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engineering
mechanical engineering
Vector Mechanics For Engineers Statics And Dynamics 8th Edition Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell - Solutions
Air from a line at 12 MPa, 15C, flows into a 500-L rigid tank that initially contained air at ambient conditions, 100 kPa 15C. The process occurs rapidly and is essentially adiabatic. The valve is closed when the pressure inside reaches some value, P2. The tank eventually cools to
An initially empty spring-loaded piston/cylinder requires 100 kPa to float the piston. A compressor with a line and valve now charges the cylinder with water to a final pressure of 1.4 MPa at which point the volume is 0.6 m3, state 2. The inlet condition to the reversible adiabatic compressor is
An initially empty canister of volume 0.2 m3 is filled with carbon dioxide from a line at 1000 kPa, 500 K. Assume the process is adiabatic and the flow continues until it stops by itself. Find the final mass and temperature of the carbon dioxide in the canister and the total entropy generated by
A 1-m3 rigid tank contains 100 kg R-22 at ambient temperature, 15C. A valve on top of the tank is opened, and saturated vapor is throttled to ambient pressure, 100 kPa, and flows to a collector system. During the process the temperature inside the tank remains at 15C. The valve is
An old abandoned salt mine, 100000 m3 in volume, contains air at 290 K, 100 kPa. The mine is used for energy storage so the local power plant pumps it up to 2.1 MPa using outside air at 290 K, 100 kPa. Assume the pump is ideal and the process is adiabatic. Find the final mass and temperature of the
A rigid steel bottle, V = 0.25 m3, contains air at 100 kPa, 300 K. The bottle is now charged with air from a line at 260 K, 6 MPa to a bottle pressure of 5 MPa, state 2, and the valve is closed. Assume that the process is adiabatic, and the charge always is uniform. In storage, the bottle slowly
An insulated 2 m3 tank is to be charged with R-134a from a line flowing the refrigerant at 3 MPa. The tank is initially evacuated, and the valve is closed when the pressure inside the tank reaches 3 MPa. The line is supplied by an insulated compressor that takes in R-134a at 5C, quality of
A horizontal, insulated cylinder has a frictionless piston held against stops by an external force of 500 kN. The piston cross-sectional area is 0.5 m2, and the initial volume is 0.25 m3. Argon gas in the cylinder is at 200 kPa, 100C. A valve is now opened to a line flowing argon at 1.2
A rigid 1.0 m3 tank contains water initially at 120C, with 50 % liquid and 50% vapor, by volume. A pressure-relief valve on the top of the tank is set to 1.0 MPa (the tank pressure cannot exceed 1.0 MPa - water will be discharged instead). Heat is now transferred to the tank from a
A frictionless piston/cylinder is loaded with a linear spring, spring constant 100 kN/m and the piston cross-sectional area is 0.1 m2. The cylinder initial volume of 20 L contains air at 200 kPa and ambient temperature, 10C. The cylinder has a set of stops that prevent its volume from
An insulated piston/cylinder contains R-22 at 20C, 85% quality, at a cylinder volume of 50 L. A valve at the closed end of the cylinder is connected to a line flowing R-22 at 2 MPa, 60C. The valve is now opened, allowing R-22 to flow in, and at the same time the external force on
Liquid water at ambient conditions, 100 kPa, 25C, enters a pump at the rate of 0.5 kg/s. Power input to the pump is 3 kW. Assuming the pump process to be reversible, determine the pump exit pressure and temperature.
A firefighter on a ladder 25 m above ground should be able to spray water an additional 10 m up with the hose nozzle of exit diameter 2.5 cm. Assume a water pump on the ground and a reversible flow (hose, nozzle included) and find the minimum required power.
A large storage tank contains liquefied natural gas (LNG), which may be assumed to be pure methane. The tank contains saturated liquid at ambient pressure, 100 kPa; it is to be pumped to 500 kPa and fed to a pipeline at the rate of 0.5 kg/s. How much power input is required for the pump, assuming
A small dam has a pipe carrying liquid water at 150 kPa, 20C with a flow rate of 2000 kg/s in a 0.5 m diameter pipe. The pipe runs to the bottom of the dam 15 m lower into a turbine with pipe diameter 0.35 m. Assume no friction or heat transfer in the pipe and find the pressure of the
A small pump is driven by a 2 kW motor with liquid water at 150 kPa, 10C entering. Find the maximum water flow rate you can get with an exit pressure of 1 MPa and negligible kinetic energies. The exit flow goes through a small hole in a spray nozzle out to the atmosphere at 100 kPa. Find
Saturated R-134a at -10C is pumped/compressed to a pressure of 1.0 MPa at the rate of 0.5 kg/s in a reversible adiabatic SSSF process. Calculate the power required and the exit temperature for the two cases of inlet state of the R-134a: a) Quality of 100 %. b) Quality of 0 %.
A small water pump on ground level has an inlet pipe down into a well at a depth H with the water at 100 kPa, 15C. The pump delivers water at 400 kPa to a building. The absolute pressure of the water must be at least twice the saturation pressure to avoid cavitation. What is the maximum
Atmospheric air at 100 kPa, 17C blows at 60 km/h towards the side of a building. Assume the air is nearly incompressible find the pressure and the temperature at the stagnation point (zero velocity) on the wall.
A small pump takes in water at 20C, 100 kPa and pumps it to 2.5 MPa at a flow rate of 100 kg/min. Find the required pump power input.
Helium gas enters a steady-flow expander at 800 kPa, 300C, and exits at 120 kPa. The mass flow rate is 0.2 kg/s, and the expansion process can be considered as a reversible polytropic process with exponent, n 1.3. Calculate the power output of the expander.
A pump/compressor pumps a substance from 100 kPa, 10C to 1 MPa in a reversible adiabatic SSSF process. The exit pipe has a small crack, so that a small amount leaks to the atmosphere at 100 kPa. If the substance is (a) water, (b) R-12, find the temperature after compression and the
A certain industrial process requires a steady 0.5 kg/s of air at 200 m/s, at the condition of 150 kPa, 300 K. This air is to be the exhaust from a specially designed turbine whose inlet pressure is 400 kPa. The turbine process may be assumed to be reversible and polytropic, with polytropic
A mixing chamber receives 5 kg/min ammonia as saturated liquid at 20C from one line and ammonia at 40C, 250 kPa from another line through a valve. The chamber also receives 325 kJ/min energy as heat transferred from a 40C reservoir. This should produce saturated
A compressor is used to bring saturated water vapor at 1 MPa up to 17.5 MPa, where the actual exit temperature is 650C. Find the isentropic compressor efficiency and the entropy generation.
Liquid water enters a pump at 15C, 100 kPa, and exits at a pressure of 5 MPa. If the isentropic efficiency of the pump is 75%, determine the enthalpy (steam table reference) of the water at the pump exit.
A centrifugal compressor takes in ambient air at 100 kPa, 15C, and discharges it at 450 kPa. The compressor has an isentropic efficiency of 80%. What is your best estimate for the discharge temperature?
Repeat Problem 9.20 assuming the steam turbine and the air compressor each have an isentropic efficiency of 80%.
A small air turbine with an isentropic efficiency of 80% should produce 270 kJ/kg of work. The inlet temperature is 1000 K and it exhausts to the atmosphere. Find the required inlet pressure and the exhaust temperature.
Carbon dioxide, CO2, enters an adiabatic compressor at 100 kPa, 300 K, and exits at 1000 kPa, 520 K. Find the compressor efficiency and the entropy generation for the process.
Repeat Problem 9.22 assuming the turbine and the pump each have an isentropic efficiency of 85%.
Air enters an insulated compressor at ambient conditions, 100 kPa 20C at the rate of 0.1 kg/s and exits at 200C. The isentropic efficiency of the compressor is 70%. What is the exit pressure? How much power is required to drive the compressor?
Steam enters a turbine at 300C and exhausts at 20 kPa. It is estimated that the isentropic efficiency of the turbine is 70%. What is the maximum turbine inlet pressure if the exhaust is not to be in the two-phase region?
A nozzle is required to produce a flow of air at 200 m/s at 20C, 100 kPa. It is estimated that the nozzle has an isentropic efficiency of 92%. What nozzle inlet pressure and temperature is required assuming the inlet kinetic energy is negligible?
A turbine receives air at 1500 K, 1000 kPa and expands it to 100 kPa. The turbine has an isentropic efficiency of 85%. Find the actual turbine exit air temperature and the specific entropy increase in the actual turbine.
Assume both the compressor and the nozzle have an isentropic efficiency of 90% the rest being unchanged. Find the actual compressor work and its exit temperature and find the actual nozzle exit velocity.
The small turbine in Problem 9.6 was ideal. Assume instead the isentropic turbine efficiency is 88%. Find the actual specific turbine work, the entropy generated in the turbine and the heat transfer in the heat exchanger.
A geothermal supply of hot water at 500 kPa, 150C is fed to an insulated flash evaporator at the rate of 1.5 kg/s. A stream of saturated liquid at 200 kPa is drained from the bottom of the chamber, and a stream of saturated vapor at 200 kPa is drawn from the top and fed to a turbine. The
Redo Problem 9.39 if the water pump has an isentropic efficiency of 85% (hose, nozzle included).
A flow of 20 kg/s steam at 10 MPa, 550C enters a two-stage turbine. The exit of the first stage is at 2 MPa where 4 kg/s is taken out for process steam and the rest continues through the second stage, which has an exit at 50 kPa. Assume both stages have an isentropic efficiency of 85% find
Air flows into an insulated nozzle at 1MPa, 1200 K with 15 m/s and mass flow rate of 2 kg/s. It expands to 650 kPa and exit temperature is 1100 K. Find the exit velocity, and the nozzle efficiency.
A nozzle is required to produce a steady stream of R–134a at 240 m/s at ambient conditions, 100 kPa 20C. The isentropic efficiency may be assumed to be 90%. Find by trial and error or verify that the inlet pressure is 375 kPa. What is the required inlet temperature in the line upstream of
Calculate the isentropic efficiency for each of the stages in the steam turbine shown in Problem 6.41. Find also the total entropy generated in the turbine.
A two-stage compressor having an inter stage cooler takes in air, 300 K, 100 kPa, and compresses it to 2 MPa. The cooler then cools the air to 340 K, after which it enters the second stage, which has an exit pressure of 15.74 MPa. The isentropic efficiency of stage one is 90% and the air exits the
A two-stage turbine receives air at 1160 K, 5.0 MPa. The first stage exit at 1 MPa then enters stage 2, which has an exit pressure of 200 kPa. Each stage has an isentropic efficiency of 85%. Find the specific work in each stage, the overall isentropic efficiency, and the total entropy generation.
A paper mill has two steam generators, one at 4.5 MPa, 300C and one at 8 MPa, 500C. Each generator feeds a turbine, both of which have an exhaust pressure of 1.2 MPa and isentropic efficiency of 87%, such that their combined power output is 20 MW. The two exhaust flows are mixed
A heat-powered portable air compressor consists of three components: (a) an adiabatic compressor; (b) a constant pressure heater (heat supplied from an outside source); and (c) an adiabatic turbine. The compressor and the turbine each have an isentropic efficiency of 85%. Ambient air enters the
Assume an actual compressor has the same exit pressure and specific heat transfer as the ideal isothermal compressor in Problem 9.4 with an isothermal efficiency of 80%. Find the specific work and exit temperature for the actual compressor.
A water cooled air compressor takes air in at 20C, 90 kPa and compresses it to 500 kPa. The isothermal efficiency is 80% and the actual compressor has the same heat transfer as the ideal one. Find the specific compressor work and the exit temperature.
Repeat Problem 9.33 when the compressor has an isentropic efficiency of 80%.
Saturated vapor R-22 enters an insulated compressor with an isentropic efficiency of 75% and the R-22 exits at 3.5 MPa, 120C, find the compressor inlet temperature by trial and error.
Air enters an insulated turbine at 50C, and exits the turbine at - 30C, 100 kPa. The isentropic turbine efficiency is 70% and the inlet volumetric flow rate is 20 L/s. What is the turbine inlet pressure and the turbine power output?
Repeat Problem 9.43 for a pump/compressor isentropic efficiency of 70%.
A certain industrial process requires a steady 0.5 kg/s supply of compressed air at 500 kPa, at a maximum temperature of 30C. This air is to be supplied by installing a compressor and after cooler. Local ambient conditions are 100 kPa, 20C. Using an isentropic compressor efficiency
The turbo charger in Problem 9.24 has isentropic efficiencies of 70% for both the compressor and the turbine. Repeat the questions when the actual compressor has the same flow rate as the ideal but a lower exit pressure.
In a heat-powered refrigerator, a turbine is used to drive the compressor using the same working fluid. Consider the combination, where the turbine produces just enough power to drive the compressor and the two exit flows are mixed together. List any assumptions made and find the ratio of mass flow
An air turbine with inlet conditions 1200 K, 1 MPa and exhaust pressure of 100 kPa pulls a sledge over a leveled plane surface, T 20C. The turbine work overcomes the friction between the sledge and the surface. Find the total entropy generation per kilogram of air through
Consider the scheme P9.84 for producing fresh water from salt water. The conditions are as shown in the figure. Assume that the properties of salt water are the same as for pure water, and that the pump is reversible and adiabatic. a. Determine the ratio (m7/m1), the fraction of salt water
A cylinder/piston containing 2 kg of ammonia at 10C, 90% quality is brought into a 20C room and attached to a line flowing ammonia at 800 kPa, 40C. The total restraining force on the piston is proportional to the cylinder volume squared. The valve is opened and
A certain industrial process requires a steady stream of saturated vapor water at 200 kPa at a rate of 2 kg/s. There are two alternatives for supplying this steam from ambient liquid water at 20C, 100 kPa. Assume pump efficiency of 80%. a. Pump the water to 200 kPa and feed it to a steam
Ammonia enters a nozzle at 800 kPa, 50C, at a velocity of 10 m/s and at the rate of 0.1 kg/s. The nozzle expansion is assumed to be a reversible, polytropic SSS F process. Ammonia exits the nozzle at 200 kPa; the rate of heat transfer to the nozzle is 8.2 kW. Verify that the exit
A cylinder fitted with a spring-loaded piston serves as the supply of steam for a steam turbine. Initially, the cylinder pressure is 2 MPa and the volume is 1.0 m3. The force exerted by the spring is zero at zero cylinder volume, and the top of the piston is open to the ambient. The cylinder
Supercharging of an engine is used to increase the inlet air density so that more fuel can be added, the result of which is an increased power output. Assume that ambient air, 100 kPa and 27C, enters the supercharger at a rate of 250 L/s. The supercharger (compressor) has an isentropic
A jet-ejector pump, shown schematically in Fig P9.90, is a device in which a low-pressure (secondary) fluid is compressed by entrainment in a high-velocity (primary) fluid stream. The compression results from the deceleration in a diffuser. For purposes of analysis this can be considered as
Steam enters a turbine at 450 lbf/in 2, 900 F, expands in a reversible adiabatic process and exhausts at 2 lbf/in.2. Changes in kinetic and potential energies between the inlet and the exit of the turbine are small. The power output of the turbine is 800 Btu/s. What is the mass flow rate of steam
In a heat pump that uses R-134a as the working fluid, the R-134a enters the compressor at 30 lbf/in 2, 20 F at a rate of 0.1 lbm/s, in the compressor the R- 134a is compressed in an adiabatic process to 150 lbf/in 2. Calculate the power input required to the compressor, assuming the process to be
Air at 1 atm, 60 F is compressed to 4 atm, after which it is expanded through a nozzle back to the atmosphere. The compressor and the nozzle are both reversible and adiabatic and kinetic energy in/out of the compressor can be neglected. Find the compressor work and its exit temperature and find the
Analyse the steam turbine described in Problem 6.86. Is it possible?
Two flow streams of water, one at 100 lbf/in.2, saturated vapor, and the other at 100 lbf/in 2, 1000 F, mix adiabatically in a SSSF process to produce a single flow out at 100 lbf/in 2, 600 F. Find the total entropy generation for this process.
A diffuser is a steady-state, steady-flow device in which a fluid flowing at high velocity is decelerated such that the pressure increases in the process. Air at 18 lbf/in 2, 90 F enters a diffuser with velocity 600 ft/s and exits with a velocity of 60ft/s assuming the process is reversible and
One technique for operating a steam turbine in part-load power output is to throttle the steam to a lower pressure before it enters the turbine. The steam line conditions are 200 lbf/in 2, 600 F, and the turbine exhaust pressure is fixed at 1 lbf/in 2. Assuming the expansion inside the turbine to
Air at 540 F, 60 lbf/in 2 with a volume flow 40 ft3/s runs through an adiabatic turbine with exhaust pressure of 15 lbf/in 2. Neglect kinetic energies and use constant specific heats. Find the lowest and highest possible exit temperature. For each case find also the rate of work and the rate of
A supply of 10 lbm/s ammonia at 80 lbf/in 2, 80 F is needed. Two sources are available one is saturated liquid at 80 F and the other is at 80 lbf/in 2, 260 F. Flows from the two sources are fed through valves to an insulated SSS F mixing chamber, which then produces the desired output state. Find
Air from a line at 1800 lbf/in.2, 60 F, flows into a 20-ft3 rigid tank that initially contained air at ambient conditions, 14.7 lbf/in 2, 60F. The process occurs rapidly and is essentially adiabatic. The valve is closed when the pressure inside reaches some value, P2. The tank eventually cools to
An old abandoned salt mine, 3.5 106 ft3 in volume, contains air at 520 R, 14.7 lbf/in 2. The mine is used for energy storage so the local power plant pumps it up to 310 lbf/in 2 using outside air at 520 R, 14.7 lbf/in 2. Assume the pump is ideal and the process is adiabatic. Find
A rigid 35 ft3 tank contains water initially at 250 F, with 50 % liquid and 50% vapor, by volume. A pressure-relief valve on the top of the tank is set to 150 lbf/in 2 (the tank pressure cannot exceed 150 lbf/in 2 - water will be discharged instead). Heat is now transferred to the tank from a 400 F
Liquid water at ambient conditions, 14.7 lbf/in 2, 75 F, enters a pump at the rate of 1 lbm/s. Power input to the pump is 3 Btu/s. Assuming the pump process to be reversible, determine the pump exit pressure and temperature.
A fireman on a ladder 80 ft above ground should be able to spray water an additional 30 ft up with the hose nozzle of exit diameter 1 in. Assume a water pump on the ground and a reversible flow (hose, nozzle included) and find the minimum required power.
Saturated R-134a at 10 F is pumped/compressed to a pressure of 150 lbf/in 2 at the rate of 1.0 lbm/s in a reversible adiabatic SSSF process. Calculate the power required and the exit temperature for the two cases of inlet state of the R-134a:a) Quality of 100 %.b) Quality of 0 %.
A small pump takes in water at 70 F, 14.7 lbf/in.2 and pumps it to 250 lbf/in 2 at a flow rate of 200lbm/min Find the required pump power input. Assume reversible pump and incompressible flow
Helium gas enters a steady-flow expander at 120 lbf/in 2, 500 F, and exits at 18 lbf/in 2. The mass flow rate is 0.4lbm/s, and the expansion process can be considered as a reversible polytropic process with exponent, n 1.3. Calculate the power output of the expander.
A mixing chamber receives 10 lbm/min ammonia as saturated liquid at 0 F from one line and ammonia at 100 F, 40 lbf/in 2 from another line through a valve. The chamber also receives 340 Btu/min energy as heat transferred from a 100-F reservoir. This should produce saturated ammonia vapor at 0 F in
A compressor is used to bring saturated water vapor at 150 lbf/in 2 up to 2500 lbf/in 2, where the actual exit temperature is 1200 F. Find the isentropic compressor efficiency and the entropy generation.
A small air turbine with an isentropic efficiency of 80% should produce 120 Btu/lbm of work. The inlet temperature is 1800 R and it exhausts to the atmosphere. Find the required inlet pressure and the exhaust temperature.
Air enters an insulated compressor at ambient conditions, 14.7 lbf/in 2, 70 F, at the rate of 0.1 lbm/s and exits at 400 F. The isentropic efficiency of the compressor is 70%. What is the exit pressure? How much power is required to drive the compressor?
Air at 1 atm, 60 F is compressed to 4 atm, after which it is expanded through a nozzle back to the atmosphere. The compressor and the nozzle both have efficiency of 90% and kinetic energy in/out of the compressor can be neglected. Find the actual compressor work and its exit temperature and find
A geothermal supply of hot water at 80 lbf/in 2, 300 F is fed to an insulated flash evaporator at the rate of 10,000 lbm/h, A stream of saturated liquid at 30 lbf/in 2 is drained from the bottom of the chamber and a stream of saturated vapor at 30 lbf/in 2 is drawn from the top and fed to a
Redo Problem 9.104 if the water pump has an isentropic efficiency of 85% (hose, nozzle included).
A nozzle is required to produce a steady stream of R-134a at 790 ft/s at ambient conditions, 14.7 lbf/in 2, 70F. The isentropic efficiency may be assumed to be 90%. What pressure and temperature are required in the line upstream of the nozzle?
A two-stage turbine receives air at 2100 R, 750 lbf/in 2. The first stage exit at 150 lbf in 2 then enters stage 2, which has an exit pressure of 30 lbf/in 2. Each stage has an isentropic efficiency of 85%. Find the specific work in each stage, the overall isentropic efficiency, and the total
A water cooled air compressor takes air in at 70 F, 14 lbf/in 2 and compresses it to 80 lbf/in 2. The isothermal efficiency is 80% and the actual compressor has the same heat transfer as the ideal one. Find the specific compressor work and the exit temperature.
Repeat Problem 9.105 for a pump/compressor isentropic efficiency of 70%.
A paper mill has two steam generators, one at 600 lbf/in 2, 550 F and one at 1250 lbf/in 2, 900 F. The setup is shown in Fig. P9.72. Each generator feeds a turbine, both of which have an exhaust pressure of 160 lbf/in.2 and isentropic efficiency of 87%, such that their combined power output is
Two forces P and Q are applied as shown at point A of a hook support. Knowing that P = 15 lb and Q = 25 lb, determine graphically the magnitude and direction of their resultant using(a) The parallelogram law,(b) The triangle rule.
Two forces P and Q are applied as shown at point A of a hook support. Knowing that P = 45 lb and Q = 15 lb, determine graphically the magnitude and direction of their resultant using(a) The parallelogram law,(b) The triangle rule.
Two forces are applied to an eye bolt fastened to a beam. Determine graphically the magnitude and direction of their resultant using(a) The parallelogram law,(b) The triangle rule.
A disabled automobile is pulled by means of ropes subjected to the two forces as shown. Determine graphically the magnitude and direction of their resultant using(a) The parallelogram law,(b) The triangle rule.
The 200-N force is to be resolved into components along lines a-a€² and b-b€². (a) Determine the angle α using trigonometry knowing that the component along a-a€² is to be 150 N. (b) What is the corresponding value of the component along b-b€²?
The 200-N force is to be resolved into components along lines a-a′ and b-b′.(a) Determine the angle α using trigonometry knowing that the component along b-b′ is to be 120 N.(b) What is the corresponding value of the component along a-a′?
Two forces are applied as shown to a hook support. Using trigonometry and knowing that the magnitude of P is 600 N, determine(a) The required angle α if the resultant R of the two forces applied to the support is to be vertical,(b) The corresponding magnitude of R.
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