UNIT I COMPRESSIBLE FLOW – FUNDAMENTALS 1) State the difference between compress ible fluid and incompressible fluid ? Compressible Incompressible 1. Fluid velocities are appreciable compared with the velocity of sound 2. Density is not constant 3. Compressibility factor is greater than one. 1. Fluid velocities are small compared with the velocity of sound 2. Density is constant 3. Compressibility factor is one 2) Define stagnation pressure? Stagnation pressure is the pressure of the fluid which is attained when it is decelerated to zero velocity at zero elevation in a reversible adiabatic (isentropic) proces. For given values of static pressure and temperature its value can be derived from the stagnation temperature. πΎ π0 πΎ − 1 2 πΎ/(πΎ−1) = (π0/π)πΎ−1 = {1 + π } π 2 3) Write the steady flow energy equation for an adiabatic flow of air. In an adiabatic flow q = 0. Therefore energy equation becomes β1+c12/2 + gZ1= h2+ c22/2+ gZ2 +Ws Adiabatic energy equation is h0= h + ½ c2 4) Define bulk modulus of elasticity. Bulk modulus of elasticity is defined as the ratio between increase in pressure and relative change in volume. Bulk modulus, K = Increase in pressure Re lative change in volume 5) 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. M= πππππ‘ππ πππππ √ ππππ π‘ππ πππππ M= ππ΄π 2 = π π √ππ΄π2 6) 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. 7) Distinguish between static and stagnation pressures. In stagnation pressure state, the velocity of the flowing fluid is zero whereas in thestatic pressure state, the fluid velocity is not equal to zero. 8) 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”. T0 = T +c2/2cp Where T = static temperature T0 = stagnation temperature c2/2cp = velocity temperature 9) What is the use of Mach number? Mach number is defined as the ratio between the local fluid velocities to the velocity of sound. i.e. Mach number M = c/ a = πππππππ‘π¦πππ ππ’ππ πΏπππππππ’πππ£ππππππ‘π¦ 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, Mcritical = π∗ = 1 π∗ Crocco number is a non – dimensional fluid velocity which is defined as the ratio of fluid velocity to its maximum fluid velocity. π πΉππ’πππ£ππππππ‘π¦ i.e cr = = π∗ πππ₯πππ’ππππ’πππ£ππππππ‘π¦ 10) Write down the relationship between stagnation and static temperature interms of the flow, mach number for the case of isentropic flow. π π0 T0 = stagnation temperature =1 + πΎ−1 2 π2 where, T = Static temperature M = Mach number 11)Name the four reference velocities that are used in expressing the fluid velocities in nondimensional form? i. Local velocity of sound a = √ γπ π ii. Stagnation velocity of sound a0 =√γπ T0 2 iii. Maximum velocity of sound Cmax= a0 √γ−1 iv. Critical velocity of sound / fluid a* = c* = √γπ π ∗ 12) What are the different regions of compressible flow. The adiabatic energy equation for a perfect gas is derived in terms of fluid velocity c 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 ο»ο 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 ο³ο 5) 13 Define coefficient of compressibility. Coefficient of compressibility is defined as the ratio of relative change in volume to change in pressure. Coefficient of compressibility, = 14) What is stagnation state ? Re lative change in volume Change in pressure Stagnation state is the state reached by the fluid, when the flow is adiabatically decelerated to zero velocity at zero elevation. 15) Distinguish between static and stagnation pressures. In the stagnation pressure state, the velocity of the flowing fluid is zero and whereas in the static pressure state, the fluid velocity is not equal to zero. 16) Define stagnation temperature. Stagnation temperature is the temperature of a fluid which is obtained when it is adiabatically decelerated at zero velocity of zero elevation. 17) What is meant by stagnation pressure? Stagnation pressure of the fluid is its pressure when it is adiabatically decelerated to zero velocity at zero elevation. 18) Define Crocco number. Crocco number is a non-dimensional fluid velocity which is defined as the ratio of fluid velocity to its maximum fluid velocity. 19) What are the different regions of compressible flow ? The adiabatic energy equation for a perfect gas is derived in terms of fluid velocity (c) and sound velocity (a). This is then plotted graphically on the c-a co-ordinates, a steady flow ellipse is obtained. The various regions are, a) Incompressible region (M 0) b) Subsonic region (M < 1) c) Transonic region (M = 0.8 to 1.2) d) Supersonic region (M > 1 and M < 5) e) Hypersonic region (M 5). 20) What are the various types of waves in closed passages? The various types of waves in closed passages are, a) Infinitesimal pressure waves (sound waves) b) Non steep pressure waves with finite amplitude c) Steep pressure waves (shock waves) d) Expansion waves. 20) Define Mach cone and Mach angle. In a supersonic flow, all the pressure disturbances are included in a cone which has the point source at its apex and the effect of disturbance is not felt upstream of the source of disturbance i.e., the point source is always ahead of the wave fronts. The cone within which the disturbances are confined is called Mach cone and half angle of the cone is known as Mach angle. 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”. 21) Find the sonic velocity in oxygen when it is at 110° C, g=1.4 and molecular weight 32. a = gRT = 1.4x259.8125x383 = 373.244m/ s 22) A plane travels at a speed of 2400 KM/h in an atmosphere of 5°C, find the mach angle. M = c/a a= γπ π The mach angle. α =sin−1 ( 1/π) 23) If an aeroplane goes to higher altitudes maintaining the same speed, the Mach number will remain constant. Say true or false. False. π w.k.t. M = π At higher altitude, the sound velocity ‘a’ will decrease and hence M will increase. Therefore, M is not constant. 24) 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. 25) 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. 26) Give the expression for π π0 and π π∗ for isentropic flow through variable area interms of Mach number. 1 π π0 π π∗ = = πΎ−1 1+ 2 π2 πΎ−1 πΎ−1 1+ 2 π2 27) Sketch the isentropic and adiabatic expansion process in P-V and T-S diagram 28) Write the equation for efficiency of the diffuser. Diffuser efficiency = static pressure rise in the actual process static pressure rise in the ideal process P2 − P1 P2’ − P1 29)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 units 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. 30) What is chocked flow? State the necessary conditions for this flow to occur in a nozzle. 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 ondition 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. π 31) Draw the variation of π0 along the length of a convergent divergent device when it functions as (a) diffuser, (b) nozzle and (c) venturi. Curves a, b, c venture d, e diffuser g nozzle 32) Give the expression for nozzle efficiency and diffuser efficiency with h – s diagram. T1− T2 π΄πΆπππ΄πΏ πΈπππ»π΄πΏππ π·π ππ Nozzle efficiency ο¨N = = πΌπ·πΈπ΄πΏ πΈπππ»π΄πΏππ π·π ππ T1− T2’ Diffuser efficiency ο¨D = πΌπ·πΈπ΄πΏ πΈπππ»π΄πΏππ π πΌππΈ π΄πΆπππ΄πΏ πΈπππ»π΄πΏππ π πΌππΈ = T2−T1 T2’ −T1 33) Describe the function of a nozzle and a diffuser. The main function of a nozzle is to accelerate the flow i.e., to increase the velocity and decrease the pressure of the flowing fluid. Whereas, the function of a diffuser is to decelerate the flow i.e., to increase the pressure and decrease the velocity of the flowing fluid. 34. Distinguish between isentropic and adiabatic flows. Sl.No. a) b) Isentropic flow Adiabatic flow The flow is reversible and The flow is irreversible and frictionless. frictional effect is considered. Both stagnation Only stagnation temperature temperature and pressure is constant but stagnation is constant. pressure is decreased due to friction. c) Change in entropy is zero. Entropy change will occur. 35). Sketch the isentropic and adiabatic expansionprocesses in p-V and T-s diagram. p02' = p01 p 1 c12 2 1 2 c 2 2 p p 02 h0= c T01= T02 2 1 c2 2 h p 2 2 ' p2 p'2= 2 2 2' ds s V 1 - 2' Isentropic expansion 1-2 Adiabatic expansion. 36) Sketch the isentropic and adiabatic compression processes in p-V and T-s diagram p01' = p02' c 12 2 p 1 c2 2 2 2' h 1 p1 s V 1 - 2' Isentropic compression 1-2 Adiabatic compression. T 01= T02 c22 2 ds 2 2 p 02 p2' = p2 37) Define impulse function. The sum of pressure force (pA) and impulse force (Ac2) gives impulse function. Impulse function, F = pA + Ac2 38) What is chocked flow? State the necessary conditions for this flow to occur in a nozzle. 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 folw to occur in the nozzle are, * The nozzle exit pressure ratio must be equal to the critical pressure ratio. * Mach number = 1. 39) What is meant by over expansion? If the chamber pressure is greater than the design pressure, the nozzle is said to be over expanding. 40 What do you mean by under expansion? If the chamber pressure is lesser than the design pressure, the nozzle is said to be under expansion. 41) Give the important difference between nozzle and venturi. Sl. Nozzle Venturi No. a) The flow is accelerated continuously i.e., Mach number and velocity increase continuously. b) Used to increase velocity, The flow is accelerated up to m = 1 and then Mach number is decreased. Used for flow measurements. Mach number. c) Generally convergent portion is short. Convergent and divergent portions are equal. 42) What will happen if the air flowing through a nozzle is heated? If the air flowing through a nozzle is heated, then the * Velocity of air will increase. * Temperature and entholpy will increase. * Pressure will increase. * Entropy will increase. 43) Mention the uses of impulse function. Impulse function F = Pressureforce pA + Inertia force Ac2. Since the unit of both the quantities are same as the unit of force, itis 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. 44) Give the variation of Mach number across a convergent divergent nozzle. M<1 M=1 Convergent Subsonic flow M>1 Throat Sonic flow Divergent Supersonic flow A compressible fluid is one in which the fluid density changes when it is subjected to high pressure-gradients. For gasses, changes in density are accompanied by changes in temperature, and this complicates considerably the analysis of compressible flow. UNIT II FLOW THROUGH DUCTS 1.Define 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. 2. Define Fanno line. The locus of the state which satisfy the continuity and energy equation for a frictional flow is known as Fanno line. 3. State the assumptions made in Fanno flow. The assumptions are, a) Perfect gas. b) One dimensional steady flow with friction through a constant area duct. c) Absence of heat, work transfer and body forces. 4.Sketch the Fanno curve on T-s diagram. pA 2 pA p0A h0 = h+½c 0 Subsonic flow A c=a = h+ A h M<1 Sonic M=1 B M>1 G 2 2 2ο² F- Critical point Fanno line Supersonic flow s Fanno curve on T-s diagram 5. Define coefficient of friction. The non-dimensional friction factor or coefficient of friction is defined as the ratio of well shear stress to the dynamic head of the stream. f = Well shear stress Dynamic head 6. What do you mean by 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 up to the limiting state where Mach number M A = 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 critical state and is constant afterwards, then the flow is said to be chocked flow. 7. 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. 8. Define isothermal flow with friction. A steady one dimensional flow with friction and heat transfer in 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 remains constant. 9 .State the assumptions made to derive the equation for isothermal flow. The following assumptions are made to derive the equation for isothermal flow. a) One dimensional flow with friction and heat transfer. b) Constant area duct. c) Perfect gas with constant specific heats and molecular weights. d) Isothermal flow i.e., temperature is constant. e) On account of constant temperature the friction factor may be assumed constant along the duct. 10. Show the static and stagnation temperature variation for isothermal flow. Give the critical Mach number. Constant pressure lines T0 A p0A ing eat 2 A 1 H At T T Stagnation state ling At Coo p A Mο½ MοΌ 1 1 B r Deceleration r MοΌ 1 r s Static and stagnation temperature variation for isothermal flow 11. Define the term Rayleigh flow. The one dimensional flow in a constant area duct with heat transfer and without friction is called Rayleigh flow. 12. Differentiate between isothermal flow and fanno flow. Isothermal flow a) Fanno flow Static temperature is Static temperature is not constant. constant. b) With heat transfer. Without heat transfer. c) Flow occurs in a long Long ducts are not required. ducts where sufficient time is required for heat transfer. d) On account of constant Friction factor is constant. temperature, the friction factor is assumed as constant. 13. Define Rayleigh line. The locus of the points of properties during a constant area frictionless flow with heat exchange T0max = T0 A Mο½ 1 h = Constant A p H M<1 (T0 – T) A Co r p = Constant R g olin A M =1 (T0–T) M > 1 h (or) T Heating s = Constant B is called Rayleigh line. s 14. What is diabetic flow? Diabetic flow is the flow which deals with the exchange of heat from the system in the absence of friction (Rayleigh flow). UNIT III NORMAL AND OBLIQUE SHOCKS 1.What are normal shock waves? When the shock waves are right angles to the direction of flow and the rise in pressure is abrupt then they are called as normal shock waves. 2. Mention the properties which change across the normal shock. In normal shock, a) Stagnation pressure decreases b) Static pressure increases. 3. Mention the properties which are constant across the normal shock. In normal shock, the unchanged properties are, a) Stagnation enthalpy b) Stagnation temperature. 4. Is the flow through a normal shock wave is an equilibrium one? No. Because all the fluid particles properties are varied during normal shock. 5. What are the disadvantages of shock wave ? The disadvantages of shock wave are as follows. a) The shock waves present in the turbo machine reduces the performance of the machine. b) Shock wave created by supersonic aircraft produces the damaging effect on human life. 6. What are the useful applications of the shock wave ? The applications of the shock wave are given below. * A moving strong shock wave is utilized to accelerate the flow to a high Mach number in a shock tube where flow behaviour at high Mach number can be studied. * Used in supersonic compressors to obtain high pressure ratios in one stage, may be as high as 10.0. 7. What is the approximate thickness of shock wave? The thickness of the shock wave is of the order of 10–3 mm which is comparable with the mean free path of the gas molecules. 8. Define shock waves. A shock wave is a steep finite pressure wave. The wave in which fluid properties change abruptly across a short distance is known as shock wave. 9. What is meant by rarefaction shock wave ? An expansion or rarefaction wave is one which reduces the pressure of the fluid through which it propagates. 10. When does a rarefaction wave occur ? An sudden outward motion of the piston in a cylinder generates an expansion wave and it is generated in a gas duct down of a valve which is suddenly closed. 11. Define compression wave. A shock wave which is at a higher pressure than the fluid into which it moves is called compression shock wave. 12. State the necessary conditions for a normal shock to occur in compressible flow. The necessary conditions required are, a) The compression wave is to be at right angle to the compressible flow. b) Flow should be supersonic. 13. Why compression shock wave is possible and not the rarefaction shock ? Compression shock wave decelerates the flow, which increases the pressure, density and entropy. Rarefaction shock waves accelerate the flow which decreases the density and entropy. But decrease in entropy with total energy conservation through a shock wave violetes the second law of theomodynamics. This rarefaction shock is not possible. 14. Define the strength of shock wave. Strength of shock wave is defined as the ratio of difference in downstream and upstrean shock pressures (py – px) to upstream shock pressure (px). It is given by ο₯. py ο p x ο₯ = 15. Name px the practical situations where this oblique shock occurs. a) Oblique shocks are found to occur at the exit of the turbine blade passages with supersonic flow. b) They are also formed at the entry of supersonic diffusers of aircraft engines. 16. Define oblique shock wave. The shock wave which is inclined at an angle to the two dimensional flow direction is called as oblique shock. 17. What is a shock polar ? The graphical representation of oblique shock properties is known as 'shock polar'. 18. Give the difference between normal and oblique shock. Sl.No. a) b) Normal shock Oblique shock The shock waves are The shock right angles to the inclined direction of flow. direction of flow. May be treated as one dimensional analysis. Oblique shock dimensional analysis. at waves an are angle to is the two UNIT IV & V JET PROPULSION AND SPACE PROPULSION 1. Write the difference between rocket and jet propulsion. Sl.No. a) Rocket propulsion Jet propulsion Air for combustion is Air supplied by separate from atmosphere. for combustion is taken oxygen chamber. b) Rocket propulsion does It has not use mechanical like turbine and compressors turbine and for propulsion. c) It uses convergent divergent nozzle for It uses for gas discharge. mechanical convergent devices device like compressor. nozzle gas discharge. 2. What is meant by thrust? The force which propels the aircraft in the forward direction at a given speed is called thrust or propulsion force. 3. What is the use of after burner? The after burner is used to provide additional thrust by burning fuel in the exit side of the turbine. 4. Why superchargers aircraft propulsion engines? are used in internal combustion At higher altitude, the density of air is very poor. Hence the mass of air inducted into the engine is reduced and it affects the engine performance. This problem is overcome by supercharged engines. 5. What is meant by jet propulsion? Propelling a craft by a high velocity hot air jet is known as jet propulsion in which air for propulsion is taken from atmosphere. 6. What are the main parts of ramjet engine? The main parts of ramjet engine are, a) Supersonic diffuser b) Subsonic diffuser c) Combustion chamber d) Discharge nozzle. 7. What are the various types of air breathing engine? The various propulsive engines are, a) Ramjet engine b) Pulse jet engine c) Turbojet engine d) Turboprop engine e) Turbofan engine. 8. What is ram effect? In ramjet 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 ram effect and the pressure rise is called the ram pressure. 9. What is thrust augmentation? To achieve better take off performance, additional fuel is burned 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. 10. 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. 11.What is mono propellant? Give one example for it. A liquid propellant which contains both the fuel and oxidizer in a single chemical is known as a mono-propellant. It is stable at normal ambient conditions and liberate thermo-chemical energy on heating. Examples : a) Nitroglycerine b) 12. What is bipropellant? Nitromethane. If the fuel and oxidizer are different from each other in its chemical nature, then the propellant is called bipropellant. Examples : Liquid oxygen - Gasoline Hydrogen peroxide - Hydrazine 13. Classify employed. the rocket engines based on source of energy On the basis of source of energy employed, rocket engine can be classified as, a) Chemical rocket engines b) Solar rocket engines c) Nuclear rocket engines d) Electrical rocket engines. 14. What is specific impulse of a rocket? The thrust developed per unit weight flow rate of the propellant is known as specific impulse. 15. What is inhibitor? Inhibitors are used to regulate the burning of propellant at some sections. 16. What is hypergolic? For some fuel and oxidizer combinations, ignition is not required to start the reaction. That is, the combustion takes place merely a contact between the fuel and the oxidizer. Such propellants are known as hypergolic. 17. Give the important requirements of rocket engine fuels. The requirements of rocket engine fuels are as follows. a) It must be able to produce a high chamber temperature. It should have a high calorific value per unit of propellant. b) It should not chemically react with motor system including tanks, piping, valves and injection nozzles. 18. Write the few advantages of liquid propellant rockets over solid propellant rockets. a) Liquid propellant can be reused or recharged. Hence it is economical. b) Increase or decrease of speed is possible when it is in operation. c) Storing and transportation is easy as the fuel and oxidizer are kept separately. d) Specific impulse is very high. 19. What is meant by restricted burning in rockets? In this case, the inhibiting materials 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. 20. What is meant by effective jet velocity? When the exhaust gases through the nozzle expand to the ambient pressure, the corresponding velocity of jet is known as effective jet velocity. 21. Define characteristic velocity of a rocket. Characteristic velocity of rocket is defined as the ratio of effective jet velocity to the thrust coefficient. 22. Define specific propellant consumption. Specific propellant consumption is defined as the weight flow rate of the propellant required to produce unit thrust of 1 N. 39. Define weight flow coefficient. Weight flow coefficient is the ratio of weight rate of flow of propellant to the force term p 0A*.