Air enters the compressor of a regenerative gas-turbine engine at 310 K and 100 kPa, where it is compressed to 900 kPa and 650 K. The regenerator has an effectiveness of 80 percent, and the air enters the turbine at 1400 K. For a turbine efficiency of 90 percent, determine (a) the amount of heat transfer in the regenerator and (b) the thermal efficiency. Assume variable specific heats for air.
> An elastic air balloon having a diameter of 30 cm is attached to the base of a container partially filled with water at +4°C, as shown in Fig. P11–41. If the pressure of the air above the water is gradually increased from 100
> The 0.5-m-radius semicircular gate shown in the figure is hinged through the top edge AB. Find the required force to be applied at the center of gravity to keep the gate closed.
> A submerged horizontal flat plate is suspended in water by a string attached at the centroid of its upper surface. Now the plate is rotated 45° about an axis that passes through its centroid. Discuss the change in the hydrostatic force acting on the top
> An air-conditioning system requires a 34-m-long section of 12-cm-diameter ductwork to be laid underwater. Determine the upward force the water will exert on the duct. Take the densities of air and water to be 1.3 kg/m3 and 1000 kg/m3, respectively.
> The weight of a body is usually measured by disregarding buoyancy force applied by the air. Consider a 20-cm-diameter spherical body of density 7800 kg/m3. What is the percentage error associated with neglecting air buoyancy?
> A cone floats in the glycerin (SG = 1.26), as shown in the figure. Find the mass of the cone.
> One of the common procedures in fitness programs is to determine the fat-to-muscle ratio of the body. This is based on the principle that the muscle tissue is denser than the fat tissue, and, thus, the higher the average density of the body, the higher i
> It is estimated that 90 percent of an iceberg’s volume is below the surface, while only 10 percent is visible above the surface. For seawater with a density of 1025 kg/m3, estimate the density of the iceberg.
> It is said that Archimedes discovered his principle during a bath while thinking about how he could determine if King Hiero’s crown was actually made of pure gold. While in the bathtub, he conceived the idea that he could determine the average density of
> The density of a liquid is to be determined by an old 1-cm-diameter cylindrical hydrometer whose division marks are completely wiped out. The hydrometer is first dropped in water, and the water level is marked. The hydrometer is then dropped into the oth
> The specific kinetic energy of a moving mass is given by ke = V2/2, where V is the velocity of the mass. Determine the specific kinetic energy of a mass whose velocity is 100 ft/s, in Btu/lbm.
> The hull of a boat has a volume of 180 m3, and the total mass of the boat when empty is 8560 kg. Determine how much load this boat can carry without sinking (a) in a lake and (b) in seawater with a specific gravity of 1.03.
> A 200-kg granite rock (ρ = 2700 kg/m3) is dropped into a lake. A man dives in and tries to lift the rock. Determine how much force the man needs to apply to lift it from the bottom of the lake. Do you think he can do it?
> Consider two identical spherical balls submerged in water at different depths. Will the buoyant forces acting on these two balls be the same or different? Explain.
> Someone claims that she can determine the magnitude of the hydrostatic force acting on a plane surface submerged in water regardless of its shape and orientation if she knows the vertical distance of the centroid of the surface from the free surface and
> Consider a 3-kg copper cube and a 3-kg copper ball submerged in a liquid. Will the buoyant forces acting on these two bodies be the same or different? Explain.
> Consider two 5-cm-diameter spherical balls—one made of aluminum, the other of iron—submerged in water. Will the buoyant forces acting on these two balls be the same or different? Explain.
> Discuss the stability of (a) a submerged and (b) a floating body whose center of gravity is above the center of buoyancy.
> What is buoyant force? What causes it? What is the magnitude of the buoyant force acting on a submerged body whose volume is V? What are the direction and the line of action of the buoyant force?
> Repeat Prob. 11–24 for a radius of 2 m for the gate. Data from Prob. 11-24: A 4-m-long quarter-circular gate of radius 3 m and of negligible weight is hinged about its upper edge A, as shown in Fig. P11–24. The gate c
> A 4-m-long quarter-circular gate of radius 3 m and of negligible weight is hinged about its upper edge A, as shown in Fig. P11–24. The gate controls the flow of water over the ledge at B, where the gate is pressed by a spring. Determine
> What is the difference between the macroscopic and microscopic forms of energy?
> Repeat Prob. 11–22 for the case of a partially filled trough with a water height of 0.35 m directly above the hinge. Data from Prob. 11-22: The two sides of a V-shaped water trough are hinged to each other at the bottom where they meet
> The two sides of a V-shaped water trough are hinged to each other at the bottom where they meet, as shown in Fig. P11–22, making an angle of 45° with the ground from both sides. Each side is 0.75 m wide, and the two parts are
> A long, solid cylinder of radius 2 ft hinged at point A is used as an automatic gate, as shown in Fig. P11–21E. When the water level reaches 12 ft, the cylindrical gate opens by turning about the hinge at point A. Determine (a) the hydr
> For a gate width of 2 m into the paper (Fig. P11–20), determine the force required to hold the gate ABC at its location.
> You may have noticed that dams are much thicker at the bottom. Explain why dams are built that way.
> Repeat Prob. 11–18E for a water height of 6 ft. Data from Prob. 11-18: The flow of water from a reservoir is controlled by a 5-ft-wide L-shaped gate hinged at point A, as shown in Fig. P11–18E. If it is desired that t
> The flow of water from a reservoir is controlled by a 5-ft-wide L-shaped gate hinged at point A, as shown in Fig. P11–18E. If it is desired that the gate open when the water height is 12 ft, determine the mass of the required weight W.
> Reconsider Prob. 11–16. Using appropriate software, investigate the effect of water depth on the force exerted on the plate by the ridge. Let the water depth vary from 0 to 5 m in increments of 0.5 m. Tabulate and plot your results. Da
> A 6-m-high, 5-m-wide rectangular plate blocks the end of a 5-m-deep freshwater channel, as shown in Fig. P11–16. The plate is hinged about a horizontal axis along its upper edge through a point A and is restrained from opening by a fixe
> Determine the resultant force acting on the 0.7-m-high and 0.7-m-wide triangular gate shown in Fig. P11–15 and its line of action.
> Is the state of the air in an isolated room completely specified by the temperature and the pressure? Explain.
> A water trough of semicircular cross section of radius 0.6 m consists of two symmetric parts hinged to each other at the bottom, as shown in Fig. P11–14. The two parts are held together by a cable and turnbuckle placed every 3 m along t
> The water side of the wall of a 70-m-long dam is a quarter circle with a radius of 7 m. Determine the hydrostatic force on the dam and its line of action when the dam is filled to the rim.
> A room in the lower level of a cruise ship has a 40-cm-diameter circular window. If the midpoint of the window is 2 m below the water surface, determine the hydrostatic force acting on the window, and the pressure center. Take the specific gravity of sea
> Consider a heavy car submerged in water in a lake with a flat bottom. The driver’s side door of the car is 1.1 m high and 0.9 m wide, and the top edge of the door is 10 m below the water surface. Determine the net force acting on the door (normal to its
> Consider an 8-m-long, 8-m-wide, and 2-m-high above ground swimming pool that is filled with water to the rim. (a) Determine the hydrostatic force on each wall and the distance of the line of action of this force from the ground. (b) If the height of the
> Define the resultant hydrostatic force acting on a submerged surface, and the center of pressure.
> What four processes make up the simple ideal Rankine cycle?
> Water enters the boiler of a steady-flow Carnot engine as a saturated liquid at 300 psia and leaves with a quality of 0.95. Steam leaves the turbine at a pressure of 20 psia. Show the cycle on a T-s diagram relative to the saturation lines, and determine
> Consider a steady-flow Carnot cycle with water as the working fluid. The maximum and minimum temperatures in the cycle are 350 and 60°C, respectively. The quality of water is 0.891 at the beginning of the heat-rejection process and 0.1 at the end. Show t
> Repeat Prob. 9–95 for a heat rejection pressure of 10 kPa. Data from Prob. 9-95: A steady-flow Carnot cycle uses water as the working fluid. Water changes from saturated liquid to saturated vapor as heat is transferred to it from a source at 250°C. Heat
> Is the number of moles of a substance contained in a system an extensive or intensive property?
> A steady-flow Carnot cycle uses water as the working fluid. Water changes from saturated liquid to saturated vapor as heat is transferred to it from a source at 250°C. Heat rejection takes place at a pressure of 20 kPa. Show the cycle on a T-s diagram re
> Why is excessive moisture in steam undesirable in steam turbines? What is the highest moisture content allowed?
> Why is the Carnot cycle not a realistic model for steam power plants?
> Repeat Prob. 9–90 for a regenerator effectiveness of 70 percent. Data from Prob. 9-90: Air enters the compressor of a regenerative gas-turbine engine at 310 K and 100 kPa, where it is compressed to 900 kPa and 650 K. The regenerator has an effectiveness
> Repeat Prob. 9–90 using constant specific heats at room temperature. Data from Prob. 9-90: Air enters the compressor of a regenerative gas-turbine engine at 310 K and 100 kPa, where it is compressed to 900 kPa and 650 K. The regenerator has an effective
> What is the difference between spark-ignition and compression-ignition engines?
> A stationary gas-turbine power plant operates on an ideal regenerative Brayton cycle (∊ = 100 percent) with air as the working fluid. Air enters the compressor at 95 kPa and 290 K and the turbine at 880 kPa and 1100 K. Heat is transferred to air from an
> A Brayton cycle with regeneration using air as the working fluid has a pressure ratio of 7. The minimum and maximum temperatures in the cycle are 310 and 1150 K. Assuming an isentropic efficiency of 75 percent for the compressor and 82 percent for the tu
> A gas-turbine engine operates on the ideal Brayton cycle with regeneration. Now the regenerator is rearranged so that the airstreams of states 2 and 5 enter at one end of the regenerator and streams 3 and 6 exit at the other end (i.e., parallel flow arra
> The specific weight of a system is defined as the weight per unit volume (note that this definition violates the normal specific property-naming convention). Is the specific weight an extensive or intensive property?
> Rework Prob. 9–85 when the compressor isentropic efficiency is 87 percent and the turbine isentropic efficiency is 90 percent. Data from Prob. 9-85: A gas turbine for an automobile is designed with a regenerator. Air enters the compres
> A gas turbine for an automobile is designed with a regenerator. Air enters the compressor of this engine at 100 kPa and 30°C. The compressor pressure ratio is 8; the maximum cycle temperature is 800°C; and the cold airstream leaves
> Develop an expression for the thermal efficiency of an ideal Brayton cycle with an ideal regenerator of effectiveness 100 percent. Use constant specific heats at room temperature.
> In 1903, Aegidius Elling of Norway designed and built an 11-hp gas turbine that used steam injection between the combustion chamber and the turbine to cool the combustion gases to a safe temperature for the materials available at the time. Currently ther
> In an ideal regenerator, is the air leaving the compressor heated to the temperature at (a) the turbine inlet, (b) the turbine exit, (c) slightly above the turbine exit?
> Somebody claims that at very high pressure ratios, the use of regeneration actually decreases the thermal efficiency of a gas-turbine engine. Is there any truth in this claim? Explain.
> Define the effectiveness of a regenerator used in gasturbine cycles.
> Can the mean effective pressure of an automobile engine in operation be less than the atmospheric pressure?
> How does regeneration affect the efficiency of a Brayton cycle, and how does it accomplish it?
> A gas-turbine power plant operates on a modified Brayton cycle shown in the figure with an overall pressure ratio of 8. Air enters the compressor at 0°C and 100 kPa. The maximum cycle temperature is 1500 K. The compressor and the turbines are
> What is the difference between intensive and extensive properties?
> A simple ideal Brayton cycle uses argon as the working fluid. At the beginning of the compression, P1 = 15 psia and T1 = 80°F; the maximum cycle temperature is 1200°F; and the pressure in the combustion chamber is 150 psia. The argon enters the compres
> A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 1600 kPa. The working fluid is air, which enters the compressor at 40°C at a rate of 850 m3/min and leaves the turbine at 650°C.
> Repeat Prob. 9–74 for a pressure ratio of 15. Data from Prob. 9-74: An aircraft engine operates on a simple ideal Brayton cycle with a pressure ratio of 10. Heat is added to the cycle at a rate of 500 kW; air passes through the engine at a rate of 1 kg/
> An aircraft engine operates on a simple ideal Brayton cycle with a pressure ratio of 10. Heat is added to the cycle at a rate of 500 kW; air passes through the engine at a rate of 1 kg/s; and the air at the beginning of the compression is at 70 kPa and 0
> Air is used as the working fluid in a simple ideal Brayton cycle that has a pressure ratio of 12, a compressor inlet temperature of 300 K, and a turbine inlet temperature of 1000 K. Determine the required mass flow rate of air for a net power output of 7
> Repeat Prob. 9–69 when the isentropic efficiencies of the turbine and compressor are 90 percent and 80 percent, respectively, and there is a 50-kPa pressure drop across the combustion chamber. Data from Prob. 9-69: A simple ideal Brayt
> Repeat Prob. 9–69 when the isentropic efficiency of the turbine is 90 percent and that of the compressor is 80 percent. Data from Prob. 9-69: A simple ideal Brayton cycle operates with air with minimum and maximum temperatures of 27&Ac
> Repeat Prob. 9–69 when the isentropic efficiency of the turbine is 90 percent. Data from Prob. 9-69: A simple ideal Brayton cycle operates with air with minimum and maximum temperatures of 27°C and 727°C. It is de
> Define the compression ratio for reciprocating engines.
> A simple ideal Brayton cycle operates with air with minimum and maximum temperatures of 27°C and 727°C. It is designed so that the maximum cycle pressure is 2000 kPa and the minimum cycle pressure is 100 kPa. Determine the net work
> How would you describe the state of the air in the atmosphere? What kind of process does this air undergo from a cool morning to a warm afternoon?
> Repeat Prob. 9–67 using constant specific heats at room temperature. Data from Prob. 9-67: A gas-turbine power plant operates on the simple Brayton cycle with air as the working fluid and delivers 32 MW of power. The minimum and maximum temperatures in
> A gas-turbine power plant operates on the simple Brayton cycle with air as the working fluid and delivers 32 MW of power. The minimum and maximum temperatures in the cycle are 310 and 900 K, and the pressure of air at the compressor exit is 8 times the v
> A stationary gas-turbine power plant operates on a simple ideal Brayton cycle with air as the working fluid. The air enters the compressor at 95 kPa and 290 K and the turbine at 760 kPa and 1100 K. Heat is transferred to air at a rate of 35,000 kJ/s. Det
> A simple ideal Brayton cycle with air as the working fluid has a pressure ratio of 10. The air enters the compressor at 520 R and the turbine at 2000 R. Accounting for the variation of specific heats with temperature, determine (a) the air temperature at
> How do the inefficiencies of the turbine and the compressor affect (a) the back work ratio and (b) the thermal efficiency of a gas-turbine engine?
> Why are the back work ratios relatively high in gas-turbine engines?
> What is the back work ratio? What are typical back work ratio values for gas-turbine engines?
> For fixed maximum and minimum temperatures, what is the effect of the pressure ratio on (a) the thermal efficiency and (b) the net work output of a simple ideal Brayton cycle?
> What four processes make up the simple ideal Brayton cycle?
> What does the area enclosed by the cycle represent on a P-v diagram? How about on a T-s diagram?
> How would you define a system to determine the temperature rise created in a lake when a portion of its water is used to cool a nearby electrical power plant?
> Repeat Prob. 9–58E if the compression ratio is reduced to 12. Data from Prob. 9-58: An air-standard dual cycle has a compression ratio of 20 and a cutoff ratio of 1.3. The pressure ratio during the constant volume heat addition process is 1.2. Determine
> An air-standard dual cycle has a compression ratio of 20 and a cutoff ratio of 1.3. The pressure ratio during the constant volume heat addition process is 1.2. Determine the thermal efficiency, amount of heat added, and the maximum gas pressure and tempe
> Repeat Prob. 9–56 using nitrogen as the working fluid. Data from Prob. 9-56: A four-cylinder, two-stroke 2.4-L diesel engine that operates on an ideal Diesel cycle has a compression ratio of 22 and a cutoff ratio of 1.8. Air is at 70°C and 97 kPa at the
> A four-cylinder, two-stroke 2.4-L diesel engine that operates on an ideal Diesel cycle has a compression ratio of 22 and a cutoff ratio of 1.8. Air is at 70°C and 97 kPa at the beginning of the compression process. Using the cold-air-standard assumptions
> Reconsider Prob. 9–54. Using appropriate software, study the effect of varying the compression ratio from 14 to 24. Plot the net work output, mean effective pressure, and thermal efficiency as a function of the compression ratio. Plot the T-s and P-v dia
> Repeat Prob. 9–53, but replace the isentropic expansion process with a polytropic expansion process with the polytropic exponent n = 1.35. Use variable specific heats. Data from Prob. 9-53: An ideal diesel engine has a compression ratio of 20 and uses a
> An ideal diesel engine has a compression ratio of 20 and uses air as the working fluid. The state of air at the beginning of the compression process is 95 kPa and 20°C. If the maximum temperature in the cycle is not to exceed 2200 K, determine (a) the th
> An ideal Diesel cycle has a maximum cycle temperature of 2000°C. The state of the air at the beginning of the compression is P1 = 95 kPa and T1 = 15°C. This cycle is executed in a four-stroke, eight-cylinder engine with a cylinder bore of 10 cm and a pis
> Repeat Prob. 9–50E using constant specific heats at room temperature. Data from Prob. 9-50: An air-standard Diesel cycle has a compression ratio of 18.2. Air is at 120°F and 14.7 psia at the beginning of the compression process and at 3200 R at the end
> An air-standard Diesel cycle has a compression ratio of 18.2. Air is at 120°F and 14.7 psia at the beginning of the compression process and at 3200 R at the end of the heat-addition process. Accounting for the variation of specific heats with temperature
> A pressure gage connected to a tank reads 50 psi at a location where the barometric reading is 29.1 in Hg. Determine the absolute pressure in the tank. Take ρHg = 848.4 lbm/ft3.
> How are the combustion and exhaust processes modeled under the air-standard assumptions?
> Repeat Prob. 9–48 using constant specific heats at room temperature. Data from Prob. 9-48: An air-standard Diesel cycle has a compression ratio of 16 and a cutoff ratio of 2. At the beginning of the compression process, air is at 95 kPa and 27°C. Accoun
