Practice Final Exam (A) Six problems. (Open-book, HW solutions, and notes) (Plus /minus 10 % error acceptable for all numerical answers)

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1 ME 3610 Practice Final Exam (A) Six problems. (Open-book, HW solutions, and notes) (Plus /minus 10 % error acceptable for all numerical answers) (18 points) 1. A gasoline engine operating on the ideal Otto cycle has a compression ratio of 10. At the beginning of the compression process, air is at 100 kpa and 300 K. The maximum air temperature in the engine is 2000 K. (a) Assume constant specific heats at room temperature, determine the heat addition rate (in kj/kg of air) during the combustion process. (b) Accounting for the variation of specific heats of air with temperature, determine the heat addition rate (in kj/kg of air) during the combustion process, and the thermal efficiency ( th ) of the engine. (12 points) 2. The T-s diagram of a simple ideal Brayton cycle is shown in Fig. 9-31(a). If the turbine inlet temperature (T 3 ) and the compressor inlet temperature (T 1 ) are both fixed, what is the effect of increasing the pressure ratio on : (1) Cycle efficiency th ) (a) increases, (b) decreases, (c) remains the same, (d) first increases, then decreases, (e) first decreases, then increases. (2) Net work output w net ) (a) increases, (b) decreases, (c) remains the same, (d) first increases, then decreases, (e) first decreases, then increases. (3) Turbine work output w t ) (a) increases, (b) decreases, (c) remains the same, (d) first increases, then decreases, (e) first decreases, then increases. (4) Heat supplied q in ) (a) increases, (b) decreases, (c) remains the same, (d) first increases, then decreases, (e) first decreases, then increases. (18 points) 3. A turbojet aircraft flies with a velocity of 400 m/s at an altitude where air is at 50 kpa and 250 K. The gases enter the turbine at 1200 K, 800 kpa, and expand isentropically to 800 K at the turbine exit. Utilizing the air-standard assumptions, determine (a) the pressure ratio of the turbine, (b) the velocity of the gases at the nozzle exit, and (c) the thrust if air enters the compressor at a rate of 1 kg/s. 4. Consider an ideal Rankine cycle with one reheat stage. Steam enters the high-pressure turbine at 150 bar and 600 o C and leaves at 30 bar. Steam is then reheated at constant pressure to 500 o C before it enters the low-pressure turbine. Use the attached T-s diagram to determine (10 points) (a) whether the steam at the exit of the high-pressure turbine is a superheated vapor or a 2 phase-mixture, and (10 points) (b) the minimum condenser pressure if the moisture content of the steam at the exit of the low-pressure turbine is not to exceed 10 %.

2 (5) (20 points) Consider a steam power plant that operates on the ideal regenerative Rankine cycle with a closed feedwater heater as shown in Fig. 5. The plant maintains the turbine inlet at 30 bar and 350 o C; and operates the condenser at 0.2 bar. Steam is extracted at 10 bar to serve the closed feedwater heater. The extracted steam is completely condensed in the heater and is pumped to 30 bar before it mixes with the feedwater at the same pressure. Neglecting the work consumed by the pumps, determine the net work output (w net ) and the heat rejected from the condenser for this cycle per unit of boiler flow rate. Fig A refrigerator with R-134a as the working fluid operates on an ideal vapor-compression refrigeration cycle. The refrigerant enters the evaporator at 0.2 MPa with a quality of 30 %. The mass flow rate of the refrigerant is 1 kg/s. Use the p-h diagram to determine: (4 points) (a) the temperature and pressure of R-134a at the compressor exit, and (4 points) (b) the power consumption of the compressor. (4 points) (c) If a 5 o C temperature difference is needed for effective heat transfer between the refrigerant and the refrigerated space (from which heat is to be removed), the refrigerated space should be maintained at approximately (a) -5 o C, (b) -10 o C, (c) -15 o C, or (d) -20 o C? Answers: 1. (a) 895 kj/kg of air, (b) 1143 kj/kg of air; th_eff = (a) (d) (a) (b) 3. (a) 5, (b) 678 m/s, (c) 278 N. 4. (a) superheated vapor, (b) 0.15 bar. 5. w_net ~ w_turb ~ 773 kj/kg. q_out_cond ~ 1570 kj/kg. 6. (a) 40 oc; 0.88 MPa, (b) Power_in = 32 kw, (c) ans(a).

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4 ME 3610 Practice Final Exam (B) Five problems. (Open-book, HW solutions, and notes) 1. A cold air-standard cycle is executed in a closed piston-cylinder system and is composed of the following 4 processes: 1-2 Isothermal compression from 100 kpa and 300 K to 1 MPa. 2-3 v = constant heat addition in amount of 500 kj/kg. 3-4 Isothermal expansion 4-1 v = constant heat rejection to the initial state. (12 points) (a) Sketch the P-v and T-s diagrams for the cycle. P T (8 points) (b) Calculate the maximum pressure in the cycle. Assume constant- specific heats at 300 K. v s 2. A four-stroke reciprocating engine operates on the ideal Diesel cycle. At the beginning of the compression process, air is at 100 kpa and 300 K. The displacement volume of the engine is 1.4 liters. The self-ignition temperature of diesel fuel is around 217 o C. (6 points) (a) Calculate the minimum compression ratio of the engine (The compression must heat the air up hot enough, so that the injected fuel will be ignited by the high air temperature) (6 points) (b) Determine the net work output of the engine per cycle if the engine delivers 10 kw of power at 1200 rpm. (8 points) (c) Determine the work input (in kj) during the compression process if the compression ratio is 15. (Use the air standard assumptions). 3. A steam power plant operates on an ideal regenerative Rankine cycle with 2 feedwater heaters, as shown in Fig. 3. Steam enters the turbine at 100 bar and 600 o C and exhausts to the condenser at 0.5 bar. Steam is extracted from the turbine at 60 bar and 20 bar. The mass flow rate of steam through the boiler is 1 kg/s. (12 points) (a) Show the cycle on a T-s diagram.

5 (8 points) (b) Determine the rate of steam extracted for the open feedwater heater (i.e., y in Fig. 3). Disregard the pump work. Fig Consider a combined gas-steam power cycle (see Fig. 4). The topping cycle is a simple ideal Brayton cycle that has a pressure ratio of 8. Air enters the compressor at 27 o C at a rate of 10 kg/s and the gas turbine at 1027 o C. The bottoming cycle is a simple ideal Rankine cycle between the pressure limits of 40 bar and 0.4 bar. Steam is heated in a heat exchanger by the exhaust gases leaving the gas turbine, and the exhaust gases leave the heat exchanger at 127 o C. The moisture content at the steam turbine exit is 10 %. Determine (8 points) (a) the mass flow rate of steam in the bottoming cycle, and (12 points) (b) the thermal efficiency of the combined cycle. Disregard the pump work of the vapor cycle, and assume variable specific heats for the gas cycle.

6 Fig A heat pump with R-134a as the working fluid operates on an ideal vapor-compression refrigeration cycle. The refrigerant enters the compressor of the heat pump at 0.1 MPa and the power input to the compressor is 7.4 kw. The mass flow rate of the refrigerant is 0.1 kg/s. (10 points) (a) Use the attached p-h diagram to determine the temperature and pressure of R- 134a at the compressor exit. (6 points) (b) If the heat pump is used to heat water from 20 to 70 o C, determine the mass flow rate of water. (4 points) (c) If a 10 o C temperature difference is needed for effective heat transfer between the refrigerant and the heat source (from which heat is extracted for the heat pump operation), the heat source should be maintained at approximately (a) 6 o C, (b) -16 o C, (c) - 26 o C, (d) 31 o C, or (d) - 36 o C? Answers: 1. (b) 3.32 MPa. 2. (a) min r = 3.45, (b) 1 kj per cycle, (c) 0.71 kj. 3. (b) 0.1 kg/s. 4. (a) 1.27 kg/s, (b) (a) 100 oc, 3 MPa, (b) kg/s, (c) ans(b).

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