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engineering
mechanical engineering
Fundamentals Of Thermodynamics 8th Edition Claus Borgnakke, Richard E. Sonntag - Solutions
Air is expanded in a nozzle from 2 MPa, 600 K, to 200 kPa. The mass flow rate through the nozzle is 5 kg/s. Assume the flow is reversible and adiabatic and determine the throat and exit areas for the nozzle.
Consider the nozzle of Problem 16.17 and determine what back pressure will cause a normal shock to stand in the exit plane of the nozzle. This is case g in Fig. 16.17. What is the mass flow rate under these conditions?
At what Mach number will the normal shock occur in the nozzle of Problem 16.17 if the back pressure is 1.4 MPa? (Trial and error on Mx) Relate the inlet and exit conditions to the shock conditions with reversible flow before and after the shock. It becomes trial and error.
Consider the nozzle of Problem 16.17. What back pressure will be required to cause subsonic flow throughout the entire nozzle with M 1 at the throat?
Determine the mass flow rate through the nozzle of Problem 16.17 for a back pressure of 1.9 MPa.
At what Mach number will the normal shock occur in the nozzle of Problem 16.16 flowing with air if the back pressure is halfway between the pressures at c and d in Fig. 16.17?
A convergent nozzle has minimum area of 0.1 m2 and receives air at 175 kPa, 1000 K flowing with 100 m/s. What is the back pressure that will produce the maximum flow rate and find that flow rate?
A convergent-divergent nozzle has a throat area of 100 mm2 and an exit area of 175 mm2. The inlet flow is helium at a total pressure of 1 MPa, stagnation temperature of 375 K. What is the back pressure that will give sonic condition at the throat, but subsonic everywhere else?
a. Determine the exit pressure, temperature, and area, and the throat area.b. Suppose that the back pressure at the nozzle exit is raised to 1.4 MPa, and that the flow remains isentropic except for a normal shock wave. Determine the exit Mach number and temperature, and the mass flow rate through
A jet plane travels through the air with a speed of 1000 km/h at an altitude of 6 km, where the pressure is 40 kPa and the temperature is 12C. Consider the inlet diffuser of the engine where air leaves with a velocity of 100 m/s. Determine the pressure and temperature leaving the
A 1-m3 insulated tank contains air at 1 MPa, 560 K. The tank is now discharged through a small convergent nozzle to the atmosphere at 100 kPa. The nozzle has an exit area of 2 105 m2. a. Find the initial mass flow rate out of the tank. b. Find the mass flow rate when half
A 1-m3 uninsulated tank contains air at 1 MPa, 560 K. The tank is now discharged through a small convergent nozzle to the atmosphere at 100 kPa while heat transfer from some source keeps the air temperature in the tank at 560 K. The nozzle has an exit area of 2 105 m2. a.
The products of combustion enter a convergent nozzle of a jet engine at a total pressure of 125 kPa, and a total temperature of 650C. The atmospheric pressure is 45 kPa and the flow is adiabatic with a rate of 25 kg/s. Determine the exit area of the nozzle.
Air is expanded in a nozzle from 700 kPa, 200C, to 150 kPa in a nozzle having an efficiency of 90%. The mass flow rate is 4 kg/s. Determine the exit area of the nozzle, the exit velocity, and the increase of entropy per kilogram of air. Compare these results with those of a reversible
Repeat Problem 16.26 assuming a diffuser efficiency of 80%.
Consider the diffuser of a supersonic aircraft flying at M 1.4 at such an altitude that the temperature is 20C, and the atmospheric pressure is 50 kPa. Consider two possible ways in which the diffuser might operate, and for each case calculate the throat area
Air enters a diffuser with a velocity of 200 m/s, a static pressure of 70 kPa, and a temperature of 6C. The velocity leaving the diffuser is 60 m/s and the static pressure at the diffuser exit is 80 kPa. Determine the static temperature at the diffuser exit and the diffuser
Steam at a pressure of 1 MPa and temperature of 400C expands in a nozzle to a pressure of 200 kPa. The nozzle efficiency is 90% and the mass flow rate is 10 kg/s. Determine the nozzle exit area and the exit velocity.
Steam at 800 kPa, 350C flows through a convergent-divergent nozzle that has a throat area of 350 mm2. The pressure at the exit plane is 150 kPa and the exit velocity is 800 m/s. The flow from the nozzle entrance to the throat is reversible and adiabatic. Determine the exit area of the
Air at 150 kPa, 290 K expands to the atmosphere at 100 kPa through a convergent nozzle with exit area of 0.01 m2. Assume an ideal nozzle. What is the percent error in mass flow rate if the flow is assumed incompressible?
A sharp-edged orifice is used to measure the flow of air in a pipe. The pipe diameter is 100 mm and the diameter of the orifice is 25 mm. Upstream of the orifice, the absolute pressure is 150 kPa and the temperature is 35C. The pressure drop across the orifice is 15 kPa, and the coefficient
A critical nozzle is used for the accurate measurement of the flow rate of air. Exhaust from a car engine is diluted with air so its temperature is 50C at a total pressure of 100 kPa. It flows through the nozzle with throat area of 700 mm2 by suction from a blower. Find the needed suction
A convergent nozzle is used to measure the flow of air to an engine. The atmosphere is at 100 kPa, 25C. The nozzle used has a minimum area of 2000 mm2 and the coefficient of discharge is 0.95. A pressure difference across the nozzle is measured to 2.5 kPa. Find the mass flow rate assuming
A convergent nozzle with exit diameter of 2 cm has an air inlet flow of 20C, 101 kPa (stagnation conditions). The nozzle has an isentropic efficiency of 95% and the pressure drop is measured to 50 cm water column. Find the mass flow rate assuming compressible adiabatic flow. Repeat
Steam at 600 kPa, 300C is fed to a set of convergent nozzles in a steam turbine. The total nozzle exit area is 0.005 m2 and they have a discharge coefficient of 0.94. The mass flow rate should be estimated from the measurement of the pressure drop across the nozzles, which is measured to be
The coefficient of discharge of a sharp-edged orifice is determined at one set of conditions by use of an accurately calibrated gasometer. The orifice has a diameter of 20 mm and the pipe diameter is 50 mm. The absolute upstream pressure is 200 kPa and the pressure drop across the orifice is 82 mm
Adv Atmospheric air is at 20C, 100 kPa with zero velocity. An adiabatic reversible compressor takes atmospheric air in through a pipe with cross-sectional area of 0.1 m2 at a rate of 1 kg/s. It is compressed up to a measured stagnation pressure of 500 kPa and leaves through a pipe with
Steam leaves a nozzle with a velocity of 800 ft/s. The stagnation pressure is 100lbf/in2 and the stagnation temperature is 500 F. What is the static pressure and temperature?
Air leaves the compressor of a jet engine at a temperature of 300 F, a pressure of 45lbf/in2, and a velocity of 400 ft/s. Determine the isentropic stagnation temperature and pressure.
A meteorite melts and burn up at temperatures of 5500 R. If it hits air at 0.75 lbf/in 2, 90 R how high a velocity should it have to reach such temperature?
A jet engine receives a flow of 500 ft/s air at 10 lbf/in 2, 40 F inlet area of 7 ft2 with an exit at 1500 ft/s, 10 lbf/in 2, 1100 R. Find the mass flow rate and thrust.
A water turbine using nozzles is located at the bottom of Hoover Dam 575 ft below the surface of Lake Mead. The water enters the nozzles at a stagnation pressure corresponding to the column of water above it minus 20% due to friction. The temperature is 60 F and the water leaves at standard
Find the speed of sound for air at 15 lbf/in.2, at the two temperatures of 32 F and 90 F. Repeat the answer for carbon dioxide and argon gases.
Air is expanded in a nozzle from 300 lbf/in 2, 1100 R to 30lbf/in 2. The mass flow rate through the nozzle is 10lbm/s. Assume the flow is reversible and adiabatic and determines the throat and exit areas for the nozzle.
A convergent nozzle has a minimum area of 1 ft2 and receives air at 25 lbf/in 2, 1800 R flowing with 330 ft/s. What is the back pressure that will produce the maximum flow rate and find that flow rate?
A jet plane travels through the air with a speed of 600 mi/h at an altitude of 20000 ft, where the pressure is 5.75 lbf/in 2 and the temperature is 25 F. Consider the diffuser of the engine where air leaves at with a velocity of 300 ft/s. Determine the pressure and temperature leaving the diffuser,
The products of combustion enter a nozzle of a jet engine at a total pressure of 18 lbf/in 2, and a total temperature of 1200 F. The atmospheric pressure is 6.75 lbf/in 2. The nozzle is convergent, and the mass flow rate is 50 lbm/s. Assume the flow is adiabatic. Determine the exit area of the
Repeat Problem 16.52 assuming a diffuser efficiency of 80%.
A 50-ft3 uninsulated tank contains air at 150 lbf/in 2, 1000 R. The tank is now discharged through a small convergent nozzle to the atmosphere at 14.7 lbf/in 2 while heat transfer from some source keeps the air temperature in the tank at 1000 R. The nozzle has an exit area of 2
Air enters a diffuser with a velocity of 600 ft/s, a static pressure of 10 lbf/in 2, and a temperature of 20 F. The velocity leaving the diffuser is 200 ft/s and the static pressure at the diffuser exit is 11.7 lbf/in 2. Determine the static temperature at the diffuser exit and the diffuser
The “standard” acceleration (at sea level and 45latitude) due to gravity is 9.80665 m/s2, what is the force needed to hold a mass of 2 kg at rest in this gravitational field? How much mass can a force of 1 N support?
A car drives at 60 km/h and is brought to a full stop with constant deceleration in 5 seconds. If the total car and driver mass is 1075 kg, find the necessary force.
A car drives at 60 km/h and is brought to a full stop with constant deceleration in 5 seconds. If the total car and driver mass is 1075 kg, find the necessary force. Discuss.
A washing machine has 2 kg of clothes spinning at a rate that generates an acceleration of 24 m/s2. What is the force needed to hold the clothes?
A 1200-kg car moving at 20 km/h is accelerated at a constant rate of 4 m/s2 up to a speed of 75 km/h. What are the force and total time required?
A steel plate of 950 kg accelerates from rest with 3 m/s2 for a period of 10s. What force is needed and what is the final velocity?
A 15 kg steel container has 1.75 kilo moles of liquid propane inside. A force of 2kN now accelerates this system. What is the acceleration?
A rope hangs over a pulley with the two equally long ends down. On one end you attach a mass of 5 kg and on the other end you attach 10 kg. Assuming standard gravitation and no friction in the pulley what is the acceleration of the 10 kg mass when released?
A bucket of concrete of total mass 200 kg is raised by a crane with an acceleration of 2 m/s2 relative to the ground at a location where the local gravitational acceleration is 9.5 m/s2. Find the required force.
On the moon the gravitational acceleration is approximately one-sixth that on the surface of the earth. A 5-kg mass is “weighed” with a beam balance on the surface on the moon. What is the expected reading? If this mass is weighed with a spring scale that reads correctly for standard gravity on
One kilogram of diatomic oxygen (O2 molecular weight 32) is contained in a 500- L tank. Find the specific volume on both a mass and mole basis (v and v).
A 5 m3 container is filled with 900 kg of granite (density 2400 kg/m3) and the rest of the volume is air with density 1.15 kg/m3. Find the mass of air and the overall (average) specific volume.
A 15-kg steel gas tank holds 300 L of liquid gasoline, having a density of 800 kg/m3. If the system is decelerated with 6 m/s2 what is the needed force?
A vertical hydraulic cylinder has a 125-mm diameter piston with hydraulic fluid inside the cylinder and an ambient pressure of 1 bar. Assuming standard gravity, find the piston mass that will create a pressure inside of 1500 kPa.
A barometer to measure absolute pressure shows a mercury column height of 725 mm. The temperature is such that the density of the mercury is 13550 kg/m3. Find the ambient pressure.
A cannon-ball of 5 kg acts as a piston in a cylinder of 0.15 m diameter. As the gunpowder is burned a pressure of 7 MPa is created in the gas behind the ball. What is the acceleration of the ball if the cylinder (cannon) is pointing horizontally?
Repeat the previous problem for a cylinder (cannon) pointing 40 degrees up relative to the horizontal direction. Discuss.
A piston/cylinder with cross sectional area of 0.01 m2 has a piston mass of 100 kg resting on the stops. With an outside atmospheric pressure of 100 kPa, what should the water pressure be to lift the piston?
The hydraulic lift in an auto-repair shop has a cylinder diameter of 0.2 m. To what pressure should the hydraulic fluid be pumped to lift 40 kg of piston/arms and 700 kg of a car?
A differential pressure gauge mounted on a vessel shows 1.25 MPa and a local barometer gives atmospheric pressure as 0.96bar. Find the absolute pressure inside the vessel.
The absolute pressure in a tank is 85 kPa and the local ambient absolute pressure is 97 kPa. If a U-tube with mercury, density 13550 kg/m3 is attached to the tank to measure the vacuum, what column height difference would it show?
A 5-kg piston in a cylinder with diameter of 100 mm is loaded with a linear spring and the outside atmospheric pressure of 100 kPa. The spring exerts no force on the piston when it is at the bottom of the cylinder and for the state shown, the pressure is 400 kPa with volume 0.4 L. The valve is
A U-tube manometer filled with water, density 1000 kg/m3 shows a height difference of 25 cm. What is the gauge pressure? If the right branch is tilted to make an angle of 30with the horizontal, what should the length of the column in the tilted tube be relative to the U-tube?
The difference in height between the columns of a manometer is 200 mm with a fluid of density 900 kg/m3. What is the pressure difference? What is the height difference if the same pressure difference is measured using mercury, density 13600 kg/ m3, as manometer fluid?
Two reservoirs, A and B, open to the atmosphere, are connected with a mercury manometer. Reservoir A is moved up/down so the two top surfaces are level at h3. Assuming that you know A, Hg and measure the heights h1, h2, and h3, find the density B.
Two vertical cylindrical storage tanks are full of liquid water, density 1000 kg/m3, the top open to the atmosphere. One is 10 m tall, 2 m diameter; the other is 2.5 m tall with diameter 4m. What is the total force from the bottom of each tank to the water and what is the pressure at the bottom of
The density of mercury changes approximately linearly with temperature as Hg = 13595 - 2.5 T kg/ m3 T in Celsius so the same pressure difference will result in a manometer reading that is influenced by temperature. If a pressure difference of 100 kPa is measured in the summer at 35C
Liquid water with density is filled on top of a thin piston in a cylinder with cross-sectional area A and total height H. Air is let in under the piston so it pushes up, spilling the water over the edge. Deduce the formula for the air pressure as a function of the piston elevation
A piston, mp= 5 kg, is fitted in a cylinder, A = 15 cm2, that contains a gas. The setup is in a centrifuge that creates an acceleration of 25 m/s2 in the direction of piston motion towards the gas. Assuming standard atmospheric pressure outside the cylinder, find the gas pressure.
A piece of experimental apparatus is located where g = 9.5 m/s2 and the temperature is 5C. An air flow inside the apparatus is determined by measuring the pressure drop across an orifice with a mercury manometer showing a height difference of 200 mm. What is the pressure drop in kPa?
Repeat the previous problem if the flow inside the apparatus is liquid water, 1000 kg/m3, instead of air. Find the pressure difference between the two holes flush with the bottom of the channel. You cannot neglect the two unequal water columns.
Two piston/cylinder arrangements, A and B, have their gas chambers connected by a pipe. Cross-sectional areas are AA = 75 cm2 and AB = 25 cm2 with the piston mass in A being mA = 25 kg. Outside pressure is 100 kPa and standard gravitation. Find the mass mB so that none of the pistons have to rest
Two hydraulic piston/cylinders are of same size and setup as in Problem 2.32, but with neglible piston masses. A single point force of 250 N presses down on piston A. Find the needed extra force on piston B so that none of the pistons have to move.
At the beach, atmospheric pressure is 1025 mbar. You dive 15 m down in the ocean and you later climb a hill up to 250 m elevation. Assume the density of water is about 1000 kg/m3 and the density of air is 1.18 kg/m3. What pressure do you feel at each place?
In the city water tower, water is pumped up to a level 25 m above ground in a pressurized tank with air at 125 kPa over the water surface. This is illustrated in Fig. P2.35. Assuming the water density is 1000 kg/m3 and standard gravity, find the pressure required to pump more water in at ground
Two cylinders are connected by a piston. Cylinder A is used as a hydraulic lift and pumped up to 500 kPa. The piston mass is 25 kg and there is standard gravity. What is the gas pressure in cylinder B?
Two cylinders are filled with liquid water, = 1000 kg/m3, and connected by a line with a closed valve. A has 100 kg and B has 500 kg of water, their cross-sectional areas are AA = 0.1 m2 and AB = 0.25 m2 and the height h is 1 m. Find the pressure on each side of the valve. The valve
Using the freezing and boiling point temperatures for water in both Celsius and Fahrenheit scales, develop a conversion formula between the scales. Find the conversion formula between Kelvin and Rankine temperature scales.
A 2500-lbm car moving at 15 mi/h is accelerated at a constant rate of 15 ft/s2 up to a speed of 50 mi/h. What are the force and total time required?
Two pound moles of diatomic oxygen gas are enclosed in a 20-lbm steel container. A force of 2000 lbf now accelerates this system. What is the acceleration?
A bucket of concrete of total mass 400 lbm is raised by a crane with an acceleration of 6 ft/s2 relative to the ground at a location where the local gravitational acceleration is 31 ft/s2. Find the required force.
One pound-mass of diatomic oxygen (O2 molecular weight 32) is contained in a 100-gal tank. Find the specific volume on both a mass and mole basis (v and v).
A 30-lbm steel gas tank holds 10 ft3 of liquid gasoline, having a density of 50 lbm/ft3 what force is needed to accelerate this combined system at a rate of 15 ft/s2?
A differential pressure gauge mounted on a vessel shows 185 lbf/in.2 and a local barometer gives atmospheric pressure as 0.96 atm. Find the absolute pressure inside the vessel.
A U-tube manometer filled with water, density 62.3 lbm/ft3, shows a height difference of 10 in. What is the gauge pressure? If the right branch is tilted to make an angle of 30with the horizontal, what should the length of the column in the tilted tube be relative to the U-tube?
A piston/cylinder with cross-sectional area of 0.1 ft2 has a piston mass of 200 lbm resting on the stops. With an outside atmospheric pressure of 1 atm, what should the water pressure be to lift the piston?
The density of mercury changes approximately linearly with temperature as Hg = 851.5 - 0.086 T lbm/ft3 T in degrees Fahrenheit so the same pressure difference will result in a manometer reading that is influenced by temperature. If a pressure difference of 14.7 lbf/in 2 is measured in the
A piston, mp = 10 lbm, is fitted in a cylinder, A = 2.5 in 2, that contains a gas. The setup is in a centrifuge that creates an acceleration of 75 ft/s2. Assuming standard atmospheric pressure outside the cylinder, find the gas pressure.
At the beach, atmospheric pressure is 1025 mbar. You dive 30 ft down in the ocean and you later climb a hill up to 300 ft elevation. Assume the density of water is about 62.3 lbm/ft3 and the density of air is 0.0735 lbm/ft3 what pressure do you feel at each place?
Water at 27C can exist in different phases dependent upon the pressure. Give the approximate pressure range in kPa for water being in each one of the three phases vapor, liquid or solid.
Find the lowest temperature at which it is possible to have water in the liquid phase. At what pressure must the liquid exist?
If density of ice is 920 kg/m3, find the pressure at the bottom of a 1000 m thick ice cap on the North Pole. What is the melting temperature at that pressure? Discuss.
A substance is at 2 MPa, 17C in a rigid tank. Using only the critical properties can the phase of the mass be determined if the substance is nitrogen, water or propane?
A cylinder fitted with a frictionless piston contains butane at 25C, 500 kPa. Can the butane reasonably be assumed to behave as an ideal gas at this state?
A 1-m3 tank is filled with a gas at room temperature 20C and pressure 100 kPa. How much mass is there if the gas is a) air, b) neon or c) propane?
A cylinder has a thick piston initially held by a pin. The cylinder contains carbon dioxide at 200 kPa and ambient temperature of 290 K. The metal piston has a density of 8000 kg/m3 and the atmospheric pressure is 101 kPa. The pin is now removed, allowing the piston to move and after a while the
A cylindrical gas tank 1 m long, inside diameter of 20 cm, is evacuated and then filled with carbon dioxide gas at 25C. To what pressure should it be charged if there should be 1.2 kg of carbon dioxide?
A 1-m3 rigid tank with air at 1 MPa, 400 K is connected to an air line. The valve is opened and air flows into the tank until the pressure reaches 5 MPa, at which point the valve is closed and the temperature inside is 450K. a. What is the mass of air in the tank before and after the process? b.
A hollow metal sphere of 150-mm inside diameter is weighed on a precision beam balance when evacuated and again after being filled to 875 kPa with an unknown gas. The difference in mass is 0.0025 kg, and the temperature is 25C. What is the gas, assuming it is a pure substance listed in
A piston/cylinder arrangement contains air at 250 kPa, 300C. The 50-kg piston has a diameter of 0.1 m and initially pushes against the stops. The atmosphere is at 100 kPa and 20C. The cylinder now cools as heat is transferred to the ambient. a. At what temperature does the piston
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