lines
1 A compression wave is a large-amplitude
compression wave which carries energy
and can propagate through a medium.
Mach lines are the weak waves
which are produced in supersonic
flow due to the sharp leading edge.
2 Across a shock there is always a rapid rise
in pressure, temperature and density of the
flow.
Across a mach wave, air velocity
increases, temperature and pressures
are reduced.
6. What are the assumptions made in the derivation of Prandtl Meyer expansion waves?
1. The flow is steady, two dimensional and isentropic throughout the flow field
2. All the streamlines are straight and parallel to the surface.
3. All the flow properties in the flow field upstream and downstream have
constant values
4. All the flow properties along each mach line is constant, each mach line is a
straight line
7. Give the expression for Prandtl Meyer function and what is the maximum value of it?
Prandtl Meyer function is written of the form v (M) in terms of Mach number as
The maximum value of the Prandtl Meyer function is
𝑣 𝑚𝑎𝑥 =
𝜋
2
(√
𝛾 + 1
𝛾 − 1
− 1)
If 𝛾=1.4, then 𝑣 𝑚𝑎𝑥=130.5°

30. 8. What is expansion hodograph?
The hodograph which shows the expansion characteristics of a Prandtl Meyer
flow is called as expansion hodograph. The hodograph characteristics for a uniform
steady two dimensional planar isentropic flow are epicycloids which is a curve generated
by rolling a circle of radius (b-1)/2 on the circumference of a circle of radius M*=1.
9. What do you mean by the reflection of shock waves?
When an oblique shock wave is intercepted by a frictionless surface, the shock
wave will be reflected. Reflections can be done on two surfaces
1. Reflection from a solid wall
2. Reflection from a free boundary
10. Differentiate like reflection and unlike reflection?
S.No Like reflection Unlike reflection
1 Reflection of an incident shock wave
from a solid boundary is called as like
reflection.
Reflection of an incident shock wave
from a free boundary is called as unlike
reflection.
2 In a like reflection, shock wave reflects
as shock wave and expansion wave
reflects as expansion waves.
In an unlike reflection, shock wave
reflects as expansion waves and
expansion wave reflects as shock wave.
11. Explain the reflection of shock wave on a solid boundary?
When a shock wave falls on a solid boundary, it is reflected. The streamlines after
passing the shock wave are directed parallel to the angle of deflection. But the
equilibrium condition is that the flow must be parallel to the wall, for that the shock wave
will be reflected from the solid wall. Due to shock reflections, Mach number decreases,
i.e. M1>M2>M3
12. What will happen when a shock wave is reflected from a free boundary?
When the incident shock wave falls on the free boundary, the static pressure after
the shock wave will be increased. But the boundary condition is that the pressure must be
reduced to the stagnation pressure for the flow to be parallel to the wall. So an expansion
wave will be formed at the point of reflection.

31. 13. Define Mach Reflection?
When an attached oblique shock wave cannot be formed at the wall, the shock
wave becomes normal to the wall and “curves out” to become tangent to the incident
shock wave. Such reflection is called as Mach Reflection. The shock wave from the wall
to the point G is called as a mach shock wave.
14. What is meant by slip line?
The line across which some of the flow properties are discontinuous is which is
formed at the junction of shock waves is called as slip line. Slip line can be neglected for
some cases, but in actual practice, slip line is essential.
15. Differentiate incident shock and reflected shock waves?
S.No Incident Shock Wave Reflected Shock Wave
1 It is the shock wave which is formed at
the corner due to the turning of the
flow through a certain angle.
It is the shock wave which is formed
after the impingement of the incident
shock wave from the boundary.
2 Streamlines after passing the incident
shock wave will be deflected towards
the flow angle deviation.
Streamlines after passing the reflected
shock wave will be deflected towards
the free stream direction

32. 16. Define neutralization of shock wave and how is it achieved?
It is also called as the cancellation of shock wave. Incident shock wave turns the
flow through the deflection angle and raises the static pressure of the flowing gas. But the
boundary condition is that the flow must be parallel to the wall. If the wall is deflected
again by the same angle, the boundary condition can be satisfied and there is no shock
wave reflection.
17. Explain the reflection of an expansion wave on a solid boundary?
When the incident expansion waves fall on a solid boundary, it will be reflected.
The streamlines after passing through this incident expansion wave will be deflected by
the deflection angle. The boundary condition of the flow is that the flow should be
parallel to the wall, so the incident expansion wave is reflected with sufficient strength to
deflect the streamlines parallel to the wall.
18. State the physical phenomenon behind the reflection of an expansion wave from a free
boundary?
When the incident expansion wave falls on a free boundary, the static pressure
after the incident expansion wave will be decreased below the static pressure. In order to
increase the pressure of the fluid after the expansion wave, this wave is reflected as a
shock wave, so that the flow will be parallel to the wall.

33. 19. What is meant by cancellation of expansion waves?
When the flow is deflected away from itself, expansion waves will be created.
When this incident expansion wave impinges on a wall, static pressure will be reduced to
the stagnation pressure. But the boundary condition is that the flow must be parallel to the
wall. If the wall is deflected again by the same angle, the boundary condition can be
satisfied and there is no reflection of expansion waves.
20. Explain how the intersection of shock waves occurs?
When two oblique shock waves are deflected inwards, they will intersect each
other at a particular point. This phenomenon is called as the intersection of waves and the
point at which this occurs is called as the point of intersection.
21. How the intersection of expansion waves occurs?
When two different surfaces are deflected by a particular angle, two expansion waves
will be formed. When these waves intersect each other, two other waves will be created. Slip
lines will be formed to bring the streamlines parallel to the wall.

34. 22. Define Mach intersection?
If the transmitted oblique shock wave cannot satisfy the flow condition, a normal
shock wave pattern will be obtained and that is called as the mach intersection.
23. Differentiate regular intersection and mach intersection?
S.No Regular intersection Mach intersection
1 If the transmitted oblique shock wave
satisfies the flow condition, normal
shock wave pattern is not formed and
that is called as the regular intersection
If the transmitted oblique shock wave
cannot satisfy the flow condition, a
normal shock wave pattern will be
obtained and that is called as the mach
intersection.
2 The transmitted shock waves adjust
themselves, so that the pressures will
be equal.
Boundary condition is satisfied by the
formation of slip lines on either side of
the mach shock wave.
24. Explain the intersection of shock waves of the same family?
When two or more shocks of the same family intersect each other, the two shock
waves merge at a particular point and become a strong shock wave. To bring the system
to equilibrium, a shock wave is reflected along the slip line which is necessary to adjust
the flow so that the flow in the two regions will be in the same direction.
25. What do you mean by mixed flow field?
The flow field in which there are regions of both subsonic flow and supersonic
flow is called as mixed flow field. Method of characteristics can be used to analyze the
flow field in this mixed flow field

35. 26. Define method of characteristics?
 It is a numerical method for solving non linear equations of motion for an
inviscid, irrotational flow.
 It is a method used for the design of two dimensional supersonic nozzles.
 The solution obtained by the method of characteristics is accurate without any
approximations.
 When the governing equation for a flow is hyperbolic, method of characteristics
was used to obtain the solution.
27. Explain the method of characteristics from various points of view?
The characteristic is a curve across which the derivatives of a physical property
may be discontinuous while the property itself remains continuous.
The characteristic is a curve along which the governing partial differential
equation reduces to an interior operator, i.e. the compatibility equation.
28. Define characteristic lines?
A characteristic line is defined as the path of propagation of a physical
disturbance. For supersonic flow, the disturbances are propagated through mach lines, so
mach lines are the characteristic lines.
29. What is meant by compatibility equation?
It is the equation where the governing partial differential equation is converted to
an interior operator or reduced to an ordinary differential equation, that equation is called
as the compatibility equation.
30. What are the points we need to solve the problems using method of characteristics
a) Initial data line
b) Wall points
c) Internal points
d) Shock points
31. What is meant by domain of dependence and region of influence in method of
characteristics?
The area between two upstream characteristics is called as domain of dependence,
because the properties at the point A depend on any disturbance in the flow in the
upstream region. The area between two downstream characteristics is called as region of
influence. It is the region influenced by the action going on at the wall point A.
32. Can we use the method of characteristics to determine the contour of a supersonic
nozzle? How?
When the flow inside the nozzle is assumed to be one dimensional, it won’t give
any information about the contour of the nozzle. But the actual nozzle flow is two
dimensional and the contour should be proper, otherwise shock waves will be formed
inside the nozzle. Method of characteristics is used to design shock free expansion.
Contour can be designed by using wall points and internal points assuming the nozzle to
be symmetrical.

36. 33. What is meant by Diamond wave pattern in Supersonic nozzle?
After the air passes through the test section in a supersonic wind tunnel, shock
waves will be formed. Due to the cross section of the duct, the shock waves will be
reflected and intersect each other. The continuous reflection and intersection of these will
represent the shape of a diamond and so this is called as the Diamond wave pattern in
Supersonic nozzle.
34. What is called as expansion section in nozzle design?
The section of the diverging nozzle where the angle of expansion is increasing is
called as the expansion section. This section is very important in nozzle design because in
this section only, the Mach number is increased.
35. Define sonic line?
The sonic line is the line which divides the subsonic and supersonic flow.
Subsonic flow will be accelerated to sonic speeds at the throat section. Before this line,
flow will be subsonic and after this line, the flow will be supersonic.
36. What is meant by limiting characteristics?
The characteristic line which emanates from the object and intersects the shock
wave at the point where the sonic line also intersects the shock waves is called as the
limiting characteristics. It prevents the intersection of any characteristic line originating
downstream with the sonic line.
37. Define simple and non simple regions?
The region where the characteristic lines of one family are straight and the other
family is curved is called as the simple region. The region where the characteristic lines
of both families are curved is called as the non simple region.
38. What are right running and left running waves in supersonic flow?
The waves which run to the left of the flow field when it is viewed upstream of
the flow is called as left running waves. It is denoted by C+.

37. The waves which run to the right of the flow field when it is viewed upstream of
the flow is called as right running waves. It is denoted by C-
39. What is meant by Fanno Flow?
Flow in a constant area duct with friction and without heat transfer and work
transfer is called as fanno flow
40. What are the assumptions made in fanno flow?
1. The area of the duct is constant
2. The flow is steady and one dimensional flow
3. There is no work or heat transfer
4. Body forces are negligible
5. There is no obstructions within the flow
6. Wall friction is the sole driving potential for the flow
41. Define fanning’s coefficient of skin friction?
The ratio between the wall shear stress to the dynamic head is defined as the
fanning’s coefficient of skin friction.
𝑓 =
wall shear stress
dynamic head
42. Draw a typical fanno curve and explain its significance?
The curve of enthalpy as a function of entropy for constant values of G, for an
adiabatic flow with wall friction is termed as fanno line. It is given by the fanno line
equation.The fanno line is the locus of all the possible thermodynamic states that are
attainable by the fluid for selected values of G.

38. 43. Write down the important governing equations for fanno flow?
44. What are the effects of friction on the downstream flow when M1>1?

39. 45. How will you find the length of the constant area duct in fanno flow?
The length of the constant area duct in fanno flow can be expressed as
Where f is the coefficient of skin friction
D is the diameter of the pipe
L is the length of the pipe
Lmax is the maximum length of the pipe
46. Give two practical examples where fanno flow occurs?
1. Flow process occurring in gas ducts of aircraft engines
2. Flow process occurring in air-conditioning systems
3. Flow process occurring in industrial plants
4. Steam pipelines
47. Find out the length of the pipe for fanno flow, if the Mach number changes from 3 at the
entry to 1.0 at the exit. Take the friction factor for the pipe surface to be 0.002?
Given data
M1 = 3.0
M2 = 1.0
f = 0.002
Solution
From fanno flow table,
For M1 = 3.0,
4𝑓 𝐿 𝑚𝑎𝑥
𝐷
= 0.522
For M2 = 1.0,
4𝑓 𝐿 𝑚𝑎𝑥
𝐷
= 0.000
4𝑓𝐿
𝐷
= 0.522 − 0.000
= 0.522
𝐿 = 0.522
𝐷
4𝑓
L = 65.25 D
48. What is meant by Rayleigh Flow?
Flow in a constant area duct with heat transfer and without friction is called as
Rayleigh flow

40. 49. Define Rayleigh line?
The line obtained by applying the Rayleigh line equations is called as a Rayleigh
line. It is denoted as R-line.
50. Show the heating and cooling processes in a Rayleigh flow for subsonic and supersonic
flow?
If the flow is subsonic, heating causes the flow Mach number to increase and the
corresponding static pressure to decrease. Cooling causes the flow Mach number to
decrease and the static pressure to increase.
If the flow is supersonic, heating causes the flow Mach number to decrease and
the corresponding static pressure to increase. Cooling causes the flow Mach number to
increase and the static pressure to decrease.
51. What are the effects of heat transfer on the downstream flow when M1>1

41. 52. What are the assumptions made in Rayleigh flow?
1. Area of the duct is constant
2. The flow is steady and one dimensional flow
3. There is no work transfer
4. Body forces and the effects of friction are negligible
5. Heat transfer is the only driving potential
53. Write down the important governing equations for Rayleigh flow?
54. Write down the expression for static pressure ratio of two sections in terms of mach
numbers in Rayleigh flow?
The static pressure ratio between two sections in a Rayleigh flow can be
expressed in terms of mach numbers as
55. Bring out two important differences between Rayleigh Flow and Fanno Flow?
S.No Rayleigh Flow Fanno Flow
1 Flow in a constant area duct with heat
transfer and without friction is called as
Rayleigh flow
Flow in a constant area duct with
friction and without heat transfer and
work transfer is called as fanno flow
2 The curve of enthalpy as a function of
entropy for constant values of G, for an
adiabatic flow with heat transfer is
termed as Rayleigh line.
The curve of enthalpy as a function of
entropy for constant values of G, for an
adiabatic flow with wall friction is
termed as fanno line.
56. Show a normal shock wave in h-S diagram with the help of Rayleigh line and Fanno line?
The flow through a shock wave satisfies the energy and continuity equations for
the F-line and the momentum and continuity equations for the R-line. The change from
state 1 to 2 is accomplished by a shock wave. The shock process is a sudden compression
that increases the pressure and entropy of the fluid but decreases the velocity from a
supersonic to a subsonic value.

43. UNIT-IV (DIFFERENTIAL EQUATIONS OF MOTION FOR STEADY
COMPRESSIBLE FLOWS)
1. Define a supersonic airfoil?
 Supersonic airfoils have a thin section formed of either angled planes or opposed
arcs called "double wedge airfoils" and "biconvex airfoils" with very sharp
leading and trailing edges designed to generate lift efficiently at supersonic
speeds.
 The need for such a design arises when an aircraft is required to operate
consistently in the supersonic flight regime.
 The sharp edges prevent the formation of a detached bow shock in front of the
airfoil as it moves through the air.
2. What are the major factors affecting the design of a supersonic wing?
a) Maximum permissible span
b) Required G capability incidence
c) Required stability
d) Speed and Trim angle
e) Structural efficiency
f) Minimum drag
3. What are the disadvantages of using sharp edged wings for supersonic flights?
 Problem with sharp leading edges is poor performance in subsonic flight.
 Lead to very high stall speeds, poor subsonic handling qualities
 Poor take off and landing performance for conventional aircraft
4. Give the expression for the velocity potential equation of motion?
The velocity potential equation of motion for a steady, inviscid, irrotational,
compressible flow over an object can be written as
Where Φ is the velocity potential function of the object
5. What is meant by perturbations?
Any small change in a physical system at equilibrium that is disturbed from the
outside is called as perturbation. The small disturbance created by the airfoil is termed as
perturbation. Due to such perturbations, the velocity components will be changed in the
flow field. The velocity is taken as the sum of the uniform flow velocity and some extra
increments in velocity and these increments are called as perturbations.
6. Define perturbation potential theory?
The theory which describes the change in flow field around an airfoil is defined as
perturbation theory. Perturbation velocity potential equation will denote the changes in
flow field due to perturbation in the flow.

44. 7. Differentiate uniform flow and perturbed flow
S.No Uniform flow Perturbed flow
1 The flow where there is no
disturbance in the flow field is
called as uniform flow
The flow where the flow field is disturbed and
unsteady is called as perturbed flow
2 It has only x component of
velocity and no y component
It has both x component and y component of
velocity
3
8. What is perturbation potential function?
The potential function which describes the changes in the flow field around an
airfoil due to slight disturbances is called as perturbation potential function.
Where is the perturbation potential function.
9. Give the linearised perturbation velocity potential equation?
When the flow field is experiencing some disturbances in the flow, the potential
equation can be written as
This equation is exact only for irrotational, isentropic flow
10. Write the equation of small perturbation potential theory?
Using some small perturbations in the flow field, the perturbation potential can be
written of the form
11. What are the assumptions of small perturbation potential theory?
 Small perturbations
 Slender bodies (thin)
 Small angle of attack
 Subsonic flows
 supersonic flows

45. 12. What are the limitations of this small perturbation potential theory?
 Large perturbations
 Thick bodies
 Large angle of attack
 Transonic flows
 Hypersonic flows
13. Derive the coefficient of pressure for compressible flows?
𝐶 𝑝 =
𝑃 − 𝑃∞
𝑞∞
𝑞∞ =
𝛾
2
𝑃∞ 𝑀∞
2
𝐶 𝑝 =
2
𝛾𝑀∞
2
(
𝑃
𝑃∞
− 1)
14. Explain linearised pressure coefficient using small perturbation potential theory?
From the small perturbation potential theory, the linearised pressure coefficient is
written as
15. Define flow tangency condition?
 Flow tangency condition is such that the flow should be tangent at the surface.
 Any solution to the linear equation must satisfy the boundary condition at infinity
and at the body surface.
 At infinity φ=constant so u’ and v’= 0 since u’ and v’ are derivatives of φ
 At the body surface, flow tangency occurs
 θ– angle between free stream and surface of the tangent
16. What is meant by affine transformation?
If all the coordinates of the system are changed by uniform ratio, then that
transformation is termed as affine. It is the transformation that preserves lines and
parallelism. It preserves straight lines and ratios of distances between points lying on a
straight line. The midpoint of a line segment remains the midpoint after transformation.

46. 17. Define Prandtl-Glauert transformation?
 Mathematical technique for solving compressible flow problems by using
incompressible-flow calculation methods.
 Approximation function which allows comparison of aerodynamic processes
occurring at different Mach numbers.
18. Explain compressibility correction?
 Corrections done to subsonic incompressible flow with account of effects of
compressibility
 Used to predict the compressible results about the original shape
 The correction done to the compressible flow using incompressible flow field is
called as the compressibility correction.
 It is denoted by the compressibility factor.
 cp - Compressible pressure coefficient
 cp0 - Incompressible pressure coefficient
 M - Mach number.
19. State Prandtl-Glauert rule? (OR) Write the Prandtl Glauert relation for subsonic flow?
Prandtl-Glauert rule states that if we know the incompressible pressure
distribution over an airfoil, then the compressible pressure distribution can be found
using Prandtl-Glauert rule.
Prandtl-Glauert rule is a correction made to subsonic aerodynamics based on
linearised perturbation velocity potential equation
20. How will you relate the slope of the airfoil in the physical plane and transformed plane?
The shape of airfoil is in physical plane y=f(x) is transformed to 𝜂 = 𝑞(𝜉) in the
transformed plane (ξ, η)
It says that the shape of the airfoil in the transformed plane is similar to the
physical plane.
df dq
dx d


47. 21. Write down the critical pressure coefficient from the Prandtl-Glauert rule?
22. Draw a typical curve relating pressure coefficient and Mach number for subsonic and
supersonic flows?
When the Mach number increases, for subsonic flow the pressure coefficient will
increase slowly and when it reaches sonic value Cp will be increased gradually.
For supersonic flow, the value of the coefficient of pressure decreases from a
maximum value and remains constant as the Mach number increases.
23. Give the compressibility correction given by Karman-Tsien?
 The Karman-Tsien transformation is a nonlinear correction factor to find the
pressure coefficient of a compressible, inviscid flow.
 It is a correction factor that tends to slightly overestimate the magnitude of the
fluid's pressure.
Where
 cp is the compressible pressure coefficient
 cp0 is the incompressible pressure coefficient
 M is the Mach number.
0
2
p
u
C
V
 
0
2
1
p
p
C
C
M



48. 24. Write the correction factor for Laitone rule?
The compressibility correction given by Laitone is expressed as Laitone rule
25. Write the Geothert’s Rule?
Geothert’s Rule states that the slope of a profile in a compressible flow pattern is
larger by the factor1/√1 − 𝑀2 than the slope of the corresponding profile in the related
incompressible flow pattern.
26. Compare the coefficient of pressure using various compressibility corrections?
When using Prandtl Glauert compressibility correction, the coefficient of pressure
can be reduced to a much lesser value as the Mach number increases than using Karman-
Tsien compressibility correction and Laitone rule
27. Give the expressions for lift and moment using Prandtl-Glauert rule?
28. At a given point in the surface of the airfoil, the pressure coefficient is -0.3 at very low
speeds. If the freestream Mach number is 0.6, calculate the pressure coefficient at this
point.
0
2 2 2 2
0
1
1 1 / 2 1
2
p
p
p
C
C
M M M M C

  

   
     
  

49. 29. The theoretical lift coefficient for a thin, symmetrical airfoil in an incompressible flow is
𝐶𝑙 = 2𝜋𝛼. Calculate the lift coefficient for 𝑀∞ = 0.7?
The effect of compressibility at mach 0.7 is to increase the lift slope by the ratio
8.8/2π=1.4 or by 40%
30. What is the need for the linearised theory of supersonic flow?
 Linearised supersonic flow is used to estimate the aerodynamic properties of
supersonic airfoils
 Linearised supersonic flow is used to obtain the solution for supersonic flow
when there is a disturbance in the flow field.
31. Write the governing equation for supersonic flows in linearised two-dimensional
supersonic theory?
The governing equation for supersonic flows can be given by
Where
32. List out the practical application of linearised two-dimensional supersonic theory?
a) Flow over a thin airfoil,
b) Flow over a mildly wavy wall,
c) Flow over a small hump in a surface
33. Sketch the different types of supersonic profiles?
1. Diamond wedge airfoil
2
0xx yy   
 2
1M  

50. 2. Biconvex airfoil
3. Flat plate
34. Write the expression for lift and drag coefficients for a flat plate using linearised theory?
35. By linearised theory, what are the expressions for the lift and drag coefficients for a
symmetric double wedge airfoil?
𝐶 𝐿 =
4𝛼
√𝑀2 − 1
𝐶 𝐷 =
4𝛼2
√𝑀2 − 1
+
4𝜃2
√𝑀2 − 1
36. By linearised theory, what are the expressions for the lift and drag coefficients for a
symmetric bi convex profile?
𝐶 𝐿 =
4𝛼
√𝑀2 − 1
𝐶 𝐷 =
4𝛼2
√𝑀2 − 1
+
16
3
(
𝑡
𝑐
)
2
√𝑀2 − 1
37. Explain the linearised pressure distribution over a biconvex airfoil

51. 38. What is the Lift curve slope and Lift drag ratio for the flat plate?
39. What are the major inferences from the linearised theory of supersonic flow?
 All the disturbances created at the wall propagate unchanged away from the
wall along Mach lines.
 All mach waves have the same slope.
 Mach waves slope downstream above the wall.
 Flowfield upstream of a disturbance does not feel the presence of the
disturbance.
 Any disturbance at the wall cannot propagate upstream.
 Disturbance propagate everywhere in subsonic flow but they cannot propagate
upstream in supersonic flow
40. How can you say that the lines along the constant potential function are mach lines?
Justify?
The slope of the lines along the constant potential function can be given by
Also the slope of the mach line is given by
In both the above cases, R.H.S is constant, so the equation can be written as
tan 𝜇 =
1
√𝑀2 − 1
From this, we can say that the lines along the constant potential function are a mach line.
41. Write the expression for coefficient of pressure using linearised theory?
 It states that Cp is directly proportional to the local surface inclination w.r.t. free
stream.
 θ is positive when measured above the horizontal and θ is negative when
measured below the horizontal
 Cp is positive on the forward portion of the hump and negative on the rear
portion of the hump
1
2
2


M
Cp


52. 42. Compare the various values of coefficient of pressure for different types of flows?
 For supersonic flow, coefficient of pressure decreases as the Mach number
increases
 For sonic flow, coefficient of pressure tends to infinity as the mach number
increases
 For subsonic flow, coefficient of pressure increases as the Mach number increases
43. Explain how lift and drag produced in supersonic profiles?
When a supersonic airfoil is at negative angle of attack at the top leading edge
there is an expansion fan and oblique shock at the bottom. The airflow over the top of the
wing is now faster and the airflow will also be accelerated through the expansion fans on
both sides. The result is much faster flow on top surface and therefore lower pressure on
the top of the airfoil.
44. What are subsonic and supersonic leading edges? Explain with sketches? (OR) Explain
how supersonic airfoil profiles are fundamentally different from subsonic airfoil profiles?
The subsonic leading edge will have a round nose and a sharp tail section. When
this airfoil moves in the air at supersonic speeds, bow shocks will be formed in front of
the leading edge.
The supersonic leading edge will have a sharp nose and a sharp tail section. When
this airfoil moves in the air at supersonic speeds, shock waves and expansion waves will
be formed in front of the leading edge.

53. 45. Using linear theory, calculate the lift and drag coefficients for a flat plate at a 5° angle of
attack in a mach 3 flow.
46. Define wave drag?
When the airfoil is at zero angle of attack, shock wave is formed on the front
surface of the airfoil and an expansion wave is formed on the rear surface. So there is a
pressure difference between the two regions. This pressure difference creates a drag force
on the airfoil and this drag is called as the wave drag. The drag formed due to the
formation of shock and expansion waves in the airfoil even when the airfoil is at zero
angle of attack is called as the wave drag.
47. How lift and drag varies with angle of attack for a supersonic profile?
48. What are the methods to reduce this wave drag
 Using a swept wing, makes it appear thinner and longer in the direction of the
airflow, making a "normal" wing shape
 Build a wing that is extremely thin.
 Fuselage shaping was changed with the introduction of the Whitcomb area rule.
 Supercritical airfoil is a new wing design that results in supersonic flow over the
wing upper surface.

54. UNIT-V (TRANSONIC FLOW OVER WINGS)
1. Explain the transonic flow over wings?
 Transonic flow is between mach 0.8 and 1.2. i.e. 600–900 mph
 This condition depends not only on the travel speed of the aircraft, but also on the
pressure and temperature of the airflow of the vehicle's local environment.
 It is formally defined as the range of speeds between the critical Mach number,
when some parts of the airflow over an air vehicle or airfoil are supersonic, and a
higher speed, typically near Mach 1.2.
2. What are the various ways of delaying the transonic wave drag rise?
(1) Use of thin airfoils;
(2) Use of a forward or backward swept wing;
(3) Low-aspect-ratio wing;
(4) Removal of boundary layer and vortex generators
(5) Supercritical and area-rule technology.
3. Explain the shock formation around an airfoil?

55. 4. Define critical Mach number of an airfoil?
 Critical Mach number (Mcr) of an aircraft is the lowest Mach number at which
the airflow over some point of the aircraft reaches the speed of sound
5. What is the importance of critical Mach number?
1. Drag coefficient increases suddenly, causing dramatically increased drag
2. Changes to the airflow over the flight control surfaces lead to deterioration in
control of the aircraft.
6. Define the factors influencing critical Mach number?
 Thickness to chord ratio
 Aspect ratio
 Wing sweep
7. Write the expression for coefficient of pressure using critical Mach number?
8. What are the types of critical Mach number?
 Upper critical mach number
 Lower critical mach number

56. 9. Distinguish between Lower Critical Mach number and Upper Critical Mach number?
 The free stream mach number at which the sonic flow is achieved first on the
upper surface of the airfoil is called as upper Critical Mach number
 The free stream mach number at which the sonic flow is achieved first on the
lower surface of the airfoil is called as lower Critical Mach number
10. Define mach tuck
Mach tuck is an aerodynamic effect, whereby the nose of an aircraft tends to pitch
downwards as the airflow around the wing reaches supersonic speeds. The aircraft will be
subsonic and traveling significantly below Mach 1.0, when it first experiences this effect.
11. Why is that airfoil designed for a high critical mach number must have a thin profile?
In thin airfoils,
1. critical Mach number is increased
2. lower minimum pressure
3. lift coefficient will decrease
4. drag rise small
5. Can fly at high free stream Mach number
12. What is meant by lift divergence?
 Lift divergence is a departure from the smooth increase in lift with increasing
airspeed that occurs just above the critical Mach number.
 The lift-divergence Mach number is the speed at which the lift reaches its
maximum.
 The airfoil shape and incidence determine exactly where the lift-divergence Mach
number is positioned.
13. Define drag divergence Mach number?
 It is the Mach number at which the aerodynamic drag on an airfoil begins to
increase rapidly as the Mach number continues to increase.
 This increase can cause the drag coefficient to rise to more than ten times its low
speed value.
 value of the drag divergence Mach number is typically greater than 0.6
 Drag coefficient peaks at Mach 1.0 and begins to decrease again after the
transition into the supersonic regime above approximately Mach 1.2.
14. How the drag coefficient varies with Mach number?

57. 15. What is meant by Sonic barrier?
 Sound barrier is the point at which an aircraft moves from transonic to supersonic
speed.
 If an aircraft flies at somewhat less than sonic speed, the pressure waves it creates
out speed their sources and spread out ahead of it.
 Once the aircraft reaches sonic speed the waves are unable to get out of its way.
 Strong local shock waves form on the wings and body; airflow around the craft
becomes unsteady with serious stability difficulties and loss of control over flight
characteristics.
16. What is sonic boom
 A sonic boom is the sound associated with the shock waves created by an object
traveling through the air faster than the speed of sound.
 Sonic booms generate enormous amounts of sound energy, sounding much like an
explosion.
 The crack of a supersonic bullet passing overhead is an example of a sonic boom
in miniature.
17. What is meant by shock induced separation?
 Shock wave interaction with the boundary layer causes separation of boundary
layer behind the shock which results in large increase in drag called as shock
induced separation.
 Also called as Shock-Boundary Layer Interaction
 Appears in transonic or supersonic flows.
18. Explain the various flow phenomenon’s which occur when shock wave interacts with
boundary layer?
When shock wave interacts with boundary layer, many types of flow phenomena
occur
1. flow separation,
2. Unsteadiness,
3. Vortical flow,
4. Pressure waves,
5. Complicated mixing,
6. Turbulence
19. What are the effects of shock induced separation?
 External flow
 Increased aerodynamic drag, loss of lift
 Aerodynamic heating
 Increased instabilities such as inlet
 Internal flow
 Total pressure loss and unsteadiness
 Loss of flow control performance

58. 20. What are the various shock boundary layer interactions?
 Weak interaction
 Moderate interaction
 Strong interaction
 Very strong interaction
21. Define the parameters influencing shock induced separation
 Mach Number
 Reynolds Number
 Pressure Gradient
 Unsteadiness
 Laminar or Turbulent flow
 Shape factor
 Boundary layer thickness
22. Explain the shock induced separation on laminar and turbulent boundary layers?
Laminar
Turbulent
23. Differentiate internal flows and external flows based on shock separation
S.No EXTERNAL FLOWS INTERNAL FLOWS
1 The pressure rise to separation is
independent of the geometry causing
the SBLI
A supersonic turbulent boundary layer
separates when subjected to a critical
pressure jump
2 Separation pressure rise depends only
on the upstream Mach number
Separation pressure jump depends only
on the upstream Mach Number
3 Onset of separation takes place at a
particular Mach number
The onset for separation in nozzles
depends only on the upstream Mach no

59. 24. List out the various aspects related to laminar interaction and turbulent interaction
S.No Laminar interaction Turbulent interaction
1 Upstream propagation of disturbances
through BL is long (10 to 100 d )
Upstream propagation of disturbances
through BL is short (10 d)
2 Leads to oblique compression waves Oblique compression waves soon coalesce
into a strong shock wave
3 Forms lambda shock pattern together
with the rear shock
Weak normal shock waves appear beyond
the main shock wave – same as rear wave in
lambda structure
4 Front shock in Lambda shock is weaker Rear shock is weak in lambda pattern
25. Sketch a typical supercritical airfoil and describe it?
 A supercritical airfoil is an airfoil designed to delay the onset of wave drag in the
transonic speed range.
 Supercritical airfoils are characterized by their flattened upper surface, highly
cambered aft section, and greater leading edge radius compared with traditional
airfoil shapes.
26. What is the difference between a supercritical airfoil and a conventional airfoil?

60. 27. What are the benefits of supercritical airfoil?
a) supercritical airfoil have a higher drag divergence Mach number
b) Shockwave is minimized and is created as far aft as possible thus reducing drag.
c) Reduce shock-induced boundary layer separation,
d) Geometry allows for more efficient wing design
e) Improves the performance of aircraft cruising in the transonic regime.
f) Enlarged leading edge gives it excellent high-lift characteristics.
28. Define a swept wing plan form?
 Wing plan form used to increase the critical Mach number and drag divergence
Mach number during transonic flight
 Delay the drag rise caused by fluid compressibility near the speed of sound.
29. Differentiate swept wings from straight wings?
 In a straight wing, streamlines see this wing in a normal direction, so more drag
 In a swept wing, streamlines see the wing in an oblique angle, so less drag
 Thickness to chord ratio is 0.106 which is 1/3rd of the straight wing
 wing behaves as a thin wing and increase the critical mach number, so less drag
30. List out the characteristics of swept wings?
 Delay the drag rise
 Increase the critical mach number
 Requires a longer chord length for a given span
 Allows all parts of the aircraft that create lift to remain in subsonic flow,
 Creates less lift for a given airspeed than a non-swept wing would.
31. Explain the concept of sweep theory?
 Description of the behavior of airflow over a wing when the wing's leading edge
encounters the airflow at oblique angle.
 This design performs more effectively at transonic and supersonic speeds.
 Sweep theory led to the oblique wing concept.

61. 32. What is meant by sweep angle?
 Angle between the lateral axis and the quarter-chord line.
 Also referred to as leading-edge sweep.
33. How can you define the behavior of swept wings in transonic flow?
 As aircraft enters the transonic speeds, wave drag starts to appear.
 Airflow accelerates around curved surfaces, and near the speed of sound the
acceleration can cause the airflow to reach supersonic speeds.
 Oblique shock wave is generated at the point where the flow slows down back to
subsonic speed.
34. Explain the behavior of swept wings in supersonic flow?
 Airflow at supersonic speeds generates lift through shock waves.
 Shock waves generate large amounts of drag.
 One of these shock waves is created by the leading edge of the wing, but
contributes little to the lift.
 To minimize the strength of this shock it needs to remain "attached" to the front
of the wing, which demands a very sharp leading edge.
35. What are the types of swept wings?
Based on direction of sweep
– Forward swept
– Backward swept
– Variable swept
Based on angle of sweep
– Slightly swept
– Moderately swept
– highly swept
36. Give some advantages of using a swept wing?
1. More lateral stability
2. Has low thickness and high fineness ratio, so less form drag
3. It is tapered, so less induced drag
4. Good for turboprop placement
5. Can fly at high speeds
37. List the major disadvantages in swept wings?
1. Stalling occurs at the tips which affects longitudinal stability
2. Has low aspect ratio, so it gives more induced drag at high incidence

62. 38. Explain the variable sweep wings and explain its features?
 Wing that may be swept back and then returned to its original position during
flight.
 It allows the aircraft's plan form to be modified in flight.
 Also called as swing wing
39. What is the effect of thickness over the performance of wings?
40. What is the effect of camber over the performance of wings?

63. 41. What is the effect of aspect ratio over the performance of wings?
42. What is meant by transonic area rule?
 It is a design technique used to reduce an aircraft's drag at transonic and
supersonic speeds, particularly between Mach 0.75 and 1.2.
 Also called as the transonic area rule or Whitcomb area rule,
43. Define Sears-Hack body
 At high-subsonic flight speeds, supersonic airflow can develop in areas where the
flow accelerates around the aircraft body and wings.
 Shock waves formed at the points of supersonic flow can bleed away a
considerable amount of power, which is experienced by the aircraft as a sudden
and very powerful form of drag, called wave drag.
 To reduce the number and power of these shock waves, an aerodynamic shape
should change in cross sectional area as smoothly as possible.
 This leads to a "perfect" aerodynamic shape known as the Sears-Hack body,
roughly shaped like a cigar but pointed at both ends.

64. 44. Explain the “coke bottle fuselage design” given by whitcomb?
In an area ruled aircraft, the fuselage cross section should be decreased in the
wing and tail regions to compensate for the addition of wing and tail cross sectional area
and this shape is called as the coke bottle fuselage design.
45. Differentiate area ruled and non area ruled aircraft designs?
The area rule also holds true at speeds higher than the speed of sound, but in this
case the body arrangement is in respect to the Mach line for the design speed. The area
rule states that minimum transonic and supersonic drag is obtained when the cross-
sectional area distribution of the airplane along the longitudinal axis can be projected into
a body of revolution that is smooth and shows no abrupt changes in cross section along
its length
46. Plot the variation of CD with Mach number with and without transonic area rule?

65. 47. Name some transonic area ruled aircraft?
1. Tupolev Tu-95 'Bear
2. Convair F-106 Delta Dart
3. Convair 990
4. Boeing 747
5. B-1B Lancer
6. Tupolev Tu-160 'Blackjack
7. F-22 Raptor
8. Airbus A380
9. Learjet 60
48. Why is there a sudden drag rise in transonic flow?
When the aircraft changes its speed from subsonic to supersonic speeds, the speed
of the airflow over some parts of the wing reaches the speed of sound and other parts will
remain subsonic. When this happens, the aircraft is said to have reached its critical Mach
number and marks the beginning of transonic speed range. At a particular point after this
critical Mach number, the drag will be increased suddenly. That is the reason for a
sudden drag rise in transonic flow
49. What are the components on the transonic wind tunnel?
50. What are the problems in designing and constructing a hyper-velocity wind tunnel?
 Supply of high temperatures and pressures for times long enough to perform a
measurement
 Reproduction of equilibrium conditions
 Structural damage produced by overheating
 Fast instrumentation
 Power requirements to run the tunnel