This document provides short questions and answers related to gas dynamics and jet propulsion for a 6th semester mechanical engineering course. It covers topics like basic concepts of compressible flow, stagnation properties, flow through nozzles and diffusers, and flow through ducts. The questions define key terms, derive important equations, and ask students to analyze example problems involving isentropic flow of air through nozzles and ducts. The document aims to test students' understanding of fundamental compressible flow concepts and their ability to apply equations of compressible flow to practical problems.

1. ME 6604
GAS DYNAMCIS
AND
JET PROPULSION
SHORT QUESTION AND ANSWERS
VI SEMESTER
DEPARTMENT OF MECHANICAL ENGINEERING
RMK COLLEGE OF ENGINEERING AND TECHNOLOGY

3. UNIT –I BASIC CONCEPTS AND ISENTROPIC FLOWS
1. State the difference between compressible fluid and incompressible fluid.
Compressible flow is that type of flow in which the density of the fluid
changes from point to point. i.e density is not constant for the fluid.
ρ is not constant
e.g gases and vapors
Incompressible flow is that type of flow in which the density of the fluid is
constant.
ρ= constant
e.g .Liquids
2. Define stagnation pressure.
Stagnation pressure is the pressure of the gas when it is isentropically
decelerated to zero velocity at zero elevation.
p0 / p = [T0/T] γ/γ-1
p0 / p =[1+(( γ-1)/2 ) M2
] γ/γ-1
p0 = stagnation pressure
p = Static pressure
M = Mach number
3. Express the stagnation enthalpy in terms of static enthalpy and velocity of flow.
Stagnation enthalpy h0=h + c2
/2
Where h-static enthalpy – J/kg ; c=Velocity of fluid – m/s

4. 4. Define Stagnation state.
Stagnation state is obtained by decelerating a gas isentropically to zero
velocity at zero elevation. The stagnation state of a gas is often used as a
reference state.
5. Define Stagnation temperature (T0).
It is the temperature of the gas when it is isentropically decelerated to zero
velocity at zero elevation.
T0 / T = [1+ (( γ-1)/2 ) M2
]
Where
T0 = stagnation temperature.
T = Static temperature.
M = Mach number
6. Define Stagnation density(ρ0)
It is the density of the gas when it is isentropically decelerated to zero
velocity at zero elevation.
ρ0 / ρ =[1+(( γ-1)/2 ) M2
] 1/γ-1
7. Explain the Mach cone and Mach angle.
Mach cone:
Tangents drawn from the source point on the spheres define a conical
surface referred to as Mach cone.
Mach angle:
The angle between the Mach line and the direction of motion of the body
(flow direction) is known as Mach angle.

5. 8. Differentiate adiabatic process and Isentropic process
In an adiabatic process there is no heat transfer between the system and the
surrounding.
i.e Q =0
Isentropic process
In isentropic process entropy remains constant and it is reversible .during
this process there is no heat transfer from the fluid to surroundings or from the
surroundings to the fluid. Therefore an isentropic process can be stated as
reversible adiabatic process.
i.e s=constant
Q=0
9. Define Reynolds number.
It is defined as the ratio between inertia force and viscous force
Re = Inertia Force / Viscous force
10.Define Mach number.
The Mach number is an index of the ratio between inertia force and elastic
force.
M2
= Inertia Force / Elastic Force
It is also defined as the fluid velocity (c ) to the velocity of sound(a ).
M = c / a
11.What are the advantages of using M*?
It is more convenient to use M* instead of M due to the following reasons.
i. At high velocities M approaches infinity but M* gives a finite value
M* = sqrt (γ+1/ γ-1)

6. ii. M is proportional to the fluid velocity(c) and sound velocity (a), but
M* is proportional to the fluid velocity alone.
12.Name the different regions of compressible fluid flow.
i. Incompressible flow region
ii. Subsonic flow region
iii. Transonic flow region
iv. Supersonic flow region
v. Hypersonic flow region
13.Distinguish between incompressible flows, subsonic flows, transonic flows,
supersonic flows and hypersonic flows.
 Incompressible flow region, fluid velocity(c) is much smaller than the
sound velocity (a) . Therefore Mach number (M=c/a) is very very low.
 The subsonic flow region is on the right of the incompressible flow region.
In subsonic flow, fluid velocity (c) is less than the sound velocity (a) and
the Mach number is always less than unity. (M=c/a) <1
 In sonic flow, fluid velocity(c) is equal to the sound velocity (a) and the
Mach number is unity. (M=c/a) =1 => c=a
 In Transonic flow region, the fluid velocity (c) close to the speed of sound
(a) , Mach value is in between 0.8 and 1.2.
 The supersonic flow region is on the right of the transonic flow region.
In supersonic flow, fluid velocity(c) is more than the sound velocity (a) and
the Mach number is always greater than unity. (M=c/a) >1
 In hypersonic flow region, fluid velocity(c) is much greater than sound
velocity (a).In this flow, Mach number value is always greater than 5.
(M=c/a) >5

7. 14.Differentiate Laminar flow and Turbulent flow
Laminar Flow:
It is sometimes called stream line flow. In this flow the fluid moves in layer and
each fluid particle follows a smooth continuous path.
Turbulent flow:
In turbulent flow, the fluid particles move in irregular paths.
15.Differentiate nozzle and diffuser.
Nozzle: It is device which is used to increase the velocity and decrease the
pressure of fluids.
Diffuser: It is a device which is used to increase the pressure and decrease the
velocity of fluids.
16.Where are the convergent nozzles and convergent –divergent nozzles used?
Convergent nozzles are used for subsonic and sonic flows. They can also be
used as flow measuring and flow regulating devices.
Convergent – Divergent nozzles are used for supersonic flows.
17.How the area and velocity vary in supersonic flow of nozzle and diffuser.
Nozzle:
Area – Decreases
Velocity – Increases
Diffuser:
Area – Increases
Velocity – Decreases

8. 18.Zone of silence is absent in subsonic flow. Why?
Spherical sound wave generated at t=3,2 and 1 seconds .It is observed that
the wave fronts move ahead of the source of disturbance and therefore the zone
of silence is absent.
19.What is the cross section of the nozzle required to increase the velocity of
compressible fluid flow from a) subsonic to supersonic b) subsonic to sonic
The cross section of the nozzle is decided based on the equation
dA / A = (dc/c) (M2
-1)
a) Subsonic to supersonic : Cross section of the nozzle is convergent divergent
b) Subsonic to sonic: Cross section of the nozzle is convergent
20.What type of nozzle used for sonic flow and supersonic flow?
Constant area duct nozzle is used for sonic flow and divergent nozzle is used
for supersonic flow.
21. What is chocked flow through a nozzle?
The mass flow rate of nozzle is increased by decreasing the back pressure.
The maximum mass flow conditions are reached when the throat pressure ratio
achieves critical value. After that there is no further increase in mass flow with
decrease in back pressure. This condition is called chocking. At chocking condition
M=1.

9. PART- B
22.A supersonic nozzle expands air from p0=25bar and T0=1050K to an exit
pressure of 4.35bar;the exit area of the nozzle is 100 cm2
.Determine
i. Throat area
ii. Pressure and temperature at the throat
iii. Temperature at exit
iv. Exit velocity as fraction of the maximum attainable velocity
v. Mass flow rate.
22. A conical diffuser has entry and exit diameters of 15cm and 30cm respectively.
The pressure, temperature and velocity of air at entry are 0.69 bar, 340 K and
180m/s respectively. Determine
i. Exit pressure
ii. The exit velocity
iii. The force exerted on the diffuser walls. Assume isentropic flow,
γ = 1.4,Cp=1.00 kJ/kg-k.
23. Air is discharged from a reservoir at P0=6.91 bar and t0=325°C through a
nozzle to an exit pressure of 0.98 bar. If the flow rate is 3600 kg/hr, determine
throat area, pressure and velocity at the throat, exit area, exit Mach number and
maximum velocity. Consider the flow is isentropic.
24.A supersonic diffuser, diffuses air in an isentropic flow from a mach number of
3 to a mach number of 1.5.The static conditions of air at inlet are 70kPa and
-7°C.If the mass flow rate of air is 125kg/s, determine the stagnation conditions,
areas at throat and exit, static conditions (pressure, temperature, velocity) of air
at exit.
25.The pressure, temperature and Mach number at the entry of a flow passage are
2.45bar, 26.5°C and 1.4 respectively. If the exit Mach number is 2.5,deternine
for adiabatic flow of a perfect gas(γ = 1.3,R=0.469 kJ/kgK)
i. Stagnation temperature
ii. Temperature and velocity of gas at exit
iii. The flow rate per square meter of the inlet cross section

10. 26.Air (γ=1.4,R=287.43 J/kgK) enters a straight axis symmetric duct at
300K,3.45bar and 150 m/s and leaves it at 277K,2.058 bar and 260m/s. The
area of cross section at entry is 500cm2
.Assuming adiabatic flow determine
i. Stagnation temperature
ii. Maximum velocity
iii. Mass flow rate
iv. Area of cross section at exit
27.Air is discharged from a receiver at Po=6.91 bar and T0=325°C,through a nozzle
to an exit pressure of 0.98 bar. If the flow rate is 3600kg/hour, determine for
isentropic flow,
i. Area, pressure and velocity at throat
ii. Area and Mach number at exit end
iii. Maximum possible velocity
28.Deduce the expression for sonic velocity in terms of the properties of air.
29.Sketch the effect of disturbance in still air as it moves from rest to supersonic
velocity for the following Mach numbers: M=0, M=0.5, M=1.0,M=2.Explain in
detail the observed phenomena.
30.Starting from the continuity equation derive the expression for the area
variation and hence obtain the shape (geometry) for both subsonic and
supersonic nozzles and diffusers.

11. 31.In an isentropic flow diffuser the inlet area is 0.15m2
.At the inlet velocity
240m/s, static temperature=300K and static pressure 0.7 bar. Air leaves the
diffuser with a velocity of 120m/s. Calculate at the exit the mass flow rate,
stagnation pressure, stagnation temperature, area and entropy change across the
diffuser.

12. UNIT – II FLOW THROUGH DUCTS
PART –A
1. Explain the difference Fanno flow and isothermal flow
Fanno flow Isothermal flow
 Flow in a constant area duct with
friction and without heat transfer is
known as Fanno flow.
 Flow in a constant area duct with
friction and heat transfer is known as
Isothermal flow
 Static temperature is not constant.  Static temperature remains constant
2. Give the assumptions made in Isothermal flow.
 One dimensional flow
 Constant area duct
 Frictional flow at constant temperature
 The gas is perfect.
3. What is the limiting Mach number on Rayleigh flow?
The limiting Mach number in isothermal flow is M= 1/ sqrt(γ) and all
processes approach this Mach number.
4. List some flow properties
 Mass density(ρ)
 Specific volume(υ)
 Specific weight(w)
 Temperature(T)
 Specific gravity(S)

13. 5. What is Rayleigh flow?
Flow in a constant area duct with heat transfer and without friction is known
as Rayleigh flow.
6. What are the assumptions regarding Rayleigh flow?
i. One dimensional steady flow
ii. Flow takes place in constant area section
iii. The gas is perfect
iv. Absence of work transfer across the boundaries.
7. Sketch the Rayleigh line on the T-s plane and explain the significance of it.
Most of the fluids in practical use have Rayleigh curves of the general form
shown in fig.
The portion of the Rayleigh curve above the point of maximum entropy
usually represents Subsonic flow (M<1) and the portion below the maximum
entropy point represents Supersonic flow (M>1).
An entropy increases due to heat addition and entropy decreases due to heat
rejection. Therefore, the Mach number is increased by heating and decreased
by cooling at subsonic speeds. On the other hand, the Mach number is
decreased by heating and increased by cooling at supersonic speeds. Therefore,
like friction, heat addition also tends to make the Mach number in the duct
approach unity. Cooling causes the Mach number to change in the direction
away from unity.

14. 8. Give two practical examples for Rayleigh flow
i. Flow in combustion chamber
ii. Flow in Regenerators
iii. Flow in Heat exchangers
iv. Flow in Intercoolers.
9. Write down the expression for the pressure ratio of two sections in terms of
Mach number in Rayleigh flow
p2/p1 = (1+γM1
2
) / (1+γM2
2
)
10.What is Fanno flow?
Flow in a constant area duct with friction and without heat transfer is known
as Fanno flow.
11.What are the assumptions made in Fanno flow?
 One dimensional steady flow
 Flow takes place in constant sectional area
 There is no heat transfer
 The gas is perfect with constant specific heats
12.What is Rayleigh line and Fanno line?
Rayleigh line: Flow in a constant area duct with heat transfer and without
friction is described by a curve is known as Rayleigh line or Rayleigh curve.
Fanno line. Flow in a constant area duct with friction and without heat
transfer is described by a curve is known as Fanno line or Fanno curve.

15. 13.Give the fanno flow h-s diagram. Show the various Mach number regions and
write the fanno flow equation.
h0=h+(G2
/2ρ2
)
Fanno Flow Equation
h=h0- ½ (G2
/ [f( s,h)]2
14.State the two governing equations used in plotting Rayleigh line.
i. Continuity Equation
ii. Momentum Equation
15.Give two practical examples for Fanno flow occurs.
i. Flow in air breathing Engines
ii. Flow in refrigeration and air conditioning
iii. Flow of fluids in long pipes
16.Write down the ratio of velocities between any two sections in terms of their
Mach numbers in a Fanno flow.
c2/c1 = (M1 / M2) [((1+(γ-1)/2) M1
2
) / ((1+(γ-1)/2)M2
2
)]1/2
17.Explain chocking in Fanno flow
In a Fanno flow, subsonic flow region, the effect of friction will increase the
velocity and Mach number and to decrease the enthalpy and pressure of the gas.
In Supersonic flow region, the effect of friction will decrease the velocity
and Mach number and to increase the enthalpy and pressure of the gas.

16. In both the cases entropy increases up to limiting state where the Mach
number is one(M=1). So the mass flow rate is maximum at M=1 and it is
constant afterwards. At this point flow is said to be chocked flow.
18.What is the value of Mach number of air at the maximum point in Rayleigh
heating process?
At maximum point in Rayleigh curve, the value of Mach number is one.
19.Define isothermal flow with friction.
Flow in a constant area duct with heat transfer and friction is known as
isothermal flow.
20.What are the three equation governing fanno processes?
i. Energy equation
ii. Continuity equation
iii. Equation of state
PART – B
21.A circular duct passes 8.25 kg/s of air at an exit Mach number of 0.5.The entry
pressure and temperature are 3.45 bar and 38°C respectively and the coefficient
of friction is 0.005.If the Mach number at entry is 0.15, determine the diameter
of the duct, length of the duct, pressure and temperature at the exit, and
stagnation pressure loss.

17. 22.The Mach number at inlet and exit for a Rayleigh flow are 3 and 1.5
respectively. At inlet static pressure is 50 kPa and stagnation temperature is
295K.Consider the fluid is air. Find
i. the static pressure, static temperature and velocity at exit
ii. stagnation pressure at inlet and exit
iii. heat transferred
iv. maximum possible heat transfer
v. change in entropy between the two sections
vi. Is it a cooling or heating process?
23.Air at p0=10 bar, T0=400K is supplied to a 50 mm diameter pipe. The friction
factor for the pipe surface is 0.002.If the Mach number changes from 3.0 at the
entry to 1.0 at the exit determine,
i. The length of the pipe
ii. The mass flow rate
24. A combustion chamber in a gas turbine plant receives air at 350K, 0.55 bar and
75 m/s. The air –fuel ratio is 29 and the calorific value of the fuel is
41.87MJ/kg. Taking γ=1.4 and R=0.287 kJ /kg k for the gas determine
i. The initial and final Mach numbers
ii. Final pressure, temperature and velocity of the gas
iii. Percent stagnation pressure loss in the combustion chamber and
iv. The maximum stagnation temperature attainable.
25.Air at p1=3.4 bar ,T1=35°C enters a circular duct at a Mach number of 0.14.the
exit Mach number is 0.6 and co-efficient of friction is 0.004.If the mass flow
rate is 8.2 kg/s, determine
i. Pressure, temperature at the exit
ii. Diameter of the duct
iii. Length of the duct
iv. Stagnation pressure loss
v. Verify the exit Mach number through exit velocity and temperature.

18. 26.The stagnation temperature of air in a combustion chamber is increased to 3.5
times its initial value. If the air at entry is at 5 bar ,105°C and a Mach number of
0.25 determine
i. Mach number, pressure and temperature at the exit
ii. Stagnation pressure loss
iii. the heat supplied per kg of air
27.Air flows with negligible friction in a constant area duct. At section one, the
flow properties are t1=60.4°C,p1=135kpa absolute and velocity 732m/s. Heat is
added to the flow between section one and section two, where the Mach
number is 1.2.Determine the flow properties at section two, the heat transfer
per unit mass and the entropy change.
28.A circular duct passes 8.25kg/s of air at an exit Mach number of 0.5.The entry
pressure and temperature are 345kPa and 311K respectively. The average
friction factor is 0.02 if the Mach number of entry is 0.15 determine,
i. The diameter of the duct
ii. Length of the duct
iii. Pressure and temperature at the exit of the duct and
iv. Stagnation pressure loss
29.A long pipe of 0.0254 m diameter has a mean co-efficient of friction of
0.003.Air enters the pipe at a Mach number of 2.5,stagnation temperature
310K and static pressure 0.507 bar. Determine for a section at which the
Mach number reaches 1.2;
i. Static pressure and temperature
ii. Stagnation pressure and temperature
iii. Velocity of air
iv. Distance of this section from the inlet and
v. Mass flow rate of air.

19. 30.The Mach number at the exit of a combustion chamber is.9.The ratio of
stagnation temperature at exit and entry is 3.74.If the pressure and
temperature of the gas at exit are 2.5 bar and 1273K respectively, determine
i. Mach number, pressure and temperature of the gas at entry
ii. The heat supplied per kg of the gas and
iii. The maximum heat that can be supplied.

20. UNIT – III NORMAL AND OBLIQUE SHOCKS
PART –A
1. How is the shock formed?
A shock wave is nothing but a steep finite pressure wave. The shock wave
may be described as a compression wave front in a supersonic flow across
which there is abrupt change in flow properties.
2. What is normal shock?
When the shock wave is at right angle to the flow, it is called normal shock.
3. What do you understand by ‘oblique shock’?
When the shock is inclined at an angle to the flow, it is called oblique shock.
4. Define “strength of a shockwave”
It is defined as the ratio of difference in downstream and upstream shock
pressures(py - px) to upstream shock pressure(px). It is denoted by ξ
ξ= (py-px) / px
5. What are the applications of moving shock wave?
i. Jet engines
ii. Shock tubes
iii. Supersonic wind tunnel
iv. Practical admission turbines

21. 6. Why expansion shock is impossible?
A shock wave, which is at a lower pressure than the fluid into which it is
moving is called as expansion shock wave or rarefaction shock wave. Once a
wave has traversed the liquid, its pressure and temperature are lowered.
Therefore, the subsequent waves will travel at lower velocities on account of
lower temperature. The wave velocities are further reduced because the fluid
motion is occurring against the direction of wave propagation. As a result of the
cumulative effect of the above phenomena, the waves generated later lag behind
the waves which were generated earlier. Therefore the wave becomes weaker as
it moves further. Hence, expansion (rarefaction) shocks are not possible.
7. Distinguish between Mach wave and normal shock
Mach wave:
The lines at which pressure difference is concentrated and which generate
the cone are called Mach lines or Mach waves.
Normal shock:
A shock wave is nothing but a steep, finite pressure wave. When the shock
wave is right angle to the flow, it is called normal shock.
8. What is Prandtl-Meyer relation?
Prandtl-Meyer relation which is the basis of other equation for shock waves.
It gives the relationships between the gas velocities before and after the normal
shock and the critical velocity of sound.
Mx
*
x My
*
= 1
cx x cy = a*2

22. 9. Shock waves cannot develop in subsonic flow? Why?
In subsonic flow, the velocity of fluid is less than the velocity of sound. Due
to this reason, deceleration is not possible in subsonic flow. So shockwaves
cannot develop in subsonic flow.
10.Define compression and rarefaction shocks? Is the latter possible.
A shock wave which is at a high pressure than the fluid into which it is
moving is called compression wave.
A shock wave which is at a lower pressure than the fluid into which it is
moving is called an expansion shock wave or rarefaction shockwave.
It is not possible.
11.State the necessary conditions for a normal shock to occur in compressible
flow.
The compression wave is to be right angle to the compressible flow.
Flow should be supersonic.
12. Is the flow through a normal shock an equilibrium one?
No, since the fluid properties like pressure, temperature and density are
changed during normal shock.
13.What are the properties changes across a normal shock?
i. Stagnation pressure decreases
ii. Stagnation temperature remains constant
iii. Static temperature and static pressure increases.

23. 14.Give the difference between normal shock and oblique shock?
Normal Shock Oblique Shock
 Shock wave is right angle to the flow.
 One dimensional flow
 Shock wave is inclined at an
angle to the flow
 Two dimensional flow
15.What do you understand by strong and weak wave?
Strong Waves:
Since shock strength is proportional to (Mx
2
-1), strong waves are a result of
very high values of the upstream Mach number. A very strong shock is one for
which p2/p1 is very large.
Weak waves: Mach waves are weak waves. A weak shock is that for which
normalized pressure jump is very small.
i.e
∆p/p1 = ((p2-p1) /p1) << 1
16.What are the situations where shocks are undesirable?
In some situations shocks are undesirable because they interfere with the
normal flow behavior. Thus the efficiencies of turbo machine experiencing
shock waves are considerably low.
Other undesirable forms of the shock waves are the sonic boom created by
supersonic aircraft and the blast waves generated by an explosion. These waves
have a damaging effect on human life and buildings.

24. 17.What are the beneficial and adverse effects of shockwaves?
Beneficial Effects:
 A strong wave is utilized to accelerate the flow to a high mach number in a
shock tube.
 On account of the abrupt changes of pressure, density, etc., across the shock
waves, they are profitably used in supersonic compressor to obtain
considerably high pressure ratio in one stage.
Adverse effects:
 Shock waves cause undesirable interference with normal flow behavior.
Therefore, the efficiency of turbo machineries decreases.
 Shockwaves create sonic flows in supersonic aircraft and damage the flow
passage.
18.Show the normal shock in h-s diagram with the help of Rayleigh line and Fanno
line.

25. 19.Calculate the strength of shock wave when normal shock appears at M=2.
ξ= (py-px) / px
ξ= (py/px) -1
Refer Normal shocks table for Mx=2 and γ=1.4
py/px =4.5 [From gas table ]
ξ= 3.5
20.What is meant by normal shock as applied to compressible flow?
Compression wave front being normal to the direction of compressible fluid
flow. It occurs when the flow is decelerating from supersonic flow. The fluid
properties jump across the normal shock.
PART – B
21.Derive the equation for Mach number in the downstream of the normal
shockwave.
22.The velocity of a normal shockwave moving into stagnant air (p=1 bar, t=17°C)
is 500 m/s. If the area of cross section of the duct is constant, determine
pressure, temperature, velocity of air, stagnation temperature, and Mach number
imparted upstream of the wave front.
23.Air approaches a symmetrical wedge (angle of deflection δ=15°) at a Mach
number of 2.Consider strong waves conditions. Determine the wave angle,
pressure ratio, density ratio, temperature ratio and downstream Mach number.
24.Derive the equation for static pressure ratio across the shock waves.
25.The ratio of the exit to entry area in a subsonic diffuser is 4.0.The Mach number
of a jet of air approaching the diffuser at p0=1.013 bar, T=290K is 2.2.There is a
standing normal shock wave just outside the diffuser entry. The flow in the
diffuser is isentropic. Determine at the exit of the diffuser.

26. i. Mach number
ii. Temperature
iii. Pressure
iv. What is the stagnation pressure loss between the initial and final stages of
the flow?
26.A gas (γ=1.3) at p1=345 mbar, T1=350K and M1=1.5 is to be isentropically
expanded to 138 mbar. Determine
i. Deflection angle
ii. Final Mach number
iii. The temperature of the gas
27.A supersonic nozzle is provided with a constant diameter circular duct at its
exit. The duct diameter is same as the nozzle exit diameter. Nozzle exit cross
section is three times that of its throat. The entry conditions of the gas
(γ=1.4,R=0.287kJ/kg-K)are P0=10 bar,T0=600K.Calculate the static pressure,
Mach number and the velocity of the gas in the duct:
(i) when the nozzle operates at its design condition
(ii)when a normal shock occurs at its exit
28.The ratio of the exit to entry area in a subsonic diffuser is 4.0.the Mach number
of a jet of air approaching the diffuser at P0=1.013bar, T=290K is 2.2.There is a
standing normal shock wave just outside the diffuser entry. The flow in the
diffuser is isentropic. Determine at the exit of the diffuser.
i. Mach number
ii. Temperature
iii. Pressure
iv. The stagnation pressure loss between the initial and final states of the
flow.
29.A converging –diverging nozzle has an exit area to throat area ratio of 2.Air
enters this nozzle with a stagnation pressure of 1000kPa and a stagnation
temperature of 360K.The throat area is 500mm2
.The divergent section of the
nozzle acts as a supersonic nozzle. Assume that a normal shock stands at a point
M=1.5.Determine the exit plane of the nozzle ,the static pressure and
temperature and Mach number.

27. 30.A convergent divergent nozzle operates at off design condition while
conducting air from a high pressure tank to a large container. A normal shock
occurs in the divergent part of the nozzle at a section where the cross section
area is 18.75 cm2
.The stagnation pressure and stagnation temperature at the
inlet of the nozzle are 0.21 Mpa and 36°C respectively. The throat area is
12.5cm2
and the exit area is 25cm2
.Estimate the exit Mach number, exit
pressure, Loss in stagnation pressure and entropy increase during the flow
between the tanks.

28. UNIT IV JET PROPULSION
PART – A
1. What is thrust or drag?
The force which propels the aircraft towards at a given speed is called
as thrust or propulsive force. This thrust mainly depends on the velocity of
gases at the exit of the nozzle.
2. Define effective speed ratio
The ratio of flight speed to jet velocity is known as effective speed
ratio.
σ = u / cj
3. Define specific thrust and Specific impulse.
The thrust developed per unit mass flow rate is known as specific thrust (Fsp)
Fsp = F/m
The thrust developed per unit weight flow rate is known as specific impulse.
Isp = F/W
= F/ (m x g)
4. Define propulsive efficiency
It is defined as the ratio of propulsive power or thrust power to the power
output of the engine.
ηp = Propulsive power / Power output

29. 5. Define thermal efficiency and overall efficiency
Thermal Efficiency :
It is the ratio of power output of the engine to the power input to the
engine through fuel.
η t = Power output of the engine / Power input to the engine
Overall Efficiency:
It is defined as the ratio of propulsive power to the power input to the
engine.
η o= Propulsive power or Thrust power / Power input to the engine
6. Give the expression for the thrust developed by a turbojet engine.
Thrust F = mcj – mau
Where m = mass of air-fuel mixture - kg/s
Cj = velocity of jet - m/s
ma = mass of air - kg/s
u = velocity of aircraft or flight speed - m/s
7. Define Thrust power or Propulsive power
Thrust power is the product of thrust and flight speed.
Thrust power (P) = Thrust (F) x Flight speed (u)
P = F x u
8. Find the ratio of jet speed to flight speed for optimum propulsive efficiency.
Propulsive efficiency η p = 2σ / (1+σ2
)
At optimum η p = 1
1 = 2σ / (1+σ2
)
1+σ2
= 2σ

30. 1+σ2
-2σ= 0
(1-σ) 2
= 0
σ=1
u / cj=1
u = cj
Where
u - Flight speed - m/s
cj - Jet speed - m/s
9. What are the main parts of Ramjet engine?
i. Supersonic diffuser
ii. Subsonic diffuser
iii. Combustion chamber
iv. Discharge nozzle
10.What are the various types of air breathing engine?
i. Ramjet engine
ii. Pulsejet engine
iii. Turbojet engine
iv. Turboprop engine
v. Turbofan engine
11. What is ram effect?
In ram jet engine the subsonic and supersonic diffusers are used to convert
the kinetic energy of the entering air into pressure energy. This energy
transformation is called the Ram effect and the pressure rise is called the Ram
pressure.

31. 12.What is the type of compressor used in turbojet? Why?
Rotary compressor is used in turbojet engine due to its high thrust and high
efficiency.
13.What is after burning in turbojet engines?
Large quantity of oxygen is available in the exhaust gas which can
support the combustion of additional fuel. When the thrust of the engine is
desired to be increased without changing the physical dimensions of the
compressor, turbine etc ., additional quantity of fuel can be burnt in a section
of the jet pipe to increase the velocity of the jet. This process is called
reheating or after burning.
14.Give the difference between Ramjet and turbojet engine.
Ramjet Engine Turbojet Engine
 Compressor and turbine are not used
 Take off thrust is zero
 Light Weight
 Cost is low
 Compressor and turbine are used
 Low Takeoff thrust
 Weight is heavy compared to Ramjet
engine.
 Cost is high
15.What is turboprop unit?
Turboprop engine is very similar to turbojet engine. In this type, a turbine
which is used to drive the compressor and propeller.

32. 16.What is the difference between turboprop and turbojet engine
Turbojet Engine Turboprop Engine
 Power produced by the turbine is
used to drive the compressor
 Low Takeoff thrust
 Low Propulsive efficiency
 Less space is needed compared to
turboprop engine.
 Reduction gear is not needed
 Power produced by the turbine is used
to drive the compressor and propeller.
 High Takeoff thrust
 Propulsive efficiency is good.
 More space is needed
 Reduction gear needed
17.Give the difference between ramjet and pulsejet
Ramjet Engine Pulsejet Engine
 Take off thrust is zero
 There is no upper limit to the flight speed
 The specific fuel consumption is better than
the other gas turbine power at high speed
 It develops thrust at zero speed
 Flight speed is limited to 750km/hr
 High rates of fuel consumption.
18.What is thrust augmentation? Mention any two methods of achieving it
To achieve better take-off performance, additional fuel is burnt in the
tail pipe between the turbine exhaust section and entrance section of the exhaust
nozzle. This method of thrust augmentation increases the jet velocity and is
known as after burning. It is used for fast and easier take off.
i. Momentum thrust
ii. Pressure thrust

33. 19.What are the benefits of thrust augmentation in a turbojet engine?
Short take-off distance
High climb rate to very high altitude
20.Why ramjet engine does not require a compressor and a turbine?
In ramjet engine due to supersonic and subsonic diffuser, the static pressure
of air is increased to ignition pressure. So there is no need of compressor and
turbine.
21.What is scramjet?
A supersonic combustion ramjet engine is known as scramjet. In scramjet,
the flow enters the combustor at supersonic velocity and comparatively lower
temperature. The static pressure is high enough to provide the required
expansion in the nozzle.
22.How is turbofan engine different from turbo prop engine?
Turbo Prop Engine Turbofan Engine
 Relatively low flight speed
 Bypass ratio is high
 Gear arrangement is necessary to reduce the
engine speed
 The total thrust produced in this engine is the
sum of the thrust produced by the propeller
and the thrust produced by the nozzle.
 High flight speed compared to turbo
prop engine
 Bypass ratio is low
 Gear arrangement is not necessary
 The total thrust produced in this engine
is the sum of the thrust produced by the
primary air and secondary air.

34. PART –B
23.Differentiate turbojet and turboprop propulsion engines with suitable
diagrams.
24.Write the equations to calculate propulsive efficiency and thermal efficiency
of an aircraft.
25.A turbojet engine operating at a Mach number of 0.8 and the altitude is
10km has the following data. Calorific value of the fuel is 42,800kJ/kg.
Thrust force is 50kN, mass flow rate of air is 45kg/s, mass flow rate of fuel
is 2.65kg/s. Determine the specific thrust, thrust specific fuel consumption,
jet velocity, thermal efficiency, propulsive efficiency and overall efficiency.
Assuming the exit pressure is equal to ambient pressure.
26.Explain the principles of operation of a turbojet engine and state its
advantages and disadvantages.
27.A turbojet aircraft flies at 875kmph at an attitude of 10,000 m above mean
sea level. Calculate
i. Air flow rate through the engine
ii. Thrust
iii. Specific thrust
iv. Specific impulse
v. Thrust power
vi. TSFC from the following data
Diameter of the air at inlet section =0.75m
Diameter of jet pipe at exit =0.5m
Velocity of the gases at the exit of the jet pipe=500 m/s
Pressure at the exit of the jet pipe =0.30 bar
Air to fuel ratio =40
28.Explain with neat sketch the principles of operation of a ramjet engine and
state its advantages and disadvantages.

35. 29.A turbojet propels an aircraft at a speed of 900km/hr, while taking 3000kg
of air per minute. The isentropic enthalpy drop in the nozzle is200kJ/kg and
the nozzle efficiency is 90%.The air-fuel ratio is 85 and the combustion
efficiency is 95%.The calorific value of the fuel is 42,000kJ/kg. Calculate
i. The propulsive power
ii. Thrust power
iii. Thermal efficiency
iv. Propulsive efficiency
30.Draw the sketch of a pulse jet engine .Write down its main advantages and
disadvantages.
31.The diameter of the propeller of an aircraft is 2.5m; it flies at a speed of
500km/hr at an altitude of 8000m. For a flight to jet speed ratio of 0.75,
determine the flow rate of air through the propeller, Thrust produced,
Specific thrust, Specific impulse and Thrust power.

36. UNIT V SPACE PROPULSION
PART – A
1. What is the difference between Jet propulsion and Rocket Propulsion?
Jet propulsion Rocket Propulsion
 Combustion takes place by using
atmospheric air
 Altitude limitation
 Flight speed is always less than jet
velocity
 Reasonable efficiency
 Thrust decreases with altitude
 Combustion takes place by using its
own oxygen supply
 No altitude limitation
 Flight speed can be greater than jet
velocity
 Low efficiency except at extremely
high flight speed
 Thrust improves slightly with altitude.
2. What are the types of liquid propellant used in rocket engines?
 Mono propellant
 Bi propellant
3. What is monopropellant? Give examples for it.
A liquid propellant which contains both the fuel and oxidizer in a single
chemical is known as a monopropellant. It is stable at normal ambient
conditions and liberate thermo-chemical energy on heating.
e.g Nitroglycerine

37. Nitromethane
4. What is meant by hypergolic propellant?
Hypergolic propellant do not require ignition.
5. What is by bi propellant?
If the fuel and oxidizer are different from each other in its chemical nature,
then the propellant is called bipropellant.
e.g Liquid oxygen - Gasoline
Hydrogen peroxide - Hydrazine
6. Give examples of liquid and solid propellants
Liquid Fuels: Liquid hydrogen, UDMH, hydrazine
Solid Fuels: Polymers, Plastics and resin material
7. Compare solid and liquid propellant rockets
Solid Propellant Liquid Propellant
 Solid fuels and oxidizers are used
 Generally stored in combustion
chamber(both oxidizer and fuel)
 Burning in the combustion chamber is
uncontrolled rate
 Liquid fuels and oxidizers are used
 Separate oxidizer and fuel tanks are
used for storing purpose.
 Burning in the combustion chamber is
controlled rate

38. 8. Mention any four applications of rocket
 Military
 Space
 Aircraft
 Communication
9. What are the types of rocket engines?
On the basis of source energy employed
i. Chemical Rocket engines
ii. Solar Rockets engines
iii. Nuclear Rockets engines
iv. Electrical Rockets engines
On the basis of propellant used
i. Liquid Propellant
ii. Solid Propellant
iii. Hybrid Propellant
10.What is bypass engine and define bypass ratio?
Bypass Engine:
Turbofan engines are usually described as bypass engine. In this type of
engine a portion of the total flow of air bypasses part of the compressor.
Bypass Ratio

39. The ratio of the mass flow rates of cold air (mc) and the hot air (mh) is
known as Bypass ratio.
11.What is rocket propulsion? Why a rocket is called a non-breathing engine?
In rocket engine, the thrust required for the propulsion of the rocket is
produced by the high velocity of gases from the nozzle which is similar to jet
propulsion.
In air breathing engines, combustion takes place by using atmospheric air.
But in rocket engines, combustion takes place by using its own oxygen supply.
So it is called as non-air breathing engines.
12.Give the important requirements of rocket engine fuels.
 It must be able to produce a high chamber temperature. It should have a
high calorific value per unit of propellant.
 It should not chemically react with motor system including tanks, piping,
valves and injection nozzles.
13.What is meant by restricted burning in rockets?
 In this case, the inhibition material or restrictions prevent the propellant
grain from all directions.
 The propellant grain burns only at some surfaces while other surfaces are
prevented from burning.
14.What is terminal velocity?
The terminal velocity of an object falling towards the earth is the velocity at
which the gravitational force pulling it downwards is equal and opposite to
the air resistance –pushing it upwards.

40. 15.Name some propellants for space applications.
 Nitroglycerine
 Nitro methane
 Hydrazine
 Hydrogen peroxide
16.Name few advantages of liquid propellant over solid propellant rockets.
 Increase or decrease of speed possible when it is in operation
 Liquid propellant can be reused or recharged. Hence it is economical
 Storing and transportation is easy as the fuel and oxidizer are kept
separately.
 Specific impulse is very high.
17.What are the advantages and disadvantages of solid propellant rockets over
liquid propellant rockets?
Advantages:
 Less maintenance
 Less vibration due to absence of moving parts
 They do not require feed systems
Disadvantages:
 In case of emergency it is not possible to stop the engine in the midway.

41.  Decrease of speed is not possible
 It is uneconomical
18.Define specific propellant consumption ,thrust coefficient
Specific Propellant Consumption:
The propellant consumption rate per unit thrust is known as specific
propellant consumption
SPC = Wp / F
Thrust coefficient:
Thrust coefficient is the ratio of thrust to thrust force.
CF = F / p0A*
19.Define propulsive efficiency, thermal efficiency and overall efficiency
Propulsive efficiency ηP = Propulsive power / Power output of the engine
Thermal efficiency ηt = Power output of the engine / Power input of the engine
Overall efficiency ηo= Propulsive power / Power input of the engine
20.Define relative mass of a rocket.
It is defined as the ratio between final mass of rocket after burnout and total
mass of rocket at take-off.
Final mass of rocket after burn out (mf)
MR = ---------------------------------------------------
Total mass of rocket at take off (mt).

42. 21.Define propellant mass fraction(ε)
It is defined as the ratio of propellant mass at take off to the total mass of
rocket at take-off.
Propellant mass at take-off (mp)
ε = ------------------------------------------------
Total mass of rocket at take-off (mt).
PART – B
22.A rocket engine has the following data. Combustion chamber pressure is 38 bar,
combustion chamber temperature is 3500K,oxidizer flow rate is 41.67kg/s,
mixture ratio is 5,and the properties of exhaust gases are Cp/Cv =1.3 and
R=0.287 kJ/kgK. The expansion takes place to the ambient pressure of 0.0582
bar. Calculate the nozzle throat area, thrust, thrust coefficient, exit velocity of
the exhaust, and maximum possible exhaust velocity.
23.Explain briefly about the propellant feed system of a liquid propellant rocket
engine with suitable schematic sketches.
24.A rocket has the following data: Propellant flow rate=5kg/s, nozzle exit
diameter =10cm, nozzle exit pressure=1.02bar, ambient pressure = 1.013bar,
thrust chamber pressure=20bar, thrust=7kN.Detrmine the effective jet velocity,
actual jet velocity, specific impulse and the specific propellant consumption.
Recalculate the values of thrust and specific impulse for an altitude where the
ambient pressure is 10mbar.
25.Explain with a neat sketch the working of a gas pressure feed system used in
liquid propellant rocket engines.
26.Describe the important properties of liquid and solid propellants desired for
rocket propulsion.
27.Explain the working of turbo pump feed system used in a liquid propellant
rocket.

43. 28.Deduce the expression for propulsive efficiency ,specific impulse and overall
efficiency of a rocket engine
29.Derive the thrust equation for rocket engines
30.The effective jet velocity from a rocket is 2700m/s. The forward flight velocity
is 1350m/s and the propellant consumption is 78.6kg/s. Calculate Thrust, Thrust
power and propulsive efficiency.
31.Calculate the thrust specific impulse, propulsive efficiency ,thermal and overall
efficiencies of a rocket engine from the following data :
Effective jet velocity=1250m/s
Flight to jet speed ratio=0.8
Oxidizer flow rate =3.5 kg/s
Fuel flow rate =1 kg/s.
Heat of reaction of exhaust gases=2500kJ/kg.