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Problems of Practices Of Fluid Mechanics Compressible Fluid Flow Prepared By Brij Bhooshan Asst. Professor B. S. A. College of Engg. And Technology Mathura, Uttar Pradesh, (India) Supported By: Purvi Bhooshan Please welcome for any correction or misprint in the entire manuscript and your valuable suggestions kindly mail us brijrbedu@gmail.com. 1 Air is isentropically expanded in a convergent-divergent nozzle from an initial pressure of 5 kg/cm 2 and 25 C to a back pressure of 1.5 kg/cm 2. The velocity of the air entering the nozzle is 100 m/s. The mass flow rate of the air is 2 kg/s. Determine (i) Mach number at inlet to the nozzle, (ii) pressure at the throat, (iii) area of flow at the throat and (iv) the area of flow at the exit of the nozzle. Assume for air to be 1.4 and R to be 29.27 kg/-m/kg K. 2 Explain what do you mean by Rayleigh Flow. What are the assumptions made? Write down the governing equations for Rayleigh Flow With the help of h-s diagram, show the occurrence of Normal Shock in Rayleigh Flow. 3 A missile is travelling with a Mach number of 7. The temperature of atmospheric air is 45 C. Find the stagnation temperature at the nose of the missile. Prove the formula used. 4 Derive a relation between the area variation and the Mach number for the flow of reversible, adiabatic, one-dimensional steady flow of an ideal gas through a nozzle. Hence deduce the proper shape for nozzles and diffusers for subsonic and supersonic flows. 5 What do you understand by stagnation property? Air at a temperature 30 C and atmospheric pressure is flowing with a velocity of 300 m/s. What will be the total temperature? Assuming the flow to be isentropic, find the stagnation pressure. Copyright by Brij Bhooshan @ 2013 Page 1

2 Problems of Practices on Compressible Fluid Flow 6 An axial flow compressor provides a total head pressure ratio of 4:1 with an overall total head isentropic efficiency of 85%, when the inlet total head temperature is 290 K. This compressor is designed for 50% reaction with inlet and outlet air angles from the rotor blades of 45 and 10⁰ respectively. The mean blade speed and axial velocity are constant throughout the compressor. Assuming a value of 201.16 m/sec for the blade speed and a work done factor of 0.86, find the number of stages required. What is the inlet Mach number relative to the motor at the mean blade height of the first stage? 7 Establish from first principles the Fanno equation and sketch. On T-s plane characteristic "Fanno Line" for a duct of constant cross-section. Mark the subsonic and supersonic parts and the sonic point. 8 Show that in flow through a tube of constant cross-sectional area with heat addition, (i) the Much number at the point of maximum temperature is equal to 1/γ and (ii) the Mach number at the point of maximum entropy is equal to unity. 9 Show that the Mach number behind a normal shock wave may be written in the form where P1 and P2 are the pressure before and after the shock wave and γ is the ratio of caloric value. 10 Heat is supplied to a perfect gas which is flowing through a parallel passage. Show that if friction is negligible p (1 + γm 2 ) is constant along the passage. Hence show that is also constant. Assume that the gas velocity is uniform over any cross-section. 11 Sketch Rayleigh line on Pressure-Specific Volume diagram and on Enthalpy- Entropy diagram. Prove that for Rayleigh line conditions. 12 Define strength of shock wave and explain its significance. 13 Air available at saturated atmospheric conditions flows through a heated constant area pipe. If the flow is decelerated from Mach number 1.5 to Mach number 1.0. determine: (i) the change in temperature; (ii) the heat addition to air 14 A double sided centrifugal compressor has eye root and tip diameters of 18 cm and 30 cm and is to deliver 16 kg of air per second at 16000 rpm. The design ambient conditions are 15 C and 1 bar and the compressor has to be a part of a stationary power plant. Determine (i) Suitable values for impeller vane angles at the root and tip of the eye if the air is given 20 of pre-whirl at all radii. The axial component of the velocity is constant throughout the impeller and is 150 m/s. (ii) The power required if the power input factor is 1.05 and mechanical efficiency is 95%, and (iii) The maximum Mach number at the eye. Copyright by Brij Bhooshan @ 2013 Page 2

Problems of Practices of Fluid Mechanics By Brij Bhooshan 3 Take for air: Cp =1.005 kj/kg K and Cp / Cv = 1.4. 15 What is Fanno flow? With the help of basic equations explain how Fanno line can be plotted on the h - s diagram. Give the effects of friction on various flow parameters and explain how choking occurs due to friction. 16 Explain clearly what do you understand by Fanno flow. Show its plot on h-s diagram and give its characteristics. Air flows in an insulated duct with a Mach number of 0.2. The initial temperature and pressure are 290 K and 2.0 bar respectively. Determine: (i) the pressure and temperature at a section of the duct where the Mach number is 0.8. (ii) the distance between these two points if the duct diameter is 10 cm and friction factor is 0.004. (iii) what will be the maximum length of the duct to avoid choking? Use the following table: M P/P* T/T* 4fLmax/D 0.2 5.455 1.19 14.533 0.8 1.289 1.064 0.073 17 Define Rayleigh flow. Give one practical example of Rayleigh flow. Show that the Mach numbers at the maximum enthalpy and maximum entropy points on the Rayleigh line are 1/ ν and 1.0 respectively. 18 The first axial-flow air compressor stage without inlet guide vanes is operating at a speed of 15000 r.p.m. in the atmospheric conditions of T0 = 288 K, P0 = 1.01 bar. The rotor mean blade ring diameter is 0.34 m and hub to tip ratio is 0.5. Atmospheric air enters the stage with a velocity of 150 m/s. Consider constant axial velocity through the stage and take stage efficiency as 0.86, mechanical efficiency as 0.97, work done factor as 0.97, Cp = 1.005 kj/kg/k and R = 0.287 kj/kg/k. Sketching the axial compressor stage with velocity diagrams and labeling with most general notations used in practice, determine-the following for attaining relative velocity ration across rotor (de Haller number) of 0.73: (i) Mass flow rate in kg/s (ii) Maximum Mach number at rotor blade at entry (iii) Angles made by relative and absolute velocity at rotor entry and exit with axial direction (iv) Power required to drive the compressor (v) Stage pressure ratio. 19 Define Rayleigh flow and mention its governing relations. Using them, establish the expression for the flow in the form p + G 2 v = Const., where G is the mass flow rate per unit area. Show the plot of this equation on h-s and p-v planes. Show also that at maximum enthalpy state 20 For the Rayleigh flow, establish the expression for T/T* terms of Mach number, M. 21 Derive an equation for a Fanno flow. Give two examples of Fanno flow in thermal system. Show that the upper and lower branches of a Fanno curve represent subsonic and supersonic flows respectively. 22 Air at 1 MPa and 600 C enters a converging nozzle with a velocity of 150 m/s. Determine the mass flow rate through the nozzle for a nozzle throat area of 50 cm 2 when the back pressure is (i) 0.7 MPa and (ii) 0.4 MPa. Given: Cp = 1.005 kj/kg-k; K = 1.4; R = 0.287 kj/kg-k. Copyright by Brij Bhooshan @ 2013 Page 3

4 Problems of Practices on Compressible Fluid Flow For, Pt/P0 = 0.670, Mat = 0.778 and Tt/T0 = 0.892 where, subscript t represents the properties at the throat. 23 Derive an expression for the Mach number after a normal shock wave occurring in a nozzle. Show the trend of this Mach number, (in the form of an x-y plot) with respect to the Mach number value before the shock. 24 Air enters a 5 cm diameter frictionless duct with a Mach number 2. Its static temperature is 250 C and stagnation pressure 6 bar. For increasing Mach number to 3, find the amount of heat to be transferred and change in static temperature. You may use the following table for air having γ = 1.4: M T/T* P/P* P0/P0* T0/T0* 2 0.5289 0.3636 1.503 0.7934 3 0.2803 0.1765 3.424 0.6534 25 Air enters a diffuser with a velocity of 250 m/s and a temperature of 30 C. It leaves with a velocity of 90 m/s, Neglecting friction and heat transfer determine (i) exit temperature (ii) exit pressure if the inlet pressure is 125 kpa and (iii) Area ratio between the exit and entrance. Will your answers change if there is friction present? Explain how. 26 For normal shock wave derive the following expression: where x and y are the conditions before and after the shock wave. 27 Show Fanno line in adiabatic flow with friction on h-s diagram & explain the physical significance. 28 Air-flow is entering to a frictionless duct of 0.3 m diameter at a velocity of 580 m/s and a Mach number of 2. A 100 kj/kg of heat is added to the flow and Mach number of 1.2 is attained. Determine (i) change in enthalpy of flow, (ii) change in kinetic energy of the flow, (iii) change in static pressure in terms of inlet pressure. Comment on result and show the process on T-φ diagram. 29 Air at the rate of 35 kg/s flows through a nozzle in which a normal shock occurs in the diverging section down- stream of the throat. The nozzle has an area of crosssection equal to 40 cm 2 at the section of shock. The pressure and velocity of fluid just before the shock are 2.5 bar and 480 m/s respectively. Find the Mach number, pressure and temperature after the shock. Comment on the results. Normal shock table: M1 M2 P2/P1 T2/T1 ρ2/ρ1 P20/P10 1.42 0.7314 2.1858 1.2676 1.7243 0.9531 1.43 0.7274 2.2190 1.2742 1.7416 0.9503 30 Air is supplied to a convergent-divergent nozzle with a static temperature of 300 K, static pressure of 5 bar and a velocity of 150 m/s. The inlet area of the nozzle is 10 cm 2. A normal shock occurs at a section of the nozzle where flow Mach number is 2. The flow Mach number downstream of shock corresponding to Mach number 2 is 0.577. The flow Mach number at the exit of the nozzle is 0.4. Considering Copyright by Brij Bhooshan @ 2013 Page 4

Problems of Practices of Fluid Mechanics By Brij Bhooshan 5 isentropic flow before and after shock and using isentropic flow relation for A/A* and Mach number provided below, find: (i) Throat area of the nozzle (ii) area of the nozzle where shock occurs (iii) exit area of the nozzle (iv) Loss of stagnation pressure across shock. Sketch the variation of pressure and Mach number along the length of the nozzle: M 2 0.577 0.4 A/A* 1.688 1.22 1.59 31 A stream of air flows in an insulated tube of constant cross-sectional area of 0.9 m 2. At a section1, the pressure is 0.6 bar, temperature is 22 C and mass velocity is 150 kg/s-m2. The pressure in space in which tube exhausts is so low that choking condition prevails. Determine, a) Mach no. at section 1. b) Mach no., temperature and pressure at the exit of tube, c) Total force exerted in axial direction which must be exerted to hold the tube stationary. Given, R = 287 J/kg-K; γ = 1.4 Fanno line (Adiabatic constant area flow with friction) table γ = 1.4 M 0.58 1.124 0.615 1.828 1.213 1.121 0.576 0.60 1.119 0.635 1.763 1.188 1.105 0.491 0.62 1.114 0.654 1.703 1.166 1.091 0.417 0.64 1.109 0.674 1.646 1.145 1.079 0.353 32 How would you define the strength of shock wave? What do you mean by weak shock? Also find the expression for the strength of shock in terms of density ratio. 33 What is the effect of Mach number on the compressibility? Derive an expression for pressure coefficient in terms of Mach number. 34 Derive an expression for entropy change across a normal shock wave occurring in a nozzle. Show the trend of this entropy change (in the form of a diagram), with respect to the Mach number value before the shock. 35 Derive the following expression for normal shock in an ideal gas: where x and y are conditions before and after the shock, γ is ratio of specific heats and M is Mach number. 36 Explain the effect of area change in subsonic and supersonic flows. A stream of air flows in a duct of 100 mm diameter at the rate of 60 kg/min. The stagnation temperature is 47 C. At one section of the duct the static pressure is 40 kpa. Calculate the Mach number, velocity and stagnation pressure at this section. Take γ = 1.4 and R = 0.287 kj/kg-k. 37 Explain clearly the following for compressible flow: (i) Static and stagnation conditions (ii) Critical velocity and maximum velocity attainable An airplane flies at an altitude, where the conditions are 216.5 K and 1.206 10 4 N/m 2 with a speed of 800 km/hr. Calculate - Copyright by Brij Bhooshan @ 2013 Page 5

6 Problems of Practices on Compressible Fluid Flow 1. the maximum possible temperature on the airplane skin; 2. the maximum possible pressure intensity on the airplane body; 3. the critical velocity of the air relative to the airplane; 4. the maximum possible velocity of the air relative to the airplane. 38 For normal shock wave in an ideal gas, prove that 1 2 P 1 x y M M y 2 P 1 x M x 2 1 M y 2 where stations x and y represent the condition before and after shock wave. 39 Air enters in a conical passage with stagnation pressure and stagnation temperature of 5 bar and 400 K respectively. The exit to inlet area ratio of the passage is 4.46. Considering flow of air as isentropic throughout, determine the change in static pressure, if the flow inlet Mach number is (i) 0.7 and (ii) 1.36. The value of A/A* at M = 0.7 and M = 1.36 is 1.094. For air take γ = 1.4 and R = 287 J/kg/K. Take at A/A* = 4.88, M = 12 and 3.15. Sketch the processes on h-s diagram and comment on the resulted change in pressure. 40 Diabetic flow of dry air takes place through a frictionless constant area duct. At some particular section of the duct, the Mach number is 4.0 while stagnation temperature and static pressure are 280 K and 0.5 bar respectively. Calculate the stagnation temperature, static and stagnation pressures at a section where the Mach number is 2.0. Also find the amount of heat transfer which causes this reduction in Mach number Take CP = 1.005 kj/kg and γ = 1.4. M P/P* T/T* T0/T0* P0/P0* 2.0 0.364 0.529 0.793 1.503 4.0 0.1026 0.168 0.589 8.227 41 A conical diffuser has entry and exit diameters of 15 cm and 30 cm respectively. The pressure, temperature and velocity of air at entry are 0.69 bar, 340 K and 180 m/s respectively. Determine (i) the exit pressure, (ii) the exit velocity (iii) the force exerted on the diffuser walls. For solution the following table may be used. Suffix '0' is corresponding to stagnation pressure values. The star (*) values are critical values corresponding to M = 1. M is Mach number and. M* is corresponding to critical velocity of sound (c*). Isentropic flow of a perfect gas (γ = 1.4) M M* T/T0 P/P0 A/A* F/F* AP/A* P0 0.00 0.00 1.000 1.000 0.05 0.0548 0.999 0.998 11.592 9.158 11.571 0.10 0.1094 0.998 0.993 5.822 4.624 5.781 0.15 0.1640 0.996 0.984 3.910 3.132 3.849 0.20 0.218 0.992 0.973 2.964 2.400 2.882 0.25 0.272 0.987 0.957 2.403 1.973 2.301 0.30 0.326 0.982 0.939 2.035 1.698 1.912 0.35 0.378 0.976 0.918 1.778 1.509 1.634 Copyright by Brij Bhooshan @ 2013 Page 6

Problems of Practices of Fluid Mechanics By Brij Bhooshan 7 0.40 0.431 0.969 0.895 1.590 1.375 1.424 0.45 0.483 0.961 0.870 1.448 1.276 1.261 0.50 0.534 0.952 0.843 1.339 1.203 1.129 0.55 0.585 0.943 0.814 1.255 1.147 1.022 0.60 0.635 0.933 0.784 1.188 1.105 0.932 0.65 0.684 0.922 0.753 1.135 1.073 0.855 0.70 0.732 0.910 0.721 1.094 1.049 0.789 0.75 0.779 0.898 0.688 1.062 1.031 0.731 0.80 0.825 0.886 0.656 1.038 1.018 0.681 42 What is a Fanno line and a Rayleigh line? Why do the end states of a normal shock lie on the Fanno line and Rayleigh line? Show these lines on a h-s diagram for various conditions. Give the physical meaning of this. 43 A nozzle is designed assuming isentropic flow with an exit Mach number of 2.6. Air flows through it with a stagnation pressure and temperature of 2 MPa and 150 C respectively. The mass flow rate is 5 kg/sec. (i) Determine the exit pressure, temperature, area and throat area. (ii) If back pressure at the nozzle exit is raised to 1.35 MPa, and the flow remains isentropic except for a normal shock wave, determine the exit Mach number and temperature, and the mass flow rate through the nozzle. Assume for the value of P/P0 of 0.675, M = 0.85 and T/T0 = 0.845 for isentropic flow. 44 For steady adiabatic flow of an ideal gas with constant specific heats through a nozzle or diffuser, show that: T0 k 1 2 1 M T 2 where T0 and T are the stagnation and static temperatures, respectively, k is the ratio of specific heats and M the Mach number. 45 In a turbo jet engine, air enters the diffuser at 0.8 bar, 240 K, with a velocity of 1000 km/hr. The pressure ratio across the compressor is 8. The turbine inlet temperature is 1200 K and the pressure at nozzle exit is 0.8 bar. The turbine work just equals the compressor work input. The diffuser, compressor, turbine and nozzle processes are isentropic an there is no pressure drop for flow through the combustor. Determine the pressure at exit from the diffuser, the compressor and the turbine, and also the velocity at the nozzle exit. Show the various processes on a temperature-entropy diagram. For air Cp = 1.001 kj/kg. K and CP/CV = 1.4. 46 What is a shock wave? Write the continuity, momentum and energy equations relating points 1 and 2, just upstream and just downstream, respectively, of a normal shock in a constant area duct. State whether the following properties of the flow stream increase, decrease or remain unchanged across a normal shock: total pressure, total energy, static temperature, density and velocity. 47 Air enters a constant-area combustion chamber at a March M number of 0.25 with a total pressure of 5.5 bars. Combustion gas leaves the chamber with a March number of 0.35. Neglecting friction and the mass of the fuel, determine the drop in total pressure of air in the combustion chamber. Assume Cp/Cv = 1/35. 48 A jet engine is flying at 300 m/s when the pressure and temperature of the atmosphere are 0.8 bar and 230 K respectively. The compressor pressure ratio is Copyright by Brij Bhooshan @ 2013 Page 7

8 Problems of Practices on Compressible Fluid Flow 4/1 and the maximum cycle temperature is 1000 K. Calculate, specific thrust, power produced, propulsive efficiency, overall thermal efficiency and the fuel consumption. Assume: isentropic efficiency of components unity; nozzle throat area 0.06 m 2 ; calorific value of fuel 43000 kj/kg; Cp and for the compression process 1.005 kj/kgk and 1.4; Cp and for the combustion and expansion processes 1.15 kj/kgk and 1.333. 49 What is impulse function? Show that F F * M 2 1 1 M 1 2 1 M 50 Air enters an insulated pipe at Mach number (M) =0.4 and leaves at M = 0.6. What portion of the duct length in percentage is required for the flow to occur at M = 0.5? Take Fanno line parameters as M fl/d 0.4 0.5770 0.5 0.2673 0.6 0.1227 51 A supersonic aeroplane flies at a Mach number 1.8 at an altitude of 700 m, where the atmospheric temperature is 10 C. What is the time that elapses, by which the acoustic disturbance reaches an observer on the ground after it is directly overhead? 52 In an aircraft flying at an altitude where the pressure was 35 kpa and temperature 38 C, stagnation pressure measured was 65.4 kpa. Calculate the speed of the aircraft. 53 Air at 10 bar and 500 K stagnation conditions flows through a nozzle. The area at the exit of nozzle is 0.25 10 4 m 2. The pressure at exit is 2 bar. Determine the velocity, specific volume and mean flow rate through the nozzle. 54 Considering isentropic flow in a nozzle show that P P * 1 0 2 1, 2 2 1 2 1 * 1 0, T * 2 T 0 1 where * refers to- M = 1 and subscript zero refers to stagnation condition. 55 An airplane flies at an altitude with a velocity of 800 km/hr. The pressure and temperature at that altitude are 1.206 10 4 N/m 2 and 217 K respectively. Calculate (i) the maximum possible temperature on the airplane skin, (ii) the maximum possible pressure intensity on the airplane body, (iii) the critical velocity of air relative to the airplane, and the maximum possible velocity of the air relative to the airplane. 56 What do you mean by Fanno flow? Show that the upper and lower branches of a Fanno curve represent subsonic and supersonic flows respectively. Prove that at the maximum entropy point Mach number is unity and all processes approach this point. 57 Derive the Rankine-Hugoniot equations for flow through a normal shock. How Copyright by Brij Bhooshan @ 2013 Page 8

Problems of Practices of Fluid Mechanics By Brij Bhooshan 9 does a normal shock differ from an oblique shock? Mention two useful applications of a normal shock. 58 Show that for sonic flow, the deviation between the compressible and incompressible flow values of the pressure coefficient of a perfect gas ( = 1.4) is about 27.5%. 59 A convergent-divergent nozzle has an exit area ratio of 2. Air enters the nozzle with a stagnation pressure of 950 kpa and a stagnation temperature of 350 K. The throat area is 490 mm2. Determine the mass flow rate, exit pressure, exit temperature, exit Mach number and exit velocity for the following conditions: (i) Sonic velocity at the throat, diverging section acting as a nozzle. (ii) Sonic velocity at the throat, diverging section acting as a diffuser. Table below gives the one-d, isentropic, compressible flow functions for an ideal gas. * represents the critical values at the throat where the Mach number is unity: M M* A/A* P/P0 T/T0 0.308 0.326 200 0.936 0.9812 1.00 1.00 100 0.528 0.8333 2.197 1.717 200 0.0939 0.5089 60 By using the energy equation d V. dv d( losses) 0 the continuity equation ρav = constant, and C show that for subsonic flow in a pipe, the velocity must increase in the downstream direction. 61 Show that oblique and normal shock waves in a gas are analogous to openchannel waves when the open channel width is constant. 62 Helium enters a 100 mm-1d pipe from a converging-diverging nozzle at M = 1.30, P = 14 kpa, T = 225 K. Estimate for an isothermal flow (i) the maximum length of pipe for no choking, (ii) the downstream conditions, and (iii) the length from the exit to the section where M = 1.0, f = 0.016. 63 An airplane is flying at a speed of 800 kmph at an altitude of 1.5 km, where the air temperature is 50 C. Find the maximum possible temperature on the airplane skin body. 64 Derive an expression for area velocity relationship for a compressible fluid in the form: da dv M 2 1 A V Further, explain the variation of velocity with change in area for: (i) subsonic velocity (ii) sonic velocity and (iii) supersonic velocity. 65 Considering the T-s diagram of Rayleigh flow and using the differential forms of the conservation equations and property relations, show that the (i) Mach number is unity at the point of maximum entropy and dp d Copyright by Brij Bhooshan @ 2013 Page 9

10 Problems of Practices on Compressible Fluid Flow (ii) Mach number is 1/ at the Point of maximum temperature. 66 Derive an expression for the area velocity relationship for a compressible fluid flow in the form of da dv 1 M A V Explain properly, with the help of diagrams, what are the important conclusions derived from the above relationship. 67 A Pitot-Static tube is used to monitor the velocity of an air stream. At the location of insertion of the probe, the static pressure is 1.5 bar and temperature is 35 C. Calculate the reading of a mercury manometer connected differentially across the static and total pressure openings of the probe, if the air stream velocity is (i) 60 m/s (ii) 200 m/s (iii) 500 m/s. Take into consideration the compressibility characteristics of the flow wherever applicable. The following values may be used Isentropic table for perfect gas, k = 1.4 M P/P0 0.54 0.820 0.56 0.808 0.58 0.796 0.70 0.720 0.72 0.708 0.74 0.695 Normal shock table for perfect gas, k = 1.4 Copyright by Brij Bhooshan @ 2013 Page 10 2 Mx My Py/Px ρy/ρx 1.38 0.748 2.055 1.655 1.40 0.739 2.120 1.689 1.42 0.731 2.185 1.724 1.44 0.723 2.252 1.759 68 Air at 1 MPa and 600 C enters a conserving nozzle with a velocity of 150 m/s. Determine the mass flow rate through the nozzle for a nozzle throat area of 50 cm 2 when the back pressure is (i) 0.7 MPa and (ii) 0.4 MPa. Assume that the flow through the nozzle is steady, one -dimensional and isentropic. You may use the following table for one - dimensional isentropic flow (for an ideal gas with = 1.4): M P/P0 ρ/ρ0 T/T0 A/A* M* 0.74 0.695 0.771 0.901 1.068 0.770 0.76 0.682 0.761 0.896 1.057 0.788 0.78 0.669 0.750 0.892 1.047 0.807 0.80 0.656 0.740 0.887 1.038 0.825 0.82 0.643 0.729 0.881 1.030 0.843 69 Explain supersaturated expansion in case of flow through nozzle and discuss, briefly, the factors causing it. Represent the phenomenon on h-s diagram indicating superheated zone. State the effects of supersaturation. 70 Air enters into a constant area frictionless duct with M = 3, P = 7 bar and T = 288 K. It is desired to reduce the flow Mach number to 2 at the exit of the duct. Determine the amount of heat added and the corresponding change in pressure.

Problems of Practices of Fluid Mechanics By Brij Bhooshan 11 For air, Cp = 1.003 kj/kgk. Take: M T0/ T0* 3 0.6534 2 0.7934 71 A constant area circular duct is connected to the convergent divergent nozzle exit. The air enters the nozzle from a tank at a pressure of 7 bar (ab) and temp, of 127 C. The pressure at the nozzle exit is 0.19 bar. If the temperature of the air is 3 C at the end of the duct, and the duct length is 17.5 diameter of the duct, find the friction co-efficient of the duct. Consider flow is adiabatic through a duct and isentropic in the nozzle. Use: M 4fLm/D 3 0.522 1.5 0.136 Copyright by Brij Bhooshan @ 2013 Page 11