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Chapter: Mechanical : Gas Dynamics and Jet Propulsion : Flow Through Ducts

Important Questions and answers: Gas Dynamics and Jet Propulsion


1.What is the basic difference between compressible and incompressible fluid flow?


1.       Fluid velocities are appreciable compared  with  the  velocity  of sound

2.       Density is not constant

3.       Compressibility factor is greater than one.



1.       Fluidvelocitiesaresmall compared  with  the  velocity  of sound

2.       Density is constant

3.       Compressibility factor is one.

2. Write the steady flow energy equation for an adiabatic flow of air.


In an adiabatic flow q = 0.  Therefore energy equation becomes.

3. Define the mach number in terms of bulk modulus of elasticity.


Mach number is a non-dimensional number and is used for the analysis of compressible fluid flows.

4. Explain the meaning of stagnation state with example.


The state of a fluid attained by isentropically decelerating it to zero velocity at zero elevation is referred as stagnation state.


(e.g.) Fluid in a reservoir (or) in a settling chamber.


5. Distinguish between static and stagnation pressures.


In stagnation pressure state, the velocity of the flowing fluid is zero whereas in the static pressure state, the fluid velocity is not equal to zero.


6. Differentiate between the static and stagnation temperatures.

The actual temperature of the fluid in a particular state is known as “static temperature”whereas the temperature of the fluid when the fluid velocity is zero at zero elevation is known as “stagnation temperature”.

7. What is the use of mach number?

 Mach number is defined as the ratio between the local fluid velocity to the velocity of  sound. 

i.e. Mach number

M =   Local fluid velocity /  Velocity of sound = c/ a

It is used for the analysis of compressible fluid flow problems. Critical mach number is a dimensionless number at which the fluid velocity is equal to its sound velocity. Therefore,

Crocco number is a non – dimensional fluid velocity which is defined as the ratio of


fluid velocity to its maximum fluid velocity.

8. Write down the relationship between stagnation and static temperature interms of the flow, mach number for the case of isentropic flow.

T0= stagnation temperature

T= Static temperature

M= Mach number.

9.Give the expression of  p/P0  for an isentropic flow through a duct.

The expression of


10. Name the four reference velocities that are used in expressing the fluid velocities in


non-dimensional form?


11.            What are the different regions of compressible flow.

The adiabatic energy equation for a perfect gas is derived in terms of fluid velocity © and sound velocity (a). This is then plotted graphically on the c- a co-ordinates, a steady flow ellipse is obtained.

The various regions of flow are:


i.Incompressible region (M  0)

(ii)              Subsonic region     (M < 1)

(iii)             Transonic region   (0.8 – 1.2)

(iv)             Supersonic region  (M > 1 and M < 5)

(v)              Hypersonic region (M ≥ 5)


12.  Define  M*  and  give  the  relation  between  M


and M*.


It is a non-dimensional mach number and is defined by the ratio between the local fluid velocity to its critical velocity of sound / fluid.


13.  If  an  aeroplane  goes  to  higher  altitudes  maintaining  the  same  speed,  the  Mach


number will remain constant.  Say true or false.



W.K.T. M = c/a

At higher altitude, the sound velocity ‘a’ will decrease and hence M will increase. Therefore, M is not constant.


14.  Show  h  –  S  diagram  for  the  flow  through  a  nozzle.   Show  how  the  stagnation


properties get affected.

1 – 2’ = Isentropic expansion


1 – 2 = Adiabatic expansion

It is assumed that, the exit pressure is same for both  cases.   But  stagnation  pressure  at  the  exit of the adiabatic  process   (P02  ) will be  less than  isentropic pressure (P02  ' ) . This   is due   to friction   and irresversibilities.  But stagnation temperature remains constant.


15. A plane travels at a speed of 2400 KM/h in an atmosphere of 5°C, find the mach angle.


16.Define mach angle and mach wedge.

Mach angle is formed, when an object is moving with supersonic speed. The wave propagation and changes are smooth. When an object is moving with hypersonic speed the changes are abrupt is shown in Fig. Hence for a supersonic flow over two – dimensional object “mach wedge” is used instead of “mach cone”.

17. How will you illustrate the role of mach number as a measure of compressibility?

If the flow is assumed to be incompressible, the value of pressure co-efficient (or) compressibility factor obtained by Bernoulli equation is unity.

By substituting different values of M, we can get different values of compressibility factor and is given in the table.


In the above table, when M increases, the compressibility factor also increases from the initial value 1. Thus the role of mach number is a measure of compressibility.


18. What is meant by isentropic flow with variable area?


A steady one dimensional isentropic flow in a variable area passages is called “variable area flow”. The heat transfer is negligible and there are no other irreversibilities due to fluid friction, etc.


19.            Define zone of action and zone of silence with neat sketch.


20.Find the sonic velocity in oxygen when it is at 110° C, γ=1.4 and molecular weight 32.

21. Give the expression for  T0 /T   and   T / T * for isentropic flow  through variable area in terms of Mach number.


Sketch the isentropic and adiabatic expansion process in P-V and T-S diagram}.

23. Represent the adiabatic flow through a diffuser on T-S diagram. Label the different states, the initial and final points.

24. Air from a reservoir is discharged through a nozzle. Show the variation of pressure along the axis of the nozzle.

25. What will happen if the air flowing through a nozzle is heated?

When the flowing air is heated in a nozzle, the following changes will occur.


Velocity of air will increase.

Increase in temperature and enthalpy


Pressure increases


Increase in entropy


26. Write the Fliegner’s formula.

Write the equation for efficiency of the diffuser.

Diffuser efficiency  = static pressure rise in the actual process /static pressure rise in the ideal process

28. What is impulse function and give its uses?


Impulse function is defined as the sum of pressure force and intertia force. Impulse function F = Pressure force ρA + intertia force ρAc2


Since the unit of both the quantities are same as unit of force, it is very convenient for solving jet propulsion problems. The thrust exerted by the flowing fluid between two sections can be obtained by using change in impulse function.


29. What is chocked flow?  State the necessary conditions for this flow to occur in a




When the back pressure is reduced in a nozzle, the mass flow rate will increase. The maximum mass flow conditions are reached when the back pressure is equal to the critical pressure. When the back pressure is reduced further, the mass flow rate will not change and is constant. The condition of flow is called “chocked flow”. The necessary conditions for this flow to occur in a nozzle is


* The nozzle exit pressure ratio must be equal to the critical pressure ratio where the mach number M = 1.

30. Draw the variation of  P /P0 along the length of a convergent divergent device when it functions as (a) diffuser, (b) nozzle and (c) venturi.



a, b, c venture


d, e diffuser


g nozzle


31. Give the expression for nozzle efficiency and diffuser efficiency with h – s diagram.

32. Give the important difference between nozzle and venturi.


1. The flow is accelerated continuously  i.e.,   Mach   number   and   velocity  increases continuously.

2. Used  to  increase  velocity and Mach  number.

3. Generally convergent portion is short.



1. The flow is accelerated upto M = 1 and then Mach number is decreased.

2. Used for flow measurement  (discharge) 

3. Convergent and  divergent  portions  are equal.

33. What is the normal shock?


When the shock waves are right angles to the direction of flow and the rise in pressure is abrupt are called normal shock waves.


34. 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.


35. Shock waves cannot develop in subsonic flow?  State the reason.


Shocks are introduced to increase the pressure and hence it is a deceleration process. Therefore, shocks are possible only when the fluid velocity is maximum. In a subsonic flow, the velocity of fluid is less then the critical velocity and hence deceleration is not possible. Thus, shock waves cannot develop in subsonic flow.


36. Define strength of a shock wave.


Strength of a shock wave is defined as the ratio of increase in static pressure across the shock to the inlet static pressure.

Strength of shock = p y  p x / p x


36.        Calculate the strength of shock wave when normal shock appears at M = 2.


From normal shock table M = 2, γ = 1.4. p y/Px = 4.5

Strength of shock =  p y /px  1 = 4.5 1 = 3.5


38. Define oblique shock where it occurs.


The shock wave which is inclined at an angle to the two dimensional flow direction is called as oblique shock. When the flow is supersonic, the oblique shock occurs at the corner due to the turning of supersonic flow.


39. Give the difference between normal and oblique shock.


(a)   The shock waves are right angles to the direction of flow.

(b)   May be treated as one dimensional analysis.


(a) The shock waves are inclined at an angle to the direction of flow.

(b) Oblique  shock  is  two  dimensional analysis.

40. What is Prandtl-Meyer relation?  What its significance?


The fundamental relation between gas velocities before and after the normal shock and the critical velocity of sound is known as Prandtl-Meyer relation.


i.e., (i) cx x cy = a*2 and (ii) M*x x M* y = 1


it signifies the velocities (before and after the shock) with the critical velocity of sound and the product of mach numbers before and after the shock is unity.


41. Shown a normal shock in h-s diagram with the help of Rayleigh line and Fanno line.

42. Define the term “Fanno flow”.


A steady one-dimensional flow in a constant area duct with friction in the absence of work and heat transfer is known as “fanno flow”.

43. Define Fanno line.


The locus of the state which satisfy the continuity and energy equation for a frictional


flow is known as “fanno line”.


44. Give fanno line in h – s diagram with isentropic stagnation line and show various


mach number regions.

The equation which yields the fanno line for the given values of h0 and G is called “fanno flow equation”.

45. Explain briefly the chocking in fanno flow.


In a fanno line, any heating process (both subsonic and supersonic) will increase the enthalpy, entropy and mass flow rate. This will go upto the limiting state where mach number M* = 1. Further heating is not possible, because the entropy change will be negative which violates the second law of thermodynamics. Hence the mass flow rate is maximum at the critical state and is constant afterwards, then the flow is said to be “chocked flow”.

46. Give two practical examples where the fanno flow occurs.


Flow occurs in gas ducts of aircraft propulsion engines, flow in air-conditioning ducts


and flow of oil in long pipes. etc.


47.Give the effect of increasing the flow length after reaching critical condition in a fanno flow.


The mass flow rate will increase only upto the critical condition and is constant afterwards. Therefore, if the length of pipe is increased afterwards will not give any effect.


48.Write down the expression for the length of duct in terms of the two mach numbers M1 and M2 for a flow through a constant area duct with the influence of friction.

49. Define isothermal flow with friction.  Give the applications.


A steady one dimensional flow with friction and heat transfer in a constant area duct is called isothermal flow with friction. Such a flow occurs in long ducts where sufficient time is available for the heat transfer to occur and therefore the temperature may remains constant. Hence the friction factor may be assumed constant along the duct. The applications of isothermal flow are oil or water flow in buried pipe.


50.            State assumptions made to derive the equations for isothermal flow.


i.           One dimensional flow with friction and heat transfer.


ii.           Constant area duct


iii.          Perfect gas with constant specific heats and molecular weights


iv.          Isothermal flow i.e., the temperature is constant


v.          On account of constant temperature the friction factor may be assumed constant along the duct.


Differentiate between isothermal flow and fanno flow.


a) Static temperature is constant

b) With heat transfer.

c) Flow  occurs  in  a  long  ducts  where  sufficient  time  is  required  for  heat  transfer.

d) On account of  constant temperature,  the  friction  factor  is  assumed  as  constant.



a) Static temperature  is not  constant

b) Without heat transfer.

c) Long ducts    are not  required.

d) Friction factor is constant.

52. Define the term “Rayleigh flow”.


The  one-dimensional flow in a  constant  area duct  with heat  transfer and without


friction is called “Rayleigh flow”.


55. Define Rayleigh line.


The locus of the points of properties during a constant area frictionless flow with heat exchange is called “Rayleigh line”.


54. What is diabatic flow?


It is the flow which deals with the exchange of heat from the system in the absence of friction (Rayleigh flow).


55.        Give the assumptions made in Rayleigh flow.


i.           Perfect gas with constant specific heats and molecular weight.


ii.          Constant area duct,


iii.          One dimensional, steady frictionless flow with heat transfer.


iv.         Absence of body forces.


56.        What do you understand by chocking in Rayleigh flow.


When the fluid is heated in a subsonic region, the entropy increases and the mach number and fluid properties move to the right unitil the maximum entropy is reached where M* = 1. When the fluid is heated in a supersonic region, the entropy increases and the mach number and the fluid properties move to the right until the maximum entropy is reached where M* = 1. Further heating is not possible because, if it is heated the change in entropy is negative which violates the second law of thermodynamics. Therefore, the type of flow when the limiting condition M* = 1 is called “chocked flow”.


57. Differentiate between Fanno flow and Rayleigh flow.


a)  One   dimensional   steady   frictional flow.

b)  Stagnation temperature is constant.

c)  Because   of   considering   the   wall friction forces it is accurate.

d)  Without heat transfer.



a) One  dimensional  steady  frictionless  flow.

b) Stagnation temperature is not constant

c) Less accurate.

d) With heat transfer.

58. What is meant by a jet propulsion system?


It is the propulsion of a jet aircraft (or)other missiles by the reaction of jet coming out with high velocity. The jet propulsion in used when the oxygen is obtained from the surrounding atmosphere.

59.            How will you classify propulsive engines?


The jet propulsion engines are classified into


i.                  Air breathing engines and


ii.               Rocket engines which do not use atmospheric air.


60.What is the difference between shaft propulsion and jet propulsion?


a) The   power   to   the   propeller   is  transmitted through a reduction gear

b) At higher altitude, the performance is  poor.   Hence it is suitable for lower  altitudes.

c) With increasing speeds and size of the  aircrafts, the shaft propulsion engine  becomes too complicated.

d) Propulsive efficiency is less.



a) There is no reduction gear.

b) Suitable for higher  altitudes. 

c) Construction is simpler.

d) More.

61.            List the different types of jet engines.


i.          Turbo-jet


ii.          Turpo-prop engine,


iii.         Ram jet engine,


iv.         Pulse jet engines.


62.            Define the principle of Ram jet engine.


The principle of jet engine is obtained from the application of Newton’s law of motion. We know that when a fluid is accelerated, a force is required to produce this acceleration is the fluid and at the same time, there is an equal and opposite reaction force of the fluid on the engine is known as the thrust, and therefore the principle of jet propulsion is based on the reaction principle.


63.            Give the components of a turbo jet.


i.          Diffuser


ii.          Mechanical compressor,


iii.         Combustion chamber,


iv.         Turbine and


v.            Exhaust nozzle.


64. Give the difference between pulse jet and ram jet engine.


a) Mechanical  valve  arrangements  are used during combustion.

b) The stagnation temperature at the  diffuser exit is comparatively less.



a) Works  without  the  aid  of  any  mechanical device and needs no  moving parts.

b) Since the mach number in Ram  jet  engine  is  supersonic,  the  stagnation  temperature  is  very  high.


65. Give the difference between turbojet and ram jet engine.


a) Compressor  and  turbine  are  used.

b) Lower  thrust  and  propulsive  efficiency at lower speeds.

c) Construction cost is more.



a) Compressor  and  turbine  are  not  used  but  diffuser  and  nozzle  are  used.

b) It  provides  high  thrust  per  unit  weight.

c) In    theabsenceof    rotating  machines,   the   construction   is  simple and cheap.


66. What is specific impulse?


Specific impulse is the thrust developed per unit weight flow rate through the propulsive device. It is a useful performance parameter in aerospace propulsion systems.

 Ispc= F/W


67.Give the difference between Jet propulsion and Rocket propulsion.



a)  Oxygen   is   obtained   from   the surrounding atmosphere for combustion purposes.

b)  The   jet   consists   of   air   plus combustion products.

c)  Mechanical devices are also used.



a) The  propulsion  unit  consists  of  its   own   oxygen   supply   for  combustion purposes.

b) Jet consists of the exhaust gases  only.

c)  Mechanical devices are not used.


68. What is the difference between turbo prop engine and turbo jet engine.


a)  The   specific   fuel   consumption based on thrust is low.

b)  Propulsive   efficiency  within  the range of operation is higher.

c)  On account of higher thrust at low speeds the take-off role is short and requiring shorter runway.

d)  Use   of   centrifugal   compressor stages increases the frontal area.

e)  Higher weight per unit thrust.



a) TSFC is comparatively higher at  lower speeds and altitudes.

b) Propulsive efficiency is low.

c) Take  –  off  role  is  longer  and  requiring longer run way.

d) Lower Frontal area. 

e) Lower weight per unit thrust.


69. Write the formula for propulsive efficiency and define the same.


The force which propels the aircraft forward at a given speed is called thrust (or)


propulsive force.


Propulsive efficiency is defined as the ratio between propulsive power (or) thrust power to the power output of the engine.

Effective speed ratio (or) flight to jet velocity


70. What is ram effect?


When an aircraft flies with high velocity, the incoming air is compressed to high pressure without external work at the expense of velocity energy is known as “ram effect”.


71. Explain specific thrust as applied to jet engines.


Specific thrust is defined as the thrust produced per unit mass flow rate through the propulsive device.

Fspec = F/m where, F = thrust and  m = mass flow rate

72. Differentiate between pressure thrust and momentum thrust.


Pressure thrust is mainly depends on the difference in pressure between the nozzle


exit pressure and the ambient pressure and is given by


Pressure thrust = (Pe – Pa) A


Momentum thrust depends on the difference in velocity between the aircraft velocity


and jet velocity is given by


Momentum thrust = m (cj – u) where,


Pe     = nozzle exit pressure


Pa     = ambient pressure


A                = Area of cross section at the nozzle exit


Cj     = jet velocity and


u                  = forward speed of aircraft


73.            What is “thrust augmentation”?


To achieve better take-off performance, higher rates of climb and increased performance at altitude during combat maneuvers, there has been a demand for increasing the thrust output of aircraft for short intervals of time. This is achieved by during additional fuel in the tail pipe between the turbine exhaust and entrance section of the exhaust nozzle. This method of thrust increases the jet velocity is called “Thrust Augmentation”.


74. Why after burners are used in turbojet engine?


Exhaust gases from the turbine have large quantity of oxygen, which can support the combustion of additional fuel. Thus if a suitable burner is installed between the turbine and exhaust nozzle, a considerable amount of fuel can be burned in this section to produce temperatures entering the nozzle as high as 1900°C. The increased temperature greatly augments the exhaust gas velocity, and hence provides the thrust increase.


75. Why a ram jet engine does not require a compressor and a turbine?


In general, the speed of a ram jet engine is supersonic (the range of Mach number) is very high. At this flight speed the contribution of the compressor to the total static pressure rise is insignificant. Hence, arm jet engine does not require compressor and turbine.


76. Define Rocket propulsion.


If the propulsion unit contains its own oxygen supply for combustion purposes, the system is known as “Rocket propulsion”.

77. Define thrust for a rocket engine and how it is produced.

The force that propels the rocket at a given velocity is known as thrust. This is produced due to the change in momentum flux of the outgoing gases as well as the difference between the nozzle exit pressure and the ambient pressure.


78. What are the types of rocket engines?


Rocket engines are classified in the following manner.


a)    On the basis of source of energy employed


i.     Chemical rockets,


ii.    Solar rockets


iii.    Nuclear rockets and


iv.    Electrical rockets


b)   On the basis of propellants used


i.     Liquid propellant


ii.    Solid propellant


iii.    Hybrid propellant rockets.


Compare solid and liquid propellant rockets.


a)  Solid fuels and oxidizers are used in rocket engines

b)  Generally  stored  in  combustion chamber (both oxidizer and fuel).

c)  Burning    in    the    combustion chamber is uncontrolled rate.



a)  Liquid  fuels  and  oxidizers  are  used.

b) Separate oxidizer and fuel tanks  are used for storing purposes.

c) Controlled rate.



80.            What are the types of liquid propellants used in rocket engines?


i. Mono propellants


ii. Bi – propellants


Give two liquid propellants.

Liquid fuels :         Liquid hydrogen, UDMH, hydrazine

Solid fuels :          Polymers, plastics and resin material

82. What is mono-propellants? Give example.


A liquid propellant which contains both the fuel and oxidizer in a single chemical is known as “mono propellant”. e.g.,


i.                  Hydrogen peroxide

ii.               Hydrazine

iii.             Nitroglycerine and

iv.             Nitromethane, etc.


v.     What is bi-propellant? Give Example.


vi.  Name some oxidizers used in rockets.


A liquid propellant which contains the fuel and oxidizer in separate units is known as


bi-propellant.  The commonly used bi-propellant combinations are:


a)       Liquid oxygen

b)      Hydrogen peroxide

c)       Nitrogen tetroxide

d)      Nitric acid



a)       Gasoline

b)      Liquid bydrogen

c)       UDMH

d)      Alcohol, ethanol


85.            Name few advantages of liquid propellant rockets over solid propellant rockets.


i.          Liquid propellant can be reused or recharged.  Hence it is economical.


ii.          Increase or decrease of speed is possible when it is in operation.


iii.         Storing and transportation is easy as the fuel and oxidizer are kept separately.


iv.         Specific impulse is very high.


86.            What is inhibitors?


Inhibitors are used to regulate (or prevent) the burning of propellant at some sections.


87.            Give the important requirements of rocket engine fuels.


i.           It must be able to produce a high chamber temperature. It should have a high calorific value per unit of propellant.


ii.           It should not chemically react with motor system including tanks, piping, valves and injection nozzles.


88.            What is meant by restricted burning in rockets?


In this case, the inhibition material (or) restrictions prevent the propellant grain from burning in all directions. The propellant grain burns only at some surfaces while other surfaces are prevented from burning.


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