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Thermodynamics An Engineering Approach 8th edition Yunus A. Cengel, Michael A. Boles - Solutions

Air enters an approximately frictionless duct with V1 = 70 m/s, T1 = 600 K, and P1 = 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.
What is sound? How is it generated? How does it travel? Can sound waves travel in a vacuum?
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
Air enters a rectangular duct at T1 = 300 K, P1 = 420 kPa, and Ma1 = 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. 17-111 assuming air is cooled in the amount of 55 kJ/kg.Prob. 17-111Air enters a rectangular duct at T1 5 300 K, P1 = 420 kPa, and Ma1 = 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
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
Consider supersonic flow of air through a 7-cmdiameter duct with negligible friction. Air enters the duct at Ma1 = 1.8, P01 = 140 kPa, and T01 = 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
What is supersaturation? Under what conditions does it occur?
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.
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
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.
Repeat Prob. 17-118 for a nozzle efficiency of 85 percent. Prob. 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
In which medium does a sound wave travel faster: in cool air or in warm air?
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 8580C. 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
Plot the mass flow parameter m"√RT0 /(AP0) versus the Mach number for k = 1.2, 1.4, and 1.6 in the range of 0 ≤ Ma ≤ 1.
Obtain Eq. 17-10 by starting with Eq. 17-9 and using the cyclic rule and the thermodynamic property relations
For ideal gases undergoing isentropic flows, obtain expressions for P/P*, T/T*, and r/r* as functions of k and Ma.
Using Eqs. 17-4, 17-13, and 17-14, verify that for the steady flow of ideal gases dT0/T = dA/A 1 (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.
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 = RT(v - b) - a/v2. 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
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?
In which medium will sound travel fastest for a given temperature: air, helium, or argon?
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
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 pressure-stagnation pressure ratio versus the back
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. 17-132 for an inlet Mach number of 0.5. Prob. 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
Nitrogen enters a converging-diverging 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 = 3.0. Calculate the pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the shock. Compare
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
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 converging-diverging?
Using the EES software and the relations in Table A-32, calculate the one-dimensional compressible flow functions for an ideal gas with k = 1.667, and present your results by duplicating Table A-32.
Using the EES software and the relations in Table A-33, calculate the one-dimensional normal shock functions for an ideal gas with k = 1.667, and present your results by duplicating Table A-33.
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?
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 A-33, generate the one dimensional normal shock functions by varying the upstream Mach number from 1 to 10 in increments of 0.5 for air with k = 1.4.
Repeat Prob. 17-141 for methane with k = 1.3. Prob. 17-141 Using EES (or other) software and the relations given in Table A-33, generate the one dimensional normal shock functions by varying the upstream Mach number from 1 to 10 in increments of 0.5 for air with k = 1.4.
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 = 0.6, P1 = 350 kPa, and T1 = 420 K at all times. Disregarding frictional losses, determine the highest rate of heat transfer to the air in the duct without affecting
Repeat Prob. 17-143 for helium.Prob. 17-143Air 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 = 0.6, P1 = 350 kPa, and T1 = 420 K at all times. Disregarding frictional losses, determine the highest rate of heat
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 the 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
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
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.
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
Using EES (or other) software, determine the shape of a converging-diverging 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
Does the Mach number of a gas flowing at a constant velocity remain constant? Explain.
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
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 A-32, calculate the one dimensional isentropic compressible-flow functions by varying the upstream Mach number from 1 to 10 in increments of 0. Z for air with k = 1.4.
Repeat Prob. 17-152 for methane with k = 1.3. Prob. 17-152 Using EES (or other) software and the relations given in Table A-32, calculate the one dimensional isentropic compressible-flow functions by varying the upstream Mach number from 1 to 10 in increments of 0. Z for air with k = 1.4.
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
Air is flowing in a wind tunnel at 250C, 80 kPa, and 250 m/s. The stagnation pressure at a probe inserted into the flow stream is (a) 87 kPa (b) 96 kPa (c) 113 kPa (d) 119 kPa (e) 125 kPa
An aircraft is reported to be cruising in still air at -200C 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
Air is approaching a converging-diverging 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
Is it realistic to approximate that the propagation of sound waves is an isentropic process? Explain.
Argon gas is approaching a converging-diverging 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
Carbon dioxide enters a converging-diverging 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 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
Combustion gases with k = 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
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 945 km/h, 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
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 approximation.
What is dynamic temperature?
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
Assuming ideal gas behavior, determine the speed of sound in refrigerant-134a at 0.9 MPa and 60°C.
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 330 m/s for both cases.
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
Reconsider Prob. 17-23E. Using EES (or other) software, compare the Mach number of steam flow over the temperature range 350 to 700°F. Plot the Mach number as a function of temperature.
Air expands isentropically from 170 psia and 200°F to 60 psia. Calculate the ratio of the initial to final speed of sound.
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.
Repeat Prob. 17-26 for helium gas. Prob. 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.
The isentropic process for an ideal gas is expressed as Pvk = constant. Using this process equation and the definition of the speed of sound (Eq. 17-9), obtain the expression for the speed of sound for an ideal gas.
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?
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 = 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?
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 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?
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 - 500C. Determine if the speed of this airplane is subsonic or supersonic.
Calculate the critical temperature, pressure, and density of (a) Air at 200 kPa, 1000C, and 250 m/s, and (b) Helium at 200 kPa, 400C, and 300 m/s.
Air at 25 psia, 3200F, and Mach number Ma= 0.7 flows through a duct. Calculate the velocity and the stag nation pressure, temperature, and density of air.
Air flows through a device such that the stagnation pressure is 0.6 MPa, the stagnation temperature is 4008C, and the velocity is 570 m/s. Determine the static pressure and temperature of the air at this state.
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?
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 - 200C, determine the speed of this engine.
Reconsider the scram jet engine discussed in Prob. 17-41. Determine the speed of this engine in miles per hour corresponding to a Mach number of 7 in air at a temperature of 00F.
Air at 200 kPa, 1008C, and Mach number Ma = 0.8 flows through a duct. Calculate the velocity and the stagnation pressure, temperature, and density of the air.
Reconsider Prob. 17-43. 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 = 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?
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.
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
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
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?

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