questions of fluid dynamics | Exercises Fluid Dynamics

Assignment 1

1. An air-standard cycle is executed within a closed piston-cylinder system and consists of

three processes as follows:

1-2 V = constant heat addition from 100 kPa and 27oC to 700 kPa

2-3 Isothermal expansion until V3 = 7V2

3-1 P = constant heat rejection to the initial state Assume air has constant properties with

cv = 0.718 kJ/kg·K, cp = 1.005 kJ/kg·K, R = 0.287 kJ/kg·K, and k = 1.4. (a) Sketch the P-v and

T-s diagrams for the cycle. (b) Determine the ratio of the compression work to the

expansion work (the back work ratio). (c) Determine the cycle thermal efficiency.

Answers: (b) 0.440, (c) 26.6 percent

2. An air-standard cycle with variable specific heats is executed in a closed system and is

composed of the following four processes:

1-2 Isentropic compression from 100 kPa and 22oC to 600 kPa

2-3 v = constant heat addition to 1500 K

3-4 Isentropic expansion to 100 kPa

4-1 P = constant heat rejection to initial state (a) Show the cycle on P-v and T-s diagrams.

(b) Calculate the net work output per unit mass. (c) Determine the thermal efficiency.

3. Consider a Carnot cycle executed in a closed system with 0.6 kg of air. The temperature

limits of the cycle are 300 and 1100 K, and the minimum and maximum pressures that

occur during the cycle are 20 and 3000 kPa. Assuming constant specific heats, determine

the net work output per cycle.

4. Consider a Carnot cycle executed in a closed system with air as the working fluid. The

maximum pressure in the cycle is 1300 kPa while the maximum temperature is 950 K. If

the entropy increase during the isothermal heat rejection process is 0.25 kJ/kg·K and the

net work output is 100 kJ/kg, determine (a) the minimum pressure in the cycle, (b) the

heat rejection from the cycle, and (c) the thermal efficiency of the cycle. (d) If an actual

heat engine cycle operates between the same temperature limits and produces 5200 kW

of power for an air flow rate of 95 kg/s, determine the second law efficiency of this cycle.

5. An ideal Otto cycle has a compression ratio of 8. At the beginning of the compression

process, air is at 95 kPa and 27oC, and 750 kJ/kg of heat is transferred to air during the

constant-volume heat-addition process. Taking into account the variation of specific heats

with temperature, determine (a) the pressure and temperature at the end of the heat-

addition process, (b) the net work output, (c) the thermal efficiency, and (d) the mean

effective pressure for the cycle. Answers: (a) 3898 kPa, 1539 K, (b) 392.4 kJ/kg, (c) 52.3

percent, (d ) 495 kPa

6. A spark-ignition engine has a compression ratio of 8, an isentropic compression efficiency

of 85 percent, and an isentropic expansion efficiency of 95 percent. At the beginning of

the compression, the air in the cylinder is at 13 psia and 60oF. The maximum gas

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Assignment 1

An air-standard cycle is executed within a closed piston-cylinder system and consists of three processes as follows: 1 - 2 V = constant heat addition from 100 kPa and 27oC to 700 kPa 2 - 3 Isothermal expansion until V3 = 7V 3 - 1 P = constant heat rejection to the initial state Assume air has constant properties with cv = 0.718 kJ/kg·K, cp = 1.005 kJ/kg·K, R = 0.287 kJ/kg·K, and k = 1.4. (a) Sketch the P-v and T-s diagrams for the cycle. (b) Determine the ratio of the compression work to the expansion work (the back work ratio). (c) Determine the cycle thermal efficiency. Answers: (b) 0.440, (c) 26.6 percent
An air-standard cycle with variable specific heats is executed in a closed system and is composed of the following four processes: 1 - 2 Isentropic compression from 100 kPa and 22oC to 600 kPa 2 - 3 v = constant heat addition to 1500 K 3 - 4 Isentropic expansion to 100 kPa 4 - 1 P = constant heat rejection to initial state (a) Show the cycle on P-v and T-s diagrams. (b) Calculate the net work output per unit mass. (c) Determine the thermal efficiency.
Consider a Carnot cycle executed in a closed system with 0.6 kg of air. The temperature limits of the cycle are 300 and 1100 K, and the minimum and maximum pressures that occur during the cycle are 20 and 3000 kPa. Assuming constant specific heats, determine the net work output per cycle.
Consider a Carnot cycle executed in a closed system with air as the working fluid. The maximum pressure in the cycle is 1300 kPa while the maximum temperature is 950 K. If the entropy increase during the isothermal heat rejection process is 0.25 kJ/kg·K and the net work output is 100 kJ/kg, determine (a) the minimum pressure in the cycle, (b) the heat rejection from the cycle, and (c) the thermal efficiency of the cycle. (d) If an actual heat engine cycle operates between the same temperature limits and produces 5200 kW of power for an air flow rate of 95 kg/s, determine the second law efficiency of this cycle.
An ideal Otto cycle has a compression ratio of 8. At the beginning of the compression process, air is at 95 kPa and 27oC, and 750 kJ/kg of heat is transferred to air during the constant-volume heat-addition process. Taking into account the variation of specific heats with temperature, determine (a) the pressure and temperature at the end of the heat- addition process, (b) the net work output, (c) the thermal efficiency, and (d) the mean effective pressure for the cycle. Answers: (a) 3898 kPa, 1539 K, (b) 392.4 kJ/kg, (c) 52. percent, (d ) 495 kPa
A spark-ignition engine has a compression ratio of 8, an isentropic compression efficiency of 85 percent, and an isentropic expansion efficiency of 95 percent. At the beginning of the compression, the air in the cylinder is at 13 psia and 60oF. The maximum gas

temperature is found to be 2300oF by measurement. Determine the heat supplied per unit mass, the thermal efficiency, and the mean effective pressure of this engine when modeled with the Otto cycle. Use constant specific heats at room temperature. Answers: 247 Btu/lbm, 47.5 percent, 49.0 psia.

An ideal Otto cycle with air as the working fluid has a compression ratio of 8. The minimum and maximum temperatures in the cycle are 540 and 2400 R. Accounting for the variation of specific heats with temperature, determine (a) the amount of heat transferred to the air during the heat-addition process, (b) the thermal efficiency, and (c) the thermal efficiency of a Carnot cycle operating between the same temperature limits.
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 27oC. Accounting for the variation of specific heats with temperature, determine (a) the temperature after the heat-addition process, (b) the thermal efficiency, and (c) the mean effective pressure. Answers: (a) 1725 K, (b) 56.3 percent, (c) 675.9 kPa
An ideal Diesel cycle has a compression ratio of 17 and a cutoff ratio of 1.3. Determine the maximum temperature of the air and the rate of heat addition to this cycle when it produces 140 kW of power and the state of the air at the beginning of the compression is 90 kPa and 57oC. Use constant specific heats at room temperature.
An ideal Diesel cycle has a maximum cycle temperature of 2300oF and a cutoff ratio of 1.4. The state of the air at the beginning of the compression is P1 = 14.4 psia and T1 = 50 oF. This cycle is executed in a four-stroke, eightcylinder engine with a cylinder bore of 4 in and a piston stroke of 4 in. The minimum volume enclosed in the cylinder is 4. percent of the maximum cylinder volume. Determine the power produced by this engine when it is operated at 1800 rpm. Use constant specific heats at room temperature.
An air-standard dual cycle has a compression ratio of 14 and a cutoff ratio of 1.2. The pressure ratio during the constant-volume heat addition process is 1.5. Determine the thermal efficiency, amount of heat added, the maximum gas pressure and temperature when this cycle is operated at 80 kPa and 20oC at the beginning of the compression. Use constant specific heats at room temperature.
An air-standard Diesel cycle has a compression ratio of 18.2. Air is at 120oF 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, determine (a) the cutoff ratio, (b) the heat rejection per unit mass, and (c) the thermal efficiency.
An ideal dual cycle has a compression ratio of 15 and a cutoff ratio of 1.4. The pressure ratio during constant volume heat addition process is 1.1. The state of the air at the beginning of the compression is P1 = 14.2 psia and T1 = 75 oF. Calculate the cycle’s net

A simple Brayton cycle using air as the working fluid has a pressure ratio of 10. The minimum and maximum temperatures in the cycle are 295 and 1240 K. Assuming an isentropic efficiency of 83 percent for the compressor and 87 percent for the turbine, determine (a) the air temperature at the turbine exit, (b) the net work output, and (c) the thermal efficiency.
Consider a simple Brayton cycle using air as the working fluid; has a pressure ratio of 12; has a maximum cycle temperature of 600oC; and operates the compressor inlet at 100 kPa and 15oC. Which will have the greatest impact on the back-work ratio: a compressor isentropic efficiency of 80 percent or a turbine isentropic efficiency of 80 percent? Use constant specific heats at room temperature.
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 70 MW, assuming both the compressor and the turbine have an isentropic efficiency of (a) 100 percent and (b) 85 percent. Assume constant specific heats at room temperature. Answers: (a) 352 kg/s, (b) 1037 kg/s.
A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 800 kPa. Air enters the compressor at 30oC and leaves at 330oC at a mass flow rate of 200 kg/s. The maximum cycle temperature is 1400 K. During operation of the cycle, the net power output is measured experimentally to be 60 MW. Assume constant properties for air at 300 K with cv = 0.718 kJ/kg·K, cp = 1 .005 kJ/kg·K, R = 0.287 kJ/kg·K, k = l.4. (a) Sketch the T-s diagram for the cycle. (b) Determine the isentropic efficiency of the turbine for these operating conditions. (c) Determine the cycle thermal efficiency.
A gas turbine for an automobile is designed with a regenerator. Air enters the compressor of this engine at 100 kPa and 308C. The compressor pressure ratio is 10; the maximum cycle temperature is 8008C; and the cold air stream leaves the regenerator 108C cooler than the hot air stream at the inlet of the regenerator. Assuming both the compressor and the tur bine to be isentropic, determine the rates of heat addition and rejection for

this cycle when it produces 115 kW. Use con stant specific heats at room temperature. Answers: 258 kW, 143 kW.

A gas turbine engine operates on the ideal Brayton cycle with regeneration, as shown in Fig. P9–99. Now the regenerator is rearranged so that the air streams 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 arrangement of a heat exchanger). Consider such a system when air enters the compressor at 100 kPa and 20oC; the compressor pressure ratio is 7; the maximum cycle temperature is 727oC; and the difference between the hot and cold air stream temperatures is 6oC at the end of the regenerator where the cold stream leaves the regenerator. Is the cycle arrangement shown in the figure more or less efficient than this arrangement? Assume both the compressor and the turbine are isentropic, and use constant specific heats at room temperature.
Consider an ideal gas-turbine cycle with two stages of compression and two stages of expansion. The pressure ratio across each stage of the compressor and turbine is 3. The air enters each stage of the compressor at 300 K and each stage of the turbine at 1200 K. Determine the back work ratio and the thermal efficiency of the cycle, assuming (a) no regenerator is used and (b) a regenerator with 75 percent effectiveness is used. Use variable specific heats.
Air enters a gas turbine with two stages of compression and two stages of expansion at 100 kPa and 17oC. This system uses a regenerator as well as reheating and intercooling. The pressure ratio across each compressor is 4; 300 kJ/kg of heat are added to the air in each combustion chamber; and the regenerator operates perfectly while increasing the temperature of the cold air by 20oC. Determine this system’s thermal efficiency. Assume isentropic operations for all compressor and the turbine.

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