Solved: Explain why the maximum flow rate per unit area

Problem 3P In air-conditioning applications, the temperature of air is measured by inserting a probe into the flow stream. Thus, the probe actually measures the stagnation temperature. Does this cause any significant error?

Problem 1P A high-speed aircraft is cruising in still air. How does the temperature of air at the nose of the aircraft differ from the temperature of air at some distance from the aircraft?

Problem 163P Combustion gases with k =1.33 enter a converging nozzle at stagnation temperature and pressure of 350°C and 400 kPa, and are discharged into the atmospheric ah at 20°C and 100 kPa. The lowest pressure that will occur within the nozzle is (a) 13 kPa ________________ (b) 100 kPa ________________ (c) 216kPa ________________ (d) 290kPa ________________ (e)315kPa

Problem 4P Air flows through a device such that the stagnation pressure is 0.6 MPa, the stagnation temperature is 400°C, and the velocity is 570 m/s. Determine the static pressure and temperature of the air at this state.

Problem 2P What is dynamic temperature?

Problem 5P Air at 320 K is flowing in a duct at a velocity of (a) 1, (b) 10, (c) 100, and (d) 1000 m/s. Determine the temperature that a stationary probe inserted into the duct will read for each case.

Problem 6P Calculate the stagnation temperature and pressure for the following substances flowing through a duct: (a) helium at 0.25 MPa, 50°C, and 240 m/s; (b) nitrogen at 0.15 MPa, 50°C, and 300 m/s; and (c) steam at 0.1 MPa, 350°C, and 480 m/s.

Problem 7P Determine the stagnation temperature and stagnation pressure of air that is flowing at 36 kPa, 238 K, and 325 m/s.

Problem 8P Steam flows through a device with a stagnation pressure of 120 psia, a stagnation temperature of 700°F, and a velocity of 900 ft/s. Assuming ideal-gas behavior, determine the static pressure and temperature of the steam at this state.

Problem 9P Air enters a compressor with a stagnation pressure of 100 kPa and a stagnation temperature of 35°C, and it is compressed to a stagnation pressure of 900 kPa. Assuming the compression process to be isentropic, determine the power input to the compressor for a mass flow rate of 0.04 kg/s.

Problem 11P What is sound? How is it generated? How does it travel? Can sound waves travel in a vacuum?

Problem 10P Products of combustion enter a gas turbine with a stagnation pressure of 0.75 MPa and a stagnation temperature of 690°C, and they expand to a stagnation pressure of 100 kPa. Taking k= 1.33 and R = 0.287 kJ/kg·K for the products of combustion, and assuming the expansion process to be isen-tropic, determine the power output of the turbine per unit mass flow.

Problem 13P In which medium will sound travel fastest for a given temperature: air, helium, or argon?

Problem 14P In which medium does a sound wave travel faster: in air at 20°C and 1 atm or in air at 20°C and 5 atm?

Problem 15P Does the Mach number of a gas flowing at a constant velocity remain constant? Explain.

Problem 16P Is it realistic to assume that the propagation of sound waves is an isentropic process? Explain.

Problem 12P In which medium does a sound wave travel faster: in cool air or in warm air?

Problem 17P Is the sonic velocity in a specified medium a fixed quantity, or does it change as the properties of the medium change? Explain.

Problem 18P The Airbus A-340 passenger plane has a maximum takeoff weight of about 260,000 kg, a length of 64 m, a wing span of 60 m, a maximum cruising speed of 945 km/h, a seating capacity of 271 passengers, maximum cruising altitude of 14,000 m, and a maximum range of 12,000 km. The air temperature at the crusing altitude is about ?60°C. Determine the Mach number of this plane for the stated limiting conditions.

Problem 19P Carbon dioxide enters an adiabatic nozzle at 1200 K with a velocity of 50 m/s and leaves at 400 K. Assuming constant specific heats at room temperature, determine the Mach number (a) at the inlet and (b) at the exit of the nozzle. Assess the accuracy of the constant specific.heat assumption.

Problem 20P Nitrogen enters a steady-flow heat exchanger at 150 kPa, 10°C, and 100 m/s, and it receives heat in the amount of 120 kJ/kg as it flows through it. Nitrogen leaves the heat. exchanger at 100 kPa with a velocity of 200 m/s. Determine the Mach number of the nitrogen at the inlet and the exit of the heat exchanger.

Problem 21P Assuming ideal gas behavior, determine the speed of sound in refrigerant-134a at 0.9 MPa and 60°C.

Problem 23P Steam flows through a device with a pressure of 120 psia, a temperature of 700°F, and a velocity of 900 ft/s. Determine the Mach number of the steam at this state by assuming ideal-gas behavior with k =1.3.

Problem 25P Air expands isentropicahy from 170 psia and 200°F to 60 psia. Calculate the ratio of the initial to final speed of sound.

Problem 22P Determine the speed of sound in air at (a) 300 K and (b) 1000 K. Also determine the Mach number of an aircraft moving in air at a velocity of 240 m/s for both cases.

Problem 26P Air expands isentropically from 2.2 MPa and 77°C to 0.4 MPa. Calculate the ratio of the initial to the final speed of sound.

Problem 27P Repeat Prob. 17–26 for helium gas. Problem 17–26 Air expands isentropically from 2.2 MPa and 77°C to 0.4 MPa. Calculate the ratio of the initial to the final speed of sound.

Problem 28P The isentropic process for an ideal gas is expressed as PVk=constant. Using this process equation and the definition of the speed sound (Eq. 17–9), obtain the expression for the speed of sound for an ideal gas (Eq. 17–11).

Problem 29P Is it possible to accelerate a gas to a supersonic velocity in a converging nozzle? Explain.

Problem 30P A gas initially at a subsonic velocity enters an adiabatic diverging duct. Discuss how this affects (a) the velocity, (b) the temperature, (c) the pressure, and (d) the density of the fluid.

Problem 32P A gas initially at a supersonic velocity enters an adiabatic converging duct. Discuss how this affects (a) the velocity, (b) the temperature, (c) the pressure, and (d) the density of the fluid.

Problem 31P A gas at a specified stagnation temperature and pressure is accelerated to Ma = 2 in a converging–diverging nozzle and to Ma = 3 in another nozzle. What can you say about the pressures at the throats of these two nozzles?

Problem 33p A gas initially at a supersonic velocity enters an adiabatic diverging duct. Discuss how this affects (a) the velocity, (b) the temperature, (c) the pressure, and (d) the density of the fluid.

Problem 34p Consider a converging nozzle with sonic speed at the exit plane. Now the nozzle exit area is reduced while the nozzle inlet conditions are maintained constant. What will happen to (a) the exit velocity and (b) the mass flow rate through the nozzle?

Problem 35p A gas initially at a subsonic velocity enters an adiabatic converging duct. Discuss how this affects (a) the velocity, (b) the temperature, (c) the pressure, and (d) the density of the fluid.

Problem 36p Helium enters a converging–diverging nozzle at 0.7 MPa, 800 K, and 100 m/s. What are the lowest temperature and pressure that can be obtained at the throat of the nozzle?

Problem 37P Consider a large commercial airplane cruising at a speed of 920 km/h in air at an altitude of 10 km where the standard air temperature is ?50°C. Determine if the speed of this airplane is subsonic or supersonic.

Problem 38P Calculate the critical temperature, pressure, and density of (a) air at 200 kPa, 100°C, and 250 m/s, and (b) helium at 200 kPa, 40°C, and 300 m/s.

Problem 40P Air enters a converging-diverging nozzle at a pressure of 1200 kPa with negligible velocity. What is the lowest pressure that can be obtained at the throat of the nozzle?

Problem 39P Air at 25 psia, 320°F, and Mach number Ma = 0.7 flows through a duct. Calculate the velocity and the stagnation pressure, temperature, and density of air.

Problem 41P In March 2004, NASA successfully launched an experimental supersonic-combustion ramjet engine (called a scramjet) that reached a record-setting Mach number of 7. Taking the air temperature to be ?20?C, determine the speed of this engine.

Problem 42P Reconsider the scram jet engine discussed in Prob. 17–37. Determine the speed of this engine in miles per hour corresponding to a Mach number of 7 in air at a temperature of 0°F.

Problem 43P Air at 200 kPa, 100°C, and Mach number Ma = 0.8 flows through a duct. Calculate the velocity and the stagnation pressure, temperature, and density of the air.

Problem 45P An aircraft is designed to cruise at Mach number Ma = 1.1 at 12,000 m where the atmospheric temperature is 236.15 K. Determine the stagnation temperature on the leading edge of the wing.

Problem 46P Quiescent carbon dioxide at 1200 kPa and 600 K is accelerated isentropicahy to a Mach number of 0.6. Determine the temperature and pressure of the carbon dioxide after acceleration.

Problem 47P Is it possible to accelerate a fluid to supersonic velocities with a velocity other than the sonic velocity at the throat? Explain

Problem 49P How does the parameter Ma* differ from the Mach number Ma?

Problem 50P Consider subsonic flow in a converging nozzle with specified conditions at the nozzle inlet and critical pressure at the nozzle exit What is the effect of dropping the back pressure well below the critical pressure on (a) the exit velocity, (b) the exit pressure, and (c) the mass flow rate through the nozzle?

Problem 51P Consider a converging nozzle and a converging–diverging nozzle having the same throat areas. For the same inlet conditions, how would you compare the mass flow rates through these two nozzles?

Problem 52P Consider gas flow through a converging nozzle with specified inlet conditions. We know that the highest velocity the fluid can have at the nozzle exit is the sonic velocity, at which point the mass flow rate through the nozzle is a maximum. If it were possible to achieve hypersonic velocities at the nozzle exit, how would it affect the mass flow rate through the nozzle?

Problem 53P Consider subsonic flow in a converging nozzle with fixed inlet conditions. What is the effect of dropping the back pressure to the critical pressure on (a) the exit velocity, (b) the exit pressure, and (c) the mass flow rate through the nozzle?

Problem 55P What would happen if we attempted to decelerate a supersonic fluid with a diverging diffuser?

Problem 54P Consider the isentropic flow of a fluid through a converging–diverging nozzle with a subsonic velocity at the throat. How does the diverging section affect (a) the velocity, (b) the pressure, and (c) the mass flow rate of the fluid?

Problem 56P Nitrogen enters a converging-diverging nozzle at 700 kPa and 400 K with a negligible velocity. Determine the critical velocity, pressure, temperature, and density in the nozzle.

Problem 57P For an ideal gas obtain an expression for the ratio of the speed of sound where Ma = 1 to the speed of sound based on the stagnation temperature, c*/c0.

Problem 58P Air enters a converging–diverging nozzle at 1.2 MPa with a negligible velocity. Approximating the flow as isentropic, determine the back pressure that would result in an exit Mach number of 1.8.

Problem 59P Air enters a nozzle at 30 psia, 630 R, and a velocity of 450 ft/s. Approximating the flow as isentropic, determine the pressure and temperature of air at a location where the air velocity equals the speed of sound. What is the ratio of the area at this location to the entrance area?

Problem 60P An ideal gas flows through a passage that first converges and then diverges during an adiabatic, reversible, steady-flow process. For subsonic flow at the inlet, sketch the variation of pressure, velocity, and Mach number along the length of the nozzle when the Mach number at the minimum flow area is equal to unity.

Problem 61P Repeat Prob. 17–63 for supersonic flow at the inlet.

Explain why the maximum flow rate per unit area for a given ideal gas depends only on \(P_{0} / \sqrt{T_{0}}\). For an ideal gas with \(k=1.4\) and \(R=0.287 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\), find the constant \(a\) such that \(\dot{m} / A^{*}=a P_{0} / \sqrt{T_{0}}\). Equation Transcription: Text Transcription: P_0/sqrt T_0 k=1.4 R=0.287 kJ/kg K a ^dot m/A*=aP_0/sqrt T_0

Problem 63P An ideal gas with k = 1.4 is flowing through a nozzle such that the Mach number is 1.8 where the flow area is 36 cm2. Approximating the flow as isentropic, determine the flow area at the location where the Mach number is 0.9.

Problem 64P Repeat Prob. 17–63 for an ideal gas with k = 1.33. Problem 17–63 An ideal gas with k = 1.4 is flowing through a nozzle such that the Mach number is 1.8 where the flow area is 36 cm2. Approximating the flow as isentropic, determine the flow area at the location where the Mach number is 0.9.

Problem 65P Air enters a converging–diverging nozzle of a supersonic wind tunnel at 150 psia and 100°F with a low velocity. The flow area of the test section is equal to the exit area of the nozzle, which is 5 ft2. Calculate the pressure, temperature, velocity, and mass flow rate in the test section for a Mach number Ma = 2. Explain why the air must be very dry for this application.

Problem 66P Air enters a nozzle at 0.5 MPa, 420 K, and a velocity of 110 m/s. Approximating the flow as isentropic, determine the pressure and temperature of air at a location where the air velocity equals the speed of sound. What is the ratio of the area at this location to the entrance area?

Problem 67P Repeat Prob. 17–66 assuming the entrance velocity is negligible. Problem 17–66 Air enters a nozzle at 0.5 MPa, 420 K, and a velocity of 110 m/s. Approximating the flow as isentropic, determine the pressure and temperature of air at a location where the air velocity equals the speed of sound. What is the ratio of the area at this location to the entrance area?

Problem 70P Repeat Prob. 17–66 assuming the entrance velocity is negligible. Problem 17–66 Air enters a nozzle at 0.5 MPa, 420 K, and a velocity of 110 m/s. Approximating the flow as isentropic, determine the pressure and temperature of air at a location where the air velocity equals the speed of sound. What is the ratio of the area at this location to the entrance area?

Problem 71P What do the states on the Fanno line and the Rayleigh line represent? What do the intersection points of these two curves represent?

Problem 73P How does the normal shock affect (a) the fluid velocity, (b) the static temperature, (c) the stagnation temperature, (d) the static pressure, and (e) the stagnation pressure?

Problem 72P It is claimed that an oblique shock can be analyzed like a normal-shock provided that the normal component of velocity (normal to the shock surface) is used in the analysis. Do you agree with this claim?

Problem 76P Can the Mach number of a fluid be greater than 1after a normal shock wave? Explain.

Problem 75P For an oblique shock to occur, does the upstream flow have to be supersonic? Does the flow downstream of an oblique shock have to be subsonic?

Problem 74P How do oblique shocks occur? How do oblique shocks differ from normal shocks?

Problem 77P Consider supersonic airflow approaching the nose of a two-dimensional wedge and experiencing an oblique shock. Under what conditions does an oblique shock detach from the nose of the wedge and form a bow wave? What is the numerical value of the shock angle of the detached shock at the nose?

Problem 78P Consider supersonic flow impinging on the rounded nose of an aircraft. Is the oblique shock that forms in front of the nose an attached or a detached shock? Explain.

Problem 79P Can a shock wave develop in the converging section of a converging–diverging nozzle? Explain.

Problem 80P Air enters a normal shock at 26 kPa, 230 K, and 815 m/s. Calculate the stagnation pressure and Mach number upstream of the shock, as well as pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the shock.

Problem 81P Calculate the entropy change of air across the normal shock wave in Problem 17–80. Problem 17–80 Air enters a normal shock at 26 kPa, 230 K, and 815 m/s. Calculate the stagnation pressure and Mach number upstream of the shock, as well as pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the shock.

Problem 82P For an ideal gas flowing through a normal shock, develop a relation for V2/V1 in terms of kMa1and Ma2.

Problem 83P Air enters a converging–diverging nozzle with low velocity at 2.0 MPa and 100°C. If the exit area of the nozzle is 3.5 times the throat area, what must the back pressure be to produce a normal shock at the exit plane of the nozzle?

Problem 87P Air enters a converging–diverging nozzle of a supersonic wind tunnel at 1 MPa and 300 K with a low velocity. If a normal shock wave occurs at the exit plane of the nozzle at Ma = 2.4, determine the pressure, temperature, Mach number, velocity, and stagnation pressure after the shock wave.

Problem 90P Air flowing at 32 kPa, 240 K, and Ma1 = 3.6 is forced to undergo an expansion turn of 15°. Determine the Mach number, pressure, and temperature of air after the expansion.

Problem 89P Consider supersonic airflow approaching the nose of a two-dimensional wedge at a Mach number of 5. Using Fig. 17–43, determine the minimum shock angle and the maximum deflection angle a straight oblique shock can have.

Consider the supersonic flow of air at upstream conditions of \(70 \mathrm{kPa}\) and \(260 \mathrm{~K}\) and a Mach number of 2.4 over a two-dimensional wedge of half-angle \(10^{\circ}\). If the axis of the wedge is tilted \(25^{\circ}\) with respect to the upstream air flow, determine the downstream Mach number, pressure, and temperature above the wedge. Equation Transcription: Text Transcription: 70 kPa 260 K 10^circ 25^circC

Problem 92P Reconsider Prob. 17–94. Determine the downstream Mach number, pressure, and temperature below the wedge for a strong oblique shock for an upstream Mach number of 5.

Problem 96P Air flowing steadily in a nozzle experiences a normal shock at a Mach number of Ma = 2.6. If the pressure and temperature of air are 58 kPa and 270 K, respectively, upstream of the shock, calculate the pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the shock. Compare these results to those for helium undergoing a nor-mal shock under the same conditions.

Problem 95P Air flowing at 60 kPa, 240 K, and a Mach number of 3.4 impinges on a two-dimensional wedge of half-angle 8°. Determine the two possible oblique shock angles, ?weak and ?strong, that could be formed by this wedge. For each case, calculate the pressure, temperature, and Mach number downstream of the oblique shock.

Problem 97P Calculate the entropy changes of air and helium across the normal shock wave in Prob. 17–96. Problem 17–96 Air flowing steadily in a nozzle experiences a normal shock at a Mach number of Ma = 2.6. If the pressure and temperature of air are 58 kPa and 270 K, respectively, upstream of the shock, calculate the pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the shock. Compare these results to those for helium undergoing a nor-mal shock under the same conditions.

Problem 98P What is the effect of heating the fluid on the flow velocity in subsonic Rayleigh flow? Answer the same ques-tions for supersonic Rayleigh flow.

Problem 84P What must the back pressure be in Prob. 17–84 for a normal shock to occur at a location where the cross-sectional area is twice the throat area?

Problem 100P What is the effect of heat gain and heat loss on the entropy of the fluid during Rayleigh flow?

Problem 99P On a T-sdiagram of Rayleigh flow, what do the points on the Rayleigh line represent?

Problem 85P Air flowing steadily in a nozzle experiences a normal shock at a Mach number of Ma = 2.5. If the pressure and temperature of air are 10.0 psia and 440.5 R, respectively, upstream of the shock, calculate the pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the shock. Compare these results to those for helium undergoing a normal shock under the same conditions.

Problem 101P Consider subsonic Rayleigh flow of air with a Mach number of 0.92. Heat is now transferred to the fluid and the Mach number increases to 0.95. Does the temperature Tof the fluid increase, decrease, or remain constant during this process? How about the stagnation temperature T0?

Problem 104P Argon gas enters a constant cross-sectional area duct at Ma1 = 0.2, P1 = 320 kPa, and T1 = 400 K at a rate of 1.2 kg/s. Disregarding frictional losses, determine the highest rate of heat transfer to the argon without reducing the mass flow rate.

Problem 102P What is the effect of heating the fluid on the flow velocity in subsonic Rayleigh flow? Answer the same questions for supersonic Rayleigh flow.

Problem 105P Air is heated as it flows subsonically through a duct. When the amount of heat transfer reaches 67 kJ/kg, the flow is observed to be choked, and the velocity and the static pressure are measured to be 680 m/s and 270 kPa. Disregarding frictional losses, determine the velocity, static temperature, and static pressure at the duct inlet.

Problem 103P Consider subsonic Rayleigh flow that is accelerated to sonic velocity (Ma = 1) at the duct exit by heating. If the fluid continues to be heated, will the flow at duct exit be supersonic, subsonic, or remain sonic?

Problem 106P Compressed air from the compressor of a gas turbine enters the combustion chamber at T1 = 700 K, P1 = 600 kPa, and Ma1 = 0.2 at a rate of 0.3 kg/s. Via combustion, heat is transferred to the air at a rate of 150 kJ/s as it flows through the duct with negligible friction. Determine the Mach number at the duct exit, and the drop in stagnation pressure P01 – P02 during this process.

Problem 107P Repeat Prob. 17–106 for a heat transfer rate of 300 kJ/s. Problem 17–106 Compressed air from the compressor of a gas turbine enters the combustion chamber at T1 = 700 K, P1 = 600 kPa, and Ma1 = 0.2 at a rate of 0.3 kg/s. Via combustion, heat is transferred to the air at a rate of 150 kJ/s as it flows through the duct with negligible friction. Determine the Mach number at the duct exit, and the drop in stagnation pressure P01 – P02 during this process.

Air enters a rectangular duct at \(T_{1}=300 \mathrm{~K}, P_{1}=\) \(420 \mathrm{kPa}\), and \(\mathrm{Ma}_{1}=2\). Heat is transferred to the air in the amount of \(55 \mathrm{~kJ} / \mathrm{kg}\) as it flows through the duct. Disregarding frictional losses, determine the temperature and Mach number at the duct exit. Equation Transcription: Text Transcription: T_1=300 K, P_1=420 kPa, Ma_1=2 55 kJ/kg

Problem 108P Air flows with negligible friction through a 4-in-diameter duct at a rate of 5 lbm/s. The temperature and pressure at the inlet are T1= 800 R and P1 = 30 psia, and the Mach number at the exit is Ma2 = 1. Determine the rate of heat transfer and the pressure drop for this section of the duct.

Problem 110P Air is heated as it flows through a 6 in × 6 in square duct with negligible friction. At the inlet, air is at T1 = 700 R, P1 = 80 psia, and V1 = 260 ft/s. Determine the rate at which heat must be transferred to the air to choke the flow at the duct exit, and the entropy change of air during this process.

Problem 112P Repeat Prob. 17–112 assuming air is cooled in the amount of 55 kJ/kg.

Consider a 16-cm-diameter tubular combustion chamber. Air enters the tube at \(450 \mathrm{~K}, 380 \mathrm{kPa}\), and \(55 \mathrm{~m} / \mathrm{s}\). Fuel with a heating value of \(39,000 \mathrm{~kJ} / \mathrm{kg}\) is burned by spraying it into the air. If the exit Mach number is 0.8, determine the rate at which the fuel is burned and the exit temperature. Assume complete combustion and disregard the increase in the mass flow rate due to the fuel mass. Equation Transcription: Text Transcription: 450 K, 380 kPa 55m/s 39,000 kJ/kg

Problem 116P Steam enters a converging nozzle at 5.0 MPa and 400°C with a negligible velocity, and it exits at 3.0 MPa. For a nozzle exit area of 60 cm2, determine the exit velocity, mass flow rate, and exit Mach number if the nozzle (a) is isentropic and (b) has an efficiency of 94 percent.

Problem 117P Steam enters a converging nozzle at 450 psia and 900°F with a negligible velocity, and it exits at 275 psia. For a nozzle exit area of 3.75 in2, determine the exit velocity, mass flow rate, and exit Mach number if the nozzle (a) is isentropic and (b) has an efficiency of 90 percent.

Problem 115P What is supersaturation? Under what conditions does it occur?

Problem 118P Steam enters a converging–diverging nozzle at 1 MPa and 500°C with a negligible velocity at a mass flow rate of 2.5 kg/s, and it exits at a pressure of 200 kPa. Assuming the flow through the nozzle to be isentropic, determine the exit area and the exit Mach number.

Problem 119P Repeat Prob. 17–118 for a nozzle efficiency of 85 percent. Problem 17–118 Steam enters a converging–diverging nozzle at 1 MPa and 500°C with a negligible velocity at a mass flow rate of 2.5 kg/s, and it exits at a pressure of 200 kPa. Assuming the flow through the nozzle to be isentropic, determine the exit area and the exit Mach number.

Problem 121P A stationary temperature probe inserted into a duct where air is flowing at 190 m/s reads 85°C. What is the actual temperature of the air?

Problem 120P The thrust developed by the engine of a Boeing 777 is about 380 kN. Assuming choked flow in the nozzles, determine the mass flow rate of air through the nozzle. Take the ambient conditions to be 220 K and 40 kPa.

Problem 122P Nitrogen enters a steady-flow heat exchanger at 150 kPa, 10°C, and 100 m/s, and it receives heat in the amount of 150 kJ/kg as it flows through it. The nitrogen leaves the heat exchanger at 100 kPa with a velocity of 200 m/s. Determine the stagnation pressure and temperature of the nitrogen at the inlet and exit states.

Plot the mass flow parameter \(\dot{m} \sqrt{R T_{0}} /\left(A P_{0}\right)\) versus the Mach number for \(k=1.2,1.4\), and 1.6 in the range of \(0 \leq \mathrm{Ma} \leq 1\). Equation Transcription: Text Transcription: ^dot m sqrt RT_0/(AP_0) k=1.2, 1.4, 1.6 0 leq Ma leq 1

Obtain Eq. 17-10 by starting with Eq. 17-9 and using the cyclic rule and the thermodynamic property relations \(\frac{c_{p}}{T}=\left(\frac{\partial s}{\partial T}\right)_{P}\) and \(\frac{c_{v}}{T}=\left(\frac{\partial s}{\partial T}\right)_{v}\). Equation Transcription: Text Transcription: C_p/T=(partial_ s/partial_T)_P C_V/T=(partial_s/partial_T)_V

Problem 125P For ideal gases undergoing isentropic flows, obtain expressions for P/P*, T/T*,and p/p*as functions of kand Ma.

Problem 127P A subsonic airplane is flying at a 5000-m altitude where the atmospheric conditions are 54 kPa and 256 K. A Pitot static probe measures the difference between the static and stagnation pressures to be 16 kPa. Calculate the speed of the airplane and the flight Mach number.

Problem 126P Using Eqs. 17–4,17-13, and 17–14, verify that for the steady flow of ideal gases dT0/T = dA/A+ (1 - Ma2) dV/V.Explain the effect of heating and area changes on the velocity of an ideal gas in steady flow for (a) subsonic flow and (b) supersonic flow.

Problem 128P Derive an expression for the speed of sound based on van der Waals' equation of state P = RT(v– b) – a/v2. Using this relation, determine the speed of sound in carbon dioxide at 80°C and 320 kPa, and compare your result to that obtained by assuming ideal-gas behavior. The van der Waals constants for carbon dioxide are a = 364.3 kPa·m6/kmol2 and b = 0.0427 m3/kmol.

Problem 129P Helium enters a nozzle at 0.6 MPa, 560 K, and a velocity of 120 m/s. Assuming isentropic flow, determine the pressure and temperature of helium at a location where the velocity equals the speed of sound. What is the ratio of the area at this location to the entrance area?

Problem 130P Repeat Problem 17–129 assuming the entrance velocity is negligible. Problem 17–129 Helium enters a nozzle at 0.6 MPa, 560 K, and a velocity of 120 m/s. Assuming isentropic flow, determine the pressure and temperature of helium at a location where the velocity equals the speed of sound. What is the ratio of the area at this location to the entrance area?

Problem 132P Nitrogen enters a duct with varying flow area at 400 K, 100 kPa, and a Mach number of 0.3. Assuming a steady, isentropic flow, determine the temperature, pressure, and Mach number at a location where the flow area has been reduced by 20 percent.

Problem 133P Repeat Prob. 17–132 for an inlet Mach number of 0.5. Problem 17–132 Nitrogen enters a duct with varying flow area at 400 K, 100 kPa, and a Mach number of 0.3. Assuming a steady, isentropic flow, determine the temperature, pressure, and Mach number at a location where the flow area has been reduced by 20 percent.

Problem 134P Nitrogen enters a converging-diverging nozzle at 620 kPa and 310 K with a negligible velocity, and it experi-ences a normal shock at a location where the Mach number is Ma = 3.0. Calculate the pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the shock. Compare these results to those of air undergoing a normal shock at the same conditions.

Problem 135P An aircraft flies with a Mach number Ma1 = 0.9 at an altitude of 7000 m where the pressure is 41.1 kPa and the temperature is 242.7 K. The diffuser at the engine inlet has an exit Mach number of Ma2 = 0.3. For a mass flow rate of 38 kg/s, determine the static pressure rise across the diffuser and the exit area.

Problem 136P Consider an equimolar mixture of oxygen and nitrogen. Determine the critical temperature, pressure, and density for stagnation temperature and pressure of 550 K and 350 kPa.

Problem 137P Helium expands in a nozzle from 220 psia, 740 R, and negligible velocity to 15 psia. Calculate the throat and exit areas for a mass flow rate of 0.2 lbm/s, assuming the nozzle is isentropic. Why must this nozzle be converging-diverging?

Air is heated as it flows subsonically through a \(10 \mathrm{~cm} \times 10 \mathrm{~cm}\) square duct. The properties of air at the inlet are maintained at \(\mathrm{Ma}_{1}=0.6, P_{1}=350 \mathrm{kPa}\), and \(T_{1}=420 \mathrm{~K}\) at all times. Disregarding frictional losses, determine the highest rate of heat transfer to the air in the duct without affecting the inlet conditions. Equation Transcription: Text Transcription: 10cm 10 cm Ma_1=0.6,P_1=350 kPa T_1=420 K

Problem 140P Helium expands in a nozzle from 1 MPa, 500 K, and negligible velocity to 0.1 MPa. Calculate the throat and exit areas for a mass flow rate of 0.46 kg/s, assuming the nozzle is isentropic. Why must this nozzle be converging-diverging?

Problem 146P Air at sonic conditions and at static temperature and pressure of 340 K and 250 kPa, respectively, is to be accelerated to a Mach number of 1.6 by cooling it as it flows through a channel with constant cross-sectional area. Disregarding frictional effects, determine the required heat transfer from the air, in kJ/kg.

Problem 147P Air is cooled as it flows through a 20-cm-diameter duct. The inlet conditions are Ma1 = 1.2, T01= 350 K, and P01, = 240 kPa and the exit Mach number is Ma2 = 2.0. Disregarding frictional effects, determine the rate of cooling of air.

Problem 148P Saturated steam enters a converging–diverging nozzle at 1.75 MPa, 10 percent moisture, and negligible velocity, and it exits at 1.2 MPa. For a nozzle exit area of 25 cm2, determine the throat area, exit velocity, mass flow rate, and exit Mach number if the nozzle (a) is isentropic and (b) has an efficiency of 92 percent.

Repeat Prob. 17–143 for helium.

Problem 151P Find the expression for the ratio of the stagnation pressure after a shock wave to the static pressure before the shock wave as a function of kand the Mach number upstream of the shock wave Ma1.

Problem 145P Air is accelerated as it is heated in a duct with negligible friction. Air enters at V1 = 100 m/s, T1 = 400 K, and P1 = 35 kPa and then exits at a Mach number of Ma2 = 0.8. Determine the heat transfer to the air, in kJ/kg. Also determine the maximum amount of heat transfer without reducing the mass flow rate of air.

Problem 155P Air is flowing in a wind tunnel at 25°C, 80 kPa, and 250 m/s. The stagnation pressure at the probe inserted into the flow section is (a)87kPa ________________ (b)93kPa ________________ (c) 113 kPa ________________ (d) 119 kPa ________________ (e)125kPa

Problem 154P An aircraft is cruising in still air at 5°C at a velocity of 400 m/s. The air temperature at the nose of the aircraft where stagnation occurs is (a) 5°C ________________ (b) 25°C ________________ (c) 55°C ________________ (d) 80°C ________________ (e) 85°C

Problem 156P An aircraft is reported to be cruising in still air at –20°C and 40 kPa at a Mach number of 0.86. The velocity of the aircraft is (a) 91 m/s (b) 220 m/s (c) 186 m/s (d) 274 m/s (e) 378 m/s

Problem 158P Consider a converging nozzle with a low velocity at the inlet and sonic velocity at the exit plane. Now the nozzle exit diameter is reduced by half while the nozzle inlet temperature and pressure are maintained the same. The nozzle exit velocity will (a) remain the same ________________ (b) double ________________ (c) quadruple ________________ (d) go down by half ________________ (e) go down to one-fourth

roblem 157P Air is flowing in a wind tunnel at 12°C and 66 kPa at a velocity of 230 m/s. The Mach number of the flow is (a) 0.54 m/s ________________ (b) 0.87 m/s ________________ (c) 3.3 m/s ________________ (d) 0.36 m/s ________________ (e) 0.68 m/s

Problem 159P Air is approaching a converging–diverging nozzle with a low velocity at 12°C and 200 kPa, and it leaves the nozzle at a supersonic velocity. The velocity of. air at the throat of the nozzle is (a) 338 m/s ________________ (b) 309 m/s ________________ (c) 280 m/s ________________ (d) 256 m/s ________________ (e) 95 m/s

Problem 162P Consider gas flow through a converging–diverging nozzle. Of the five following statements, select the one that is incorrect: (a) The fluid velocity at the throat can never exceed the speed of sound. ________________ (b) If the fluid velocity at the throat is below the speed of sound, the diversion section will act like a diffuser. ________________ (c) If the fluid enters the diverging section with a Mach number greater than one, the flow at the nozzle exit will be supersonic. ________________ (d) There will be no flow through the nozzle-if the back pressure equals the stagnation pressure. ________________ (e) The fluid velocity decreases, the entropy increases, and stagnation enthalpy remains constant during flow through a normal shock.

Problem 160P Argon gas is approaching a converging–diverging nozzle with a low velocity at 20°C and 120 kPa, and it leaves the nozzle at a supersonic velocity. If the cross-sectional area of the throat is 0.015 m2, the mass flow rate of argon through the nozzle is (a) 0.41 kg/s ________________ (b) 3.4 kg/s ________________ (c) 5.3 kg/s ________________ (d) 17 kg/s ________________ (e) 22 kg/s

Problem 161P Carbon dioxide enters a converging–diverging nozzle at 60 m/s, 310°C, and 300 kPa, and it leaves the nozzle at a supersonic velocity. The velocity of carbon dioxide at the throat of the nozzle is (a) 125 m/s ________________ (b) 225 m/s ________________ (c) 312 m/s ________________ (d) 353 m/s ________________ (e) 377 m/s

A high-speed aircraft is cruising in still air. How does the temperature of air at the nose of the aircraft differ from the temperature of air at some distance from the aircraft?

What is dynamic temperature?

In air-conditioning applications, the temperature of air is measured by inserting a probe into the flow stream. Thus, the probe actually measures the stagnation temperature. Does this cause any significant error?

Air flows through a device such that the stagnation pressure is , the stagnation temperature is , and the velocity is . Determine the static pressure and temperature of the air at this state.

Air at is flowing in a duct at a velocity of (a) 1, (b) 10, (c) 100, and (d) . Determine the temperature that a stationary probe inserted into the duct will read for each case.

Calculate the stagnation temperature and pressure for the following substances flowing through a duct: (a) helium at , , and ; (b) nitrogen at , , and ; and (c) steam at , , and .

Determine the stagnation temperature and stagnation pressure of air that is flowing at , , and .

Steam flows through a device with a stagnation pressure of , a stagnation temperature of , and a velocity of . Assuming ideal-gas behavior, determine the static pressure and temperature of the steam at this state.

Air enters a compressor with a stagnation pressure of and a stagnation temperature of , and it is compressed to a stagnation pressure of . Assuming the compression process to be isentropic, determine the power input to the compressor for a mass flow rate of .

Products of combustion enter a gas turbine with a stagnation pressure of and a stagnation temperature of , and they expand to a stagnation pressure of . Taking and for the products of combustion, and assuming the expansion process to be isentropic, determine the power output of the turbine per unit mass flow.

What is sound? How is it generated? How does it travel? Can sound waves travel in a vacuum?

In which medium does a sound wave travel faster: in cool air or in warm air?

In which medium will sound travel fastest for a given temperature: air, helium, or argon?

In which medium does a sound wave travel faster: in air at and or in air at and ?

Does the Mach number of a gas flowing at a constant velocity remain constant? Explain.

Is it realistic to approximate that the propagation of sound waves is an isentropic process? Explain.

Is the sonic velocity in a specified medium a fixed quantity, or does it change as the properties of the medium change? Explain.

The Airbus A-340 passenger plane has a maximum takeoff weight of about 260,000 kg, a length of 64 m, a wing span of 60 m, a maximum cruising speed of , a seating capacity of 271 passengers, a maximum cruising altitude of 14,000 m, and a maximum range of 12,000 km. The air temperature at the cruising altitude is about . Determine the Mach number of this plane for the stated limiting conditions.

Carbon dioxide enters an adiabatic nozzle at with a velocity of and leaves at . Assuming constant specific heats at room temperature, determine the Mach number (a) at the inlet and (b) at the exit of the nozzle. Assess the accuracy of the constant specific heat approximation.

Nitrogen enters a steady-flow heat exchanger at , , and , and it receives heat in the amount of as it flows through it. Nitrogen leaves the heat exchanger at with a velocity of . Determine the Mach number of the nitrogen at the inlet and the exit of the heat exchanger.

Assuming ideal gas behavior, determine the speed of sound in refrigerant-134a at and .

Determine the speed of sound in air at (a) 300 K and (b) 800 K. Also determine the Mach number of an aircraft moving in air at a velocity of for both cases.

Steam flows through a device with a pressure of 120 psia, a temperature of 700F, and a velocity of 900 ft/s. Determine the Mach number of the steam at this state by assuming ideal-gas behavior with k 5 1.3. A

Reconsider Prob. 1723E. Using EES (or other) software, compare the Mach number of steam flow over the temperature range 350 to 700F. Plot the Mach number as a function of temperature.

Air expands isentropically from 170 psia and 200F to 60 psia. Calculate the ratio of the initial to final speed of sound.

Air expands isentropically from 2.2 MPa and 77C to 0.4 MPa. Calculate the ratio of the initial to the final speed of sound.

Repeat Prob. 1726 for helium gas.

The isentropic process for an ideal gas is expressed as Pvk 5 constant. Using this process equation and the definition of the speed of sound (Eq. 179), obtain the expression for the speed of sound for an ideal gas (Eq. 1711).

Is it possible to accelerate a gas to a supersonic velocity in a converging nozzle? Explain.

A gas initially at a subsonic velocity enters an adiabatic diverging duct. Discuss how this affects (a) the velocity, (b) the temperature, (c) the pressure, and (d) the density of the fluid

A gas at a specified stagnation temperature and pressure is accelerated to Ma 5 2 in a convergingdiverging nozzle and to Ma 5 3 in another nozzle. What can you say about the pressures at the throats of these two nozzles?

A gas initially at a supersonic velocity enters an adiabatic converging duct. Discuss how this affects (a) the velocity, (b) the temperature, (c) the pressure, and (d) the density of the fluid.

A gas initially at a supersonic velocity enters an adiabatic diverging duct. Discuss how this affects (a) the velocity, (b) the temperature, (c) the pressure, and (d) the density of the fluid.

Consider a converging nozzle with sonic speed at the exit plane. Now the nozzle exit area is reduced while the nozzle inlet conditions are maintained constant. What will happen to (a) the exit velocity and (b) the mass flow rate through the nozzle?

A gas initially at a subsonic velocity enters an adiabatic converging duct. Discuss how this affects (a) the velocity, (b) the temperature, (c) the pressure, and (d) the density of the fluid.

Helium enters a convergingdiverging nozzle at 0.7 MPa, 800 K, and 100 m/s. What are the lowest temperature and pressure that can be obtained at the throat of the nozzle?

Consider a large commercial airplane cruising at a speed of 1050 km/h in air at an altitude of 10 km where the standard air temperature is 2508C. Determine if the speed of this airplane is subsonic or supersonic.

Calculate the critical temperature, pressure, and density of (a) air at 200 kPa, 1008C, and 250 m/s, and (b) helium at 200 kPa, 408C, and 300 m/s.

Air at 25 psia, 3208F, and Mach number Ma 5 0.7 flows through a duct. Calculate the velocity and the stag nation pressure, temperature, and density of air.

Air enters a convergingdiverging nozzle at a pressure of 1200 kPa with negligible velocity. What is the lowest pressure that can be obtained at the throat of the nozzle?

In March 2004, NASA successfully launched an experimental supersonic-combustion ramjet engine (called a scramjet) that reached a record-setting Mach number of 7. Taking the air temperature to be 2208C, determine the speed of this engine.

Reconsider the scram jet engine discussed in Prob. 1741. Determine the speed of this engine in miles per hour corresponding to a Mach number of 7 in air at a temperature of 08F.

Air at 200 kPa, 1008C, and Mach number Ma 5 0.8 flows through a duct. Calculate the velocity and the stagnation pressure, temperature, and density of the air.

Reconsider Prob. 1743. Using EES (or other) software, study the effect of Mach numbers in the range 0.1 to 2 on the velocity, stagnation pressure, temperature, and density of air. Plot each parameter as a function of the Mach number.

An aircraft is designed to cruise at Mach number Ma 5 1.1 at 12,000 m where the atmospheric temperature is 236.15 K. Determine the stagnation temperature on the leading edge of the wing.

Quiescent carbon dioxide at 1200 kPa and 600 K is accelerated isentropically to a Mach number of 0.6. Determine the temperature and pressure of the carbon dioxide after acceleration.

Is it possible to accelerate a fluid to supersonic velocities with a velocity other than the sonic velocity at the throat? Explain

What would happen if we tried to further accelerate a supersonic fluid with a diverging diffuser?

How does the parameter Ma* differ from the Mach number Ma?

Consider subsonic flow in a converging nozzle with specified conditions at the nozzle inlet and critical pressure at the nozzle exit. What is the effect of dropping the back pressure well below the critical pressure on (a) the exit velocity, (b) the exit pressure, and (c) the mass flow rate through the nozzle?

Consider a converging nozzle and a converging diverging nozzle having the same throat areas. For the same inlet conditions, how would you compare the mass flow rates through these two nozzles?

Consider gas flow through a converging nozzle with specified inlet conditions. We know that the highest velocity the fluid can have at the nozzle exit is the sonic velocity, at which point the mass flow rate through the nozzle is a maximum. If it were possible to achieve hypersonic velocities at the nozzle exit, how would it affect the mass flow rate through the nozzle?

Consider subsonic flow in a converging nozzle with fixed inlet conditions. What is the effect of dropping the back pressure to the critical pressure on (a) the exit velocity, (b) the exit pressure, and (c) the mass flow rate through the nozzle?

Consider the isentropic flow of a fluid through a convergingdiverging nozzle with a subsonic velocity at the throat. How does the diverging section affect (a) the velocity, (b) the pressure, and (c) the mass flow rate of the fluid?

What would happen if we attempted to decelerate a supersonic fluid with a diverging diffuser?

Nitrogen enters a convergingdiverging nozzle at 700 kPa and 400 K with a negligible velocity. Determine the critical velocity, pressure, temperature, and density in the nozzle.

For an ideal gas obtain an expression for the ratio of the speed of sound where Ma 5 1 to the speed of sound based on the stagnation temperature, c*/c0.

Air enters a convergingdiverging nozzle at 1.2 MPa with a negligible velocity. Approximating the flow as isentropic, determine the back pressure that would result in an exit Mach number of 1.8.

Air enters a nozzle at 30 psia, 630 R, and a velocity of 450 ft/s. Approximating the flow as isentropic, determine the pressure and temperature of air at a location where the air velocity equals the speed of sound. What is the ratio of the area at this location to the entrance area?

An ideal gas flows through a passage that first converges and then diverges during an adiabatic, reversible, steady-flow process. For subsonic flow at the inlet, sketch the variation of pressure, velocity, and Mach number along the length of the nozzle when the Mach number at the minimum flow area is equal to unity.

Repeat Prob. 1760 for supersonic flow at the inlet.

Explain why the maximum flow rate per unit area for a given ideal gas depends only on P0 /!T0. For an ideal gas with k 5 1.4 and R 5 0.287 kJ/kgK, find the constant a such that m # /A* 5 aP0 /!T 0.

An ideal gas with k 5 1.4 is flowing through a nozzle such that the Mach number is 1.8 where the flow area is 36 cm2 . Approximating the flow as isentropic, determine the flow area at the location where the Mach number is 0.9.

Repeat Prob. 1763 for an ideal gas with k 5 1.33.

Air enters a convergingdiverging nozzle of a supersonic wind tunnel at 150 psia and 1008F with a low velocity. The flow area of the test section is equal to the exit area of the nozzle, which is 5 ft2 . Calculate the pressure, temperature, velocity, and mass flow rate in the test section for a Mach number Ma 5 2. Explain why the air must be very dry for this application.

Air enters a nozzle at 0.5 MPa, 420 K, and a velocity of 110 m/s. Approximating the flow as isentropic, determine the pressure and temperature of air at a location where the air velocity equals the speed of sound. What is the ratio of the area at this location to the entrance area?

Repeat Prob. 1766 assuming the entrance velocity is negligible.

Air at 900 kPa and 400 K enters a converging nozzle with a negligible velocity. The throat area of the nozzle is 10 cm2 . Approximating the flow as isentropic, calculate and plot the exit pressure, the exit velocity, and the mass flow rate versus the back pressure Pb for 0.9 $ Pb $ 0.1 MPa.

Reconsider Prob. 1768. Using EES (or other) software, solve the problem for the inlet conditions of 0.8 MPa and 1200 K.

Are the isentropic relations of ideal gases applicable for flows across (a) normal shock waves, (b) oblique shock waves, and (c) PrandtlMeyer expansion waves?

What do the states on the Fanno line and the Rayleigh line represent? What do the intersection points of these two curves represent?

It is claimed that an oblique shock can be analyzed like a normal shock provided that the normal component of velocity (normal to the shock surface) is used in the analysis. Do you agree with this claim?

How does the normal shock affect (a) the fluid velocity, (b) the static temperature, (c) the stagnation temperature, (d ) the static pressure, and (e) the stagnation pressure?

How do oblique shocks occur? How do oblique shocks differ from normal shocks?

For an oblique shock to occur, does the upstream flow have to be supersonic? Does the flow downstream of an oblique shock have to be subsonic?

Can the Mach number of a fluid be greater than 1 after a normal shock wave? Explain.

Consider supersonic airflow approaching the nose of a two-dimensional wedge and experiencing an oblique shock. Under what conditions does an oblique shock detach from the nose of the wedge and form a bow wave? What is the numerical value of the shock angle of the detached shock at the nose?

Consider supersonic flow impinging on the rounded nose of an aircraft. Is the oblique shock that forms in front of the nose an attached or a detached shock? Explain.

Can a shock wave develop in the converging section of a convergingdiverging nozzle? Explain.

Air enters a normal shock at 26 kPa, 230 K, and 815 m/s. Calculate the stagnation pressure and Mach number upstream of the shock, as well as pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the shock.

Calculate the entropy change of air across the normal shock wave in Problem 1780.

For an ideal gas flowing through a normal shock, develop a relation for V2/V1 in terms of k, Ma1, and Ma2.

Air enters a convergingdiverging nozzle with low velocity at 2.0 MPa and 1008C. If the exit area of the nozzle is 3.5 times the throat area, what must the back pressure be to produce a normal shock at the exit plane of the nozzle?

What must the back pressure be in Prob. 1783 for a normal shock to occur at a location where the cross-sectional area is twice the throat area?

Air flowing steadily in a nozzle experiences a normal shock at a Mach number of Ma 5 2.5. If the pressure and temperature of air are 10.0 psia and 440.5 R, respectively, upstream of the shock, calculate the pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the shock. Compare these results to those for helium undergoing a normal shock under the same conditions.

Reconsider Prob. 1785E. Using EES (or other) software, study the effects of both air and helium flowing steadily in a nozzle when there is a normal shock at a Mach number in the range 2 , Ma1 , 3.5. In addition to the required information, calculate the entropy change of the air and helium across the normal shock. Tabulate the results in a parametric table.

Air enters a convergingdiverging nozzle of a supersonic wind tunnel at 1 MPa and 300 K with a low velocity. If a normal shock wave occurs at the exit plane of the nozzle at Ma 5 2.4, determine the pressure, temperature, Mach number, velocity, and stagnation pressure after the shock wave.

Using EES (or other) software, calculate and plot the entropy change of air across the normal shock for upstream Mach numbers between 0.5 and 1.5 in increments of 0.1. Explain why normal shock waves can occur only for upstream Mach numbers greater than Ma 5 1.

Consider supersonic airflow approaching the nose of a two-dimensional wedge at a Mach number of 5. Using Fig. 1743, determine the minimum shock angle and the maximum deflection angle a straight oblique shock can have.

Air flowing at 32 kPa, 240 K, and Ma1 5 3.6 is forced to undergo an expansion turn of 158. Determine the Mach number, pressure, and temperature of air after the expansion

Consider the supersonic flow of air at upstream conditions of 70 kPa and 260 K and a Mach number of 2.4 over a two-dimensional wedge of half-angle 108. If the axis of the wedge is tilted 258 with respect to the upstream air flow, determine the downstream Mach number, pressure, and temperature above the wedge.

Reconsider Prob. 1791. Determine the downstream Mach number, pressure, and temperature below the wedge for a strong oblique shock for an upstream Mach number of 5.

Air at 12 psia, 308F, and a Mach number of 2.0 is forced to turn upward by a ramp that makes an 88 angle off the flow direction. As a result, a weak oblique shock forms. Determine the wave angle, Mach number, pressure, and temperature after the shock.

Air flowing at 8 psia, 480 R, and Ma1 5 2.0 is forced to undergo a compression turn of 158. Determine the Mach number, pressure, and temperature of air after the compression.

Air flowing at 60 kPa, 240 K, and a Mach number of 3.4 impinges on a two-dimensional wedge of half-angle 88. Determine the two possible oblique shock angles, bweak and bstrong, that could be formed by this wedge. For each case, calculate the pressure, temperature, and Mach number downstream of the oblique shock.

Air flowing steadily in a nozzle experiences a normal shock at a Mach number of Ma 5 2.6. If the pressure and temperature of air are 58 kPa and 270 K, respectively, upstream of the shock, calculate the pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the shock. Compare these results to those for helium undergoing a normal shock under the same conditions.

Calculate the entropy changes of air and helium across the normal shock wave in Prob. 1796.

What is the effect of heating the fluid on the flow velocity in subsonic Rayleigh flow? Answer the same questions for supersonic Rayleigh flow.

On a T-s diagram of Rayleigh flow, what do the points on the Rayleigh line represent?

What is the effect of heat gain and heat loss on the entropy of the fluid during Rayleigh flow?

Consider subsonic Rayleigh flow of air with a Mach number of 0.92. Heat is now transferred to the fluid and the Mach number increases to 0.95. Does the temperature T of the fluid increase, decrease, or remain constant during this process? How about the stagnation temperature T0?

What is the characteristic aspect of Rayleigh flow? What are the main assumptions associated with Rayleigh flow?

Consider subsonic Rayleigh flow that is accelerated to sonic velocity (Ma 5 1) at the duct exit by heating. If the fluid continues to be heated, will the flow at duct exit be supersonic, subsonic, or remain sonic?

Argon gas enters a constant cross-sectional area duct at Ma1 5 0.2, P1 5 320 kPa, and T1 5 400 K at a rate of 1.2 kg/s. Disregarding frictional losses, determine the highest rate of heat transfer to the argon without reducing the mass flow rate.

Air is heated as it flows subsonically through a duct. When the amount of heat transfer reaches 67 kJ/kg, the flow is observed to be choked, and the velocity and the static pressure are measured to be 680 m/s and 270 kPa. Disregarding frictional losses, determine the velocity, static temperature, and static pressure at the duct inlet.

Compressed air from the compressor of a gas turbine enters the combustion chamber at T1 5 700 K, P1 5 600 kPa, and Ma1 5 0.2 at a rate of 0.3 kg/s. Via combustion, heat is transferred to the air at a rate of 150 kJ/s as it flows through the duct with negligible friction. Determine the Mach number at the duct exit, and the drop in stagnation pressure P01 2 P02 during this process.

Repeat Prob. 17106 for a heat transfer rate of 300 kJ/s.

Air flows with negligible friction through a 4-indiameter duct at a rate of 5 lbm/s. The temperature and pressure at the inlet are T1 5 800 R and P1 5 30 psia, and the Mach number at the exit is Ma2 5 1. Determine the rate of heat transfer and the pressure drop for this section of the duct.

Air enters an approximately frictionless duct with V1 5 70 m/s, T1 5 600 K, and P1 5 350 kPa. Letting the exit temperature T2 vary from 600 to 5000 K, evaluate the entropy change at intervals of 200 K, and plot the Rayleigh line on a T-s diagram.

Air is heated as it flows through a 6 in 3 6 in square duct with negligible friction. At the inlet, air is at T1 5 700 R, P1 5 80 psia, and V1 5 260 ft/s. Determine the rate at which heat must be transferred to the air to choke the flow at the duct exit, and the entropy change of air during this process.

Air enters a rectangular duct at T1 5 300 K, P1 5 420 kPa, and Ma1 5 2. Heat is transferred to the air in the amount of 55 kJ/kg as it flows through the duct. Disregarding frictional losses, determine the temperature and Mach number at the duct exit.

Repeat Prob. 17111 assuming air is cooled in the amount of 55 kJ/kg.

Consider a 16-cm-diameter tubular combustion chamber. Air enters the tube at 450 K, 380 kPa, and 55 m/s. Fuel with a heating value of 39,000 kJ/kg is burned by spraying it into the air. If the exit Mach number is 0.8, determine the rate at which the fuel is burned and the exit temperature. Assume complete combustion and disregard the increase in the mass flow rate due to the fuel mass.

Consider supersonic flow of air through a 7-cmdiameter duct with negligible friction. Air enters the duct at Ma1 5 1.8, P01 5 140 kPa, and T01 5 600 K, and it is decelerated by heating. Determine the highest temperature that air can be heated by heat addition while the mass flow rate remains constant.

What is supersaturation? Under what conditions does it occur?

Steam enters a converging nozzle at 5.0 MPa and 400C with a negligible velocity, and it exits at 3.0 MPa. For a nozzle exit area of 60 cm2 , determine the exit velocity, mass flow rate, and exit Mach number if the nozzle (a) is isentropic and (b) has an efficiency of 94 percent.

Steam enters a converging nozzle at 450 psia and 900F with a negligible velocity, and it exits at 275 psia. For a nozzle exit area of 3.75 in2 , determine the exit velocity, mass flow rate, and exit Mach number if the nozzle (a) is isentropic and (b) has an efficiency of 90 percent.

Steam enters a convergingdiverging nozzle at 1 MPa and 500C with a negligible velocity at a mass flow rate of 2.5 kg/s, and it exits at a pressure of 200 kPa. Assuming the flow through the nozzle to be isentropic, determine the exit area and the exit Mach number.

Repeat Prob. 17118 for a nozzle efficiency of 85 percent.

The thrust developed by the engine of a Boeing 777 is about 380 kN. Assuming choked flow in the nozzles, determine the mass flow rate of air through the nozzle. Take the ambient conditions to be 220 K and 40 kPa.

A stationary temperature probe inserted into a duct where air is flowing at 190 m/s reads 858C. What is the actual temperature of the air?

Nitrogen enters a steady-flow heat exchanger at 150 kPa, 108C, and 100 m/s, and it receives heat in the amount of 150 kJ/kg as it flows through it. The nitrogen leaves the heat exchanger at 100 kPa with a velocity of 200 m/s. Determine the stagnation pressure and temperature of the nitrogen at the inlet and exit states.

Plot the mass flow parameter m # "RT0 /(AP0) versus the Mach number for k 5 1.2, 1.4, and 1.6 in the range of 0 # Ma # 1.

Obtain Eq. 1710 by starting with Eq. 179 and using the cyclic rule and the thermodynamic property relations cp T 5 a 0s 0T b P and cv T 5 a 0s 0T b v

For ideal gases undergoing isentropic flows, obtain expressions for P/P*, T/T*, and r/r* as functions of k and Ma.

Using Eqs. 174, 1713, and 1714, verify that for the steady flow of ideal gases dT0/T 5 dA/A 1 (1 2 Ma2 ) dV/V. Explain the effect of heating and area changes on the velocity of an ideal gas in steady flow for (a) subsonic flow and (b) supersonic flow.

A subsonic airplane is flying at a 5000-m altitude where the atmospheric conditions are 54 kPa and 256 K. A Pitot static probe measures the difference between the static and stagnation pressures to be 16 kPa. Calculate the speed of the airplane and the flight Mach number.

Derive an expression for the speed of sound based on van der Waals equation of state P 5 RT(v 2 b) 2 a/v 2 . Using this relation, determine the speed of sound in carbon dioxide at 808C and 320 kPa, and compare your result to that obtained by assuming ideal-gas behavior. The van der Waals constants for carbon dioxide are a 5 364.3 kPam6 /kmol2 and b 5 0.0427 m3 /kmol.

Helium enters a nozzle at 0.6 MPa, 560 K, and a velocity of 120 m/s. Assuming isentropic flow, determine the pressure and temperature of helium at a location where the velocity equals the speed of sound. What is the ratio of the area at this location to the entrance area?

Repeat Problem 17129 assuming the entrance velocity is negligible.

Air at 0.9 MPa and 400 K enters a converging nozzle with a velocity of 180 m/s. The throat area is 10 cm2 . Assuming isentropic flow, calculate and plot the mass flow rate through the nozzle, the exit velocity, the exit Mach number, and the exit pressurestagnation pressure ratio versus the back pressurestagnation pressure ratio for a back pressure range of 0.9 $ Pb $ 0.1 MPa.

Nitrogen enters a duct with varying flow area at 400 K, 100 kPa, and a Mach number of 0.3. Assuming a steady, isentropic flow, determine the temperature, pressure, and Mach number at a location where the flow area has been reduced by 20 percent.

Repeat Prob. 17132 for an inlet Mach number of 0.5.

Nitrogen enters a convergingdiverging nozzle at 620 kPa and 310 K with a negligible velocity, and it experiences a normal shock at a location where the Mach number is Ma 5 3.0. Calculate the pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the shock. Compare these results to those of air undergoing a normal shock at the same conditions.

An aircraft flies with a Mach number Ma1 5 0.9 at an altitude of 7000 m where the pressure is 41.1 kPa and the temperature is 242.7 K. The diffuser at the engine inlet has an exit Mach number of Ma2 5 0.3. For a mass flow rate of 38 kg/s, determine the static pressure rise across the diffuser and the exit area.

Consider an equimolar mixture of oxygen and nitrogen. Determine the critical temperature, pressure, and density for stagnation temperature and pressure of 550 K and 350 kPa.

Helium expands in a nozzle from 220 psia, 740 R, and negligible velocity to 15 psia. Calculate the throat and exit areas for a mass flow rate of 0.2 lbm/s, assuming the nozzle is isentropic. Why must this nozzle be convergingdiverging?

Using the EES software and the relations in Table A32, calculate the one-dimensional compressible flow functions for an ideal gas with k 5 1.667, and present your results by duplicating Table A32.

Using the EES software and the relations in Table A33, calculate the one-dimensional normal shock functions for an ideal gas with k 5 1.667, and present your results by duplicating Table A33.

Helium expands in a nozzle from 1 MPa, 500 K, and negligible velocity to 0.1 MPa. Calculate the throat and exit areas for a mass flow rate of 0.46 kg/s, assuming the nozzle is isentropic. Why must this nozzle be converging diverging?

Using EES (or other) software and the relations given in Table A33, generate the onedimensional normal shock functions by varying the upstream Mach number from 1 to 10 in increments of 0.5 for air with k 5 1.4.

Repeat Prob. 17141 for methane with k 5 1.3.

Air is heated as it flows subsonically through a 10 cm 3 10 cm square duct. The properties of air at the inlet are maintained at Ma1 5 0.6, P1 5 350 kPa, and T1 5 420 K at all times. Disregarding frictional losses, determine the highest rate of heat transfer to the air in the duct without affecting the inlet conditions.

Repeat Prob. 17143 for helium

Air is accelerated as it is heated in a duct with negligible friction. Air enters at V1 5 100 m/s, T1 5 400 K, and P1 5 35 kPa and the exits at a Mach number of Ma2 5 0.8. Determine the heat transfer to the air, in kJ/kg. Also determine the maximum amount of heat transfer without reducing the mass flow rate of air.

Air at sonic conditions and at static temperature and pressure of 340 K and 250 kPa, respectively, is to be accelerated to a Mach number of 1.6 by cooling it as it flows through a channel with constant cross-sectional area. Disregarding frictional effects, determine the required heat transfer from the air, in kJ/kg.

Air is cooled as it flows through a 20-cm-diameter duct. The inlet conditions are Ma1 5 1.2, T01 5 350 K, and P01 5 240 kPa and the exit Mach number is Ma2 5 2.0. Disregarding frictional effects, determine the rate of cooling of air

Saturated steam enters a convergingdiverging nozzle at 1.75 MPa, 10 percent moisture, and negligible velocity, and it exits at 1.2 MPa. For a nozzle exit area of 25 cm2 , determine the throat area, exit velocity, mass flow rate, and exit Mach number if the nozzle (a) is isentropic and (b) has an efficiency of 92 percent.

Using EES (or other) software, determine the shape of a convergingdiverging nozzle for air for a mass flow rate of 3 kg/s and inlet stagnation conditions of 1400 kPa and 2008C. Approximate the flow as isentropic. Repeat the calculations for 50-kPa increments of pressure drop to an exit pressure of 100 kPa. Plot the nozzle to scale. Also, calculate and plot the Mach number along the nozzle.

Steam at 6.0 MPa and 700 K enters a converging nozzle with a negligible velocity. The nozzle throat area is 8 cm2 . Approximating the flow as isentropic, plot the exit pressure, the exit velocity, and the mass flow rate through the nozzle versus the back pressure Pb for 6.0 $ Pb $ 3.0 MPa. Treat the steam as an ideal gas with k 5 1.3, cp 5 1.872 kJ/kgK, and R 5 0.462 kJ/kgK.

Find the expression for the ratio of the stagnation pressure after a shock wave to the static pressure before the shock wave as a function of k and the Mach number upstream of the shock wave Ma1.

Using EES (or other) software and the relations given in Table A32, calculate the onedimensional isentropic compressible-flow functions by varying the upstream Mach number from 1 to 10 in increments of 0.5 for air with k 5 1.4.

Repeat Prob. 17152 for methane with k 5 1.3.

An aircraft is cruising in still air at 58C at a velocity of 400 m/s. The air temperature at the nose of the aircraft where stagnation occurs is (a) 58C (b) 258C (c) 558C (d ) 808C (e) 858C

Air is flowing in a wind tunnel at 258C, 80 kPa, and 250 m/s. The stagnation pressure at the location of a probe inserted into the flow section is (a) 87 kPa (b) 93 kPa (c) 113 kPa (d ) 119 kPa (e) 125 kPa

An aircraft is reported to be cruising in still air at 2208C and 40 kPa at a Mach number of 0.86. The velocity of the aircraft is (a) 91 m/s (b) 220 m/s (c) 186 m/s (d ) 274 m/s (e) 378 m/s

Air is flowing in a wind tunnel at 128C and 66 kPa at a velocity of 230 m/s. The Mach number of the flow is (a) 0.54 m/s (b) 0.87 m/s (c) 3.3 m/s (d ) 0.36 m/s (e) 0.68 m/s

Consider a converging nozzle with a low velocity at the inlet and sonic velocity at the exit plane. Now the nozzle exit diameter is reduced by half while the nozzle inlet temperature and pressure are maintained the same. The nozzle exit velocity will (a) remain the same (b) double (c) quadruple (d ) go down by half (e) go down by one-fourth

Air is approaching a convergingdiverging nozzle with a low velocity at 128C and 200 kPa, and it leaves the nozzle at a supersonic velocity. The velocity of air at the throat of the nozzle is (a) 338 m/s (b) 309 m/s (c) 280 m/s (d ) 256 m/s (e) 95 m/s

Argon gas is approaching a convergingdiverging nozzle with a low velocity at 208C and 120 kPa, and it leaves the nozzle at a supersonic velocity. If the cross-sectional area of the throat is 0.015 m2 , the mass flow rate of argon through the nozzle is (a) 0.41 kg/s (b) 3.4 kg/s (c) 5.3 kg/s (d ) 17 kg/s (e) 22 kg/s

Carbon dioxide enters a convergingdiverging nozzle at 60 m/s, 3108C, and 300 kPa, and it leaves the nozzle at a supersonic velocity. The velocity of carbon dioxide at the throat of the nozzle is (a) 125 m/s (b) 225 m/s (c) 312 m/s (d ) 353 m/s (e) 377 m/s

Consider gas flow through a convergingdiverging nozzle. Of the five following statements, select the one that is incorrect: (a) The fluid velocity at the throat can never exceed the speed of sound. (b) If the fluid velocity at the throat is below the speed of sound, the diversion section will act like a diffuser. (c) If the fluid enters the diverging section with a Mach number greater than one, the flow at the nozzle exit will be supersonic. (d ) There will be no flow through the nozzle if the back pressure equals the stagnation pressure. (e) The fluid velocity decreases, the entropy increases, and stagnation enthalpy remains constant during flow through a normal shock.

Combustion gases with k 5 1.33 enter a converging nozzle at stagnation temperature and pressure of 3508C and 400 kPa, and are discharged into the atmospheric air at 208C and 100 kPa. The lowest pressure that will occur within the nozzle is (a) 13 kPa (b) 100 kPa (c) 216 kPa (d ) 290 kPa (e) 315 kPa

Find out if there is a supersonic wind tunnel on your campus. If there is, obtain the dimensions of the wind tunnel and the temperatures and pressures as well as the Mach number at several locations during operation. For what typical experiments is the wind tunnel used?

Assuming you have a thermometer and a device to measure the speed of sound in a gas, explain how you can determine the mole fraction of helium in a mixture of helium gas and air.

Design a 1-m-long cylindrical wind tunnel whose diameter is 25 cm operating at a Mach number of 1.8. Atmospheric air enters the wind tunnel through a converging diverging nozzle where it is accelerated to supersonic velocities. Air leaves the tunnel through a convergingdiverging diffuser where it is decelerated to a very low velocity before entering the fan section. Disregard any irreversibilities. Specify the temperatures and pressures at several locations as well as the mass flow rate of air at steady-flow conditions. Why is it often necessary to dehumidify the air before it enters the wind tunnel?