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engineering
mechanical engineering
Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions
Consider supersonic airflow approaching the nose of a two-dimensional wedge at a Mach number of 5. Using Fig. 17–41, determine the minimum shock angle and the maximum deflection angle a straight oblique shock can have.
Air flowing at 60 kPa, 240 K, and a Mach number of 3.4 impinges on a two-dimensional wedge of half-angle 12°. Determine the two possible oblique shock angles, b weak and b strong that could be formed by this wedge. For each case, calculate the pressure, temperature, and Mach number downstream of
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 10°. If the axis of the wedge is tilted 25° with respect to the upstream airflow, determine the downstream Mach number, pressure, and
Reconsider Prob. 17–91. 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 8 psia, 20°F, and a Mach number of 2.0 is forced to turn upward by a ramp that makes an 8° 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 P1 = 40 kPa, T1 = 280 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.
Air flowing at P1 = 6 psia, T1 = 480 R, and Ma1 = 2.0 is forced to undergo a compression turn of 15°. Determine the Mach number, pressure, and temperature of air after the compression.
What is the characteristic aspect of Rayleigh flow? What are the main assumptions associated with 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. Will the temperature T of the fluid increase, decrease, or remain constant during this process? How about the stagnation temperature T0?
Consider a 12-cm-diameter tubular combustion chamber. Air enters the tube at 500 K, 400 kPa, and 70 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
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. 17–103 assuming air is cooled in the amount of 55 kJ/kg.
Air is heated as it flows subsonically through a duct. When the amount of heat transfer reaches 60 kJ/kg, the flow is observed to be choked, and the velocity and the static pressure are measured to be 620 m/s and 270 kPa. Disregarding frictional losses, determine the velocity, static temperature,
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 = 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.
Air enters a 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.
Air is heated as it flows through a 4 in x 4 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
Compressed air from the compressor of a gas turbine enters the combustion chamber at T1 = 550 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 200 kJ/s as it flows through the duct with negligible friction. Determine the Mach number
Repeat Prob. 17–109 for a heat transfer rate of 300 kJ/s.
Argon gas enters a constant cross-sectional-area duct at Ma1 = 0.2, P1 = 320 kPa, and T1 = 400 K at a rate of 0.8 kg/s. Disregarding frictional losses, determine the highest rate of heat transfer to the argon without reducing the mass flow rate.
Consider supersonic flow of air through a 6-cmdiameter duct with negligible friction. Air enters the duct at Ma1 = 1.8, P01 = 210 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 super saturation? Under what conditions does it occur?
Steam enters a converging nozzle at 3.0 MPa and 500°C with a negligible velocity, and it exits at 1.8 MPa. For a nozzle exit area of 32 cm2, 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 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. 17–116 for a nozzle efficiency of 95 percent.
Air in an automobile tire is maintained at a pressure of 220 kPa (gauge) in an environment where the atmospheric pressure is 94 kPa. The air in the tire is at the ambient temperature of 25°C. Now a 4-mm-diameter leak develops in the tire as a result of an accident. Assuming isentropic flow,
The thrust developed by the engine of a Boeing 777 is about 380 kN. Assuming choked flow in the nozzle determine the mass flow rate of air through the nozzle. Take the ambient conditions to be 265 K and 85 kPa.
A stationary temperature probe inserted into a duct where air is flowing at 250 m/s reads 85°C. What is the actual temperature of air?
Nitrogen enters a steady-flow heat exchanger at 150 kPa, 10°C, and 100 m/s, and it receives heat in the amount of 125 kJ/kg as it flows through it. The nitrogen leaves the heat exchanger at 100 kPa with a velocity of 180 m/s. Determine the stagnation pressure and temperature of the nitrogen at the
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 50°C and 200 kPa, and compare your result to that obtained by assuming ideal-gas behavior. The van der Waals
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 - 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 3000-m altitude where the atmospheric conditions are 70.109 kPa and 268.65 K. A Pitot static probe measures the difference between the static and stagnation pressures to be 35 kPa. Calculate the speed of the airplane and the flight Mach number.
Plot the mass flow parameter m/(AP0) versus the Mach number for k 1.2, 1.4, and 1.6 in the range of 0 < Ma
Helium enters a nozzle at 0.8 MPa, 500 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 Prob. 17–128 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 pressure–stagnation pressure ratio versus the back
Steam at 6.0 MPa and 700 K enters a converging nozzle with a negligible velocity. The nozzle throat area is 8 cm2. Assuming isentropic flow, 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
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.
Nitrogen enters a converging–diverging nozzle at 700 kPa and 300 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 = 0.8 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 65 kg/s, determine the static pressure rise across the diffuser and
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 0.25 kg/s, assuming the nozzle is isentropic. Why must this nozzle be converging– diverging?
Helium expands in a nozzle from 150 psia, 900 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 = 1.667, and present your results by duplicating Table A–33.
Consider an equimolar mixture of oxygen and nitrogen. Determine the critical temperature, pressure, and density for stagnation temperature and pressure of 800 K and 500 kPa.
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 200°C. Assume the flow is isentropic. Repeat the calculations for 50-kPa increments of pressure drops to an exit pressure of
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 0.5 for air with k = 1.4.
Repeat Prob. 17–141 for methane with k = 1.3.
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. 17–143 for methane with k =1.3.
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.
Air is heated as it flows subsonically through a 10 cm = 10 cm square duct. The properties of air at the inlet are maintained at Ma1 = 0.4, P1 = 400 kPa, and T1 = 360 K at all times. Disregarding frictional losses, determine the highest rate of heat transfer to the air in the duct without affecting
Repeat Prob. 17–146 for helium
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
Air at sonic conditions and static temperature and pressure of 500 K and 420 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
Saturated steam enters a converging–diverging nozzle at 3.0 MPa, 5 percent moisture, and negligible velocity, and it exits at 1.2 MPa. For a nozzle exit area of 16 cm2, determine the throat area, exit velocity, mass flow rate, and exit Mach number if the nozzle (a) is isentropic and (b) has an
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 15°C, 80 kPa, and 200 m/s. The stagnation pressure at the probe inserted into the flow section is (a) 82 kPa (b) 91 kPa (c) 96 kPa (d) 101 kPa (e) 114 kPa
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) 280 m/s (e) 378 m/s
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
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)
Air is approaching a converging–diverging nozzle with a low velocity at 20°C and 300 kPa, and it leaves the nozzle at a supersonic velocity. The velocity of air at the throat of the nozzle is (a) 290 m/s (b) 98 m/s (c) 313 m/s (d) 343 m/s (e) 412 m/s
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
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
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
Combustion gases with k = 1.33 enter a converging nozzle at stagnation temperature and pressure of 400°C and 800 kPa, and are discharged into the atmospheric air at 20°C and 100 kPa. The lowest pressure that will occur within the nozzle is (a) 26 kPa (b) 100 kPa (c) 321 kPa (d) 432 kPa
Calculate the reversible work and irreversibility for the process described, assuming that the heat transfer is with the surroundings at20C.
Calculate the reversible work and irreversibility for the process described in Problem 5.65, assuming that the heat transfer is with the surroundings at20C.
The compressor in a refrigerator takes refrigerant R-134a in at 100 kPa, 20C and compresses it to 1 MPa, 40C. With the room at 20C find the minimum compressor work.
Calculate the reversible work out of the two-stage turbine shown in Problem 6.41, assuming the ambient is at 25C. Compare this to the actual work which was found to be 18.08 MW.
A household refrigerator has a freezer at TF and a cold space at TC from which energy is removed and rejected to the ambient at TA as shown in Fig. P10.5
An air compressor takes air in at the state of the surroundings 100 kPa, 300 K. The air exits at 400 kPa, 200C at the rate of 2 kg/s, determine the minimum compressor work input.
A supply of steam at 100 kPa, 150C is needed in a hospital for cleaning purposes at a rate of 15 kg/s. A supply of steam at 150 kPa, 250C is available from a boiler and tap water at 100 kPa, 15C is also available. The two sources are then mixed in an SSSF mixing chamber to
Two flows of air both at 200 kPa of equal flow rates mix in an insulated mixing chamber. One flow is at 1500 K and the other is at 300 K. Find the irreversibility in the process per kilogram of air flowing out.
A steam turbine receives steam at 6 MPa, 800C. It has a heat loss of 49.7 kJ/kg and an isentropic efficiency of 90%. For an exit pressure of 15 kPa and surroundings at 20C, find the actual work and the reversible work between the inlet and the exit.
A 2-kg piece of iron is heated from room temperature 25C to 400C by a heat source at 600C. What is the irreversibility in the process?
A 2-kg/s flow of steam at 1 MPa, 700C should be brought to 500C by spraying in liquid water at 1 MPa, 20C in an SSSF setup. Find the rate of irreversibility, assuming that surroundings are at 20C.
Fresh water can be produced from saltwater by evaporation and subsequent condensation. An example is shown in Fig. P10.12 where 150-kg/s saltwater, state 1, comes from the condenser in a large power plant, the water is throttled to the saturated pressure in the flash evaporator and the vapor, state
An air compressor receives atmospheric air at T0 = 17°C, 100 kPa, and compresses it up to 1400 kPa. The compressor has an isentropic efficiency of 88% and it loses energy by heat transfer to the atmosphere as 10% of the isentropic work. Calculate the actual exit temperature and the reversible work.
An air compressor receives atmospheric air at T0 = 17C, 100 kPa, and compresses it up to 1400 kPa. The compressor has an isentropic efficiency of 88% and it loses energy by heat transfer to the atmosphere as 10% of the isentropic work. Find the actual exit temperature and the reversible
Air flows through a constant pressure heating device, shown in Fig. P10.15. It is heated up in a reversible process with a work input of 200 kJ/kg air flowing. The device exchanges heat with the ambient at 300 K. The air enters at 300 K, 400 kPa. Assuming constant specific heat develop an
Air enters the turbocharger compressor of an automotive engine at 100 kPa, 30C, and exits at 170 kPa, the air is cooled by 50C in an intercooler before entering the engine. The isentropic efficiency of the compressor is 75%. Determine the temperature of the air entering the engine
A car air-conditioning unit has a 0.5-kg aluminum storage cylinder that is sealed with a valve and it contains 2 L of refrigerant R-134a at 500 kPa and both are at room temperature 20C. It is now installed in a car sitting outside where the whole system cools down to ambient temperature at
A steady combustion of natural gas yields 0.15 kg/s of products (having approximately the same properties as air) at 1100C, 100 kPa. The products are passed through a heat exchanger and exit at 550C. What is the maximum theoretical power output from a cyclic heat engine operating on
A counter flowing heat exchanger cools air at 600 K, 400 kPa to 320 K using a supply of water at 20C, 200 kPa. The water flow rate is 0.1 kg/s and the air flow rate is 1 kg/s. Assume this can be done in a reversible process by the use of heat engines and neglect kinetic energy changes. Find
Water as saturated liquid at 200 kPa goes through a constant pressure heat exchanger. The heat input is supplied from a reversible heat pump extracting heat from the surroundings at 17C. The water flow rate is 2 kg/min and the whole process is reversible, that is, there is no overall net
Calculate the irreversibility for the process described in Problem 6.63, assuming that heat transfer is with the surroundings at 17C.
The high-temperature heat source for a cyclic heat engine is a SSSF heat exchanger where R-134a enters at 80C, saturated vapor, and exits at 80C, saturated liquid at a flow rate of 5 kg/s. Heat is rejected from the heat engine to a SSSF heat exchanger where air enters at 150 kPa and
A control mass gives out 10 kJ of energy in the form of a. Electrical work from a battery b. Mechanical work from a spring c. Heat transfer at 500C Find the change in availability of the control mass for each of the three cases.
Calculate the availability of the water at the initial and final states of Problem, and the irreversibility of the process.
A steady stream of R-22 at ambient temperature, 10C, and at 750 kPa enters a solar collector. The stream exits at 80C, 700 kPa. Calculate the change in availability of the R-22 between these two states.
Nitrogen flows in a pipe with velocity 300 m/s at 500 kPa, 300C. What is its availability with respect to an ambient at 100 kPa, 20C?
A 10-kg iron disk brake on a car is initially at 10C; suddenly the brake pad hangs up, increasing the brake temperature by friction to 110C while the car maintains constant speed. Find the change in availability of the disk and the energy depletion of the car’s gas tank due to
A 1 kg block of copper at 350C is quenched in a 10 kg oil bath initially at ambient temperature of 20C. Calculate the final uniform temperature (no heat transfer to/from ambient) and the change of availability of the system (copper and oil).
Calculate the availability of the system (aluminum plus gas) at the initial and final states, and also the process irreversibility. State 1: T1 = 200 oC, v1 = V1/ m = 0.05 / 1.1186 = 0.0447 State 2: v2 = v1 (2 / 1.5) (298.15 / 473.15) = 0.03756
Consider the springtime melting of ice in the mountains, which gives cold water running in a river at 2C while the air temperature is 20C. What is the availability of the water (SSSF) relative to the temperature of the ambient?
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