SP1 Due by 4:30 pm EST on Friday 13 January 2017 to your division GradeScope site

Transcription

1 SP1 Due by 4:30 pm EST on Friday 13 January 2017 to your division GradeScope site The LED Helicopter is available online. It consists of a four-bladed pinwheel housing a battery and LED, along with a rubber band launcher. See the inset at the top of the figure. Treat the helicopter as your system. Identify all energy transfers from the point that the rubber launcher is released and the helicopter begins its upward flight until the time it falls to the ground. Paul E. Sojka, January 2017

2 SP2 - Due by 4:30 pm EST on Friday 13 January 2017 to your division GradeScope site The human heart is pictured below. Treat it as your system and draw the corresponding EFD. Be careful that you include all energy flows and make certain the corresponding arrows are oriented in the correct direction. Paul E. Sojka, January 2017

3 SP 3 Due by 4:30 pm EST on Friday 20 January 2017 to your division GradeScope site Your child is given a Power Wheels Wild Thing as a gift. You are worried that they might be able to drive it so far that they ll be out of sight. Having taken ME 200 you know how to answer that question. Given that your child s weight is 50 lbf (222 N) and the Power Wheels Wild Thing also weighs 222N, and that the Wild Thing tires are 30.5 cm diameter, and that the 12 V battery has a capacity of 9 A-hr you can determine the maximum distance traveled on a single battery charge. Report your answer in meters. Do so by assuming that there are no frictional, resistive, or other losses and that the battery/electric motor combination produces exactly the torque required to move your child in the Wild Thing forward. You may assume that the coefficient of friction between the ground and wheels is 1. from: toysrus.com Paul E. Sojka, January 2017

4 SP4 Due by 4:30 pm EST on Friday 20 January 2017 to your division GradeScope site The pressure-volume behavior for the Yamaha KT100 engines used in Purdue Grand Prix carts is approximated by four steps (processes). The first process is a compression that obeys p 1.4 = a where the initial and final specific volumes are 1 and 2, respectively, and a is a constant. This is followed by a constant pressure expansion process (p = p2 where p2 is the constant pressure), a p 1.4 = b expansion process (where b is a different constant), and a constant pressure compression process (p = p1, where p1 is the constant pressure). The initial and final specific volumes for the second, third and fourth process are, respectively, 2 and 3, 3 and 4, and 4 and. Calculate the moving boundary work for each of the four processes. Report answers in terms of p 1 p 1, 2, 3, and 4. ow sketch the four sequential processes on a p- plot, with p as the vertical axis and as the horizontal one. Paul E. Sojka, January 2017

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6 SP5-Due by 4:30 pm EDT on Friday 27 January 2017 to your division GradeScope site A wand blender has a 200 W motor that can rotate at speeds of 8000 and rpm. What is the torque supplied in each case? Report your answer in N-m. Copyright January 2017 by Beth Hess and Paul E. Sojka. All rights reserved.

7 SP6-Due by 4:30 pm EDT on Friday 27 January 2017 to your division GradeScope site Reconsider the LED helicopter problem. Given a spring constant of 80 N/m for the rubber ban that s used for launch, an extension distance of 25 cm, and a copter weight of 5 g, what is the highest altitude the copter could reach? Report your answer in m. If the copter s actual height is 20 ft (~6 m), what is the energy efficiency of the launch process? Report your answer in %. If the copter returns to earth at a speed of 0.5 m/s, what fraction of the spring energy is left at touch down? Report your answer in %. Copyright January 2017 by Beth Hess and Paul E. Sojka. All rights reserved.

8 SP7-Due by 4:30 pm EDT on Friday 27 January 2017 to your division GradeScope site Data for a four step cyclic process are presented below. The first process is an expansion and the third process is a compression. Process Q, kj W, kj U, kj KE PE p=5 bar; 0.4 V 1.2 m V = p=1.5 bar; 0.4 V 1.2 m V = 0 Fill in the missing table entries. Copyright January 2017 by Beth Hess and Paul E. Sojka. All rights reserved.

9 SP8 Due by 4:30 pm EDT on Friday 3 February 2017 to your division GradeScope site Many cooking processes can be analyzed by accounting for energy flows. An example is the double boiler shown below. The double boiler is used when a uniform temperature is required on the bottom surface of a cooking pot, in this case Can 1. Temperature uniformity is achieved by isolating the upper pot from the stove heating element through by interposing a pot of boiling water (Can 2). Sketch the thermodynamic process on a P-v diagram and a T-v diagram for water contained in the lower pot as energy enters via heat transfer. The water always starts as a liquid at 1 bar and 25 C, and always ends up boiling. Initially, Can 2 is sealed and matter escapes as soon its pressure reaches 1.1 bar (the gap between the Can 1 and Can 2 rim opens when the water pressure reaches 1.1 bar). Paul E. Sojka, August 2016

10 SP9 Due by 4:30 pm EDT on Friday 3 February 2017 to your division GradeScope site The CO2 in a paintball gun cartridge is originally at 50 bar and m 3 /kg. Repeated firings increase the specific volume to 0.05 m 3 /kg m 3 /kg while the CO 2 pressure falls to 10 bar. Since firing is not in full automatic mode there is time for heat transfer from the surrounding air to occur. This results in an approximately constant temperature process. What is the original state of the CO 2? What is the final state of the CO 2? Sketch the thermodynamic process the CO 2 follows during firing on a P-v and T-v diagram. Paul E. Sojka, August 2016

11 SP10-Due by 4:30 pm EST on Friday 3 February 2017 to your division GradeScope site Your parents certainly admonished you not to leave the outside door open when it was cold or hot outside. They claimed it ran up the home power bill. Let s see if they were right. The rate of infiltration through a standard residential exterior door (~2 m tall and ~0.91 m wide) can be computed from = 1 3 w h C dis g h T in T out T out where V is the infiltration volume flow rate, in m 3 /s, w and h are the door width and height, both in m, g is the acceleration due to gravity, and Tin and Tout are the interior and exterior temperatures, in K. Assume C dis is 0.6. Assume a door open time of 5 s, along with interior and exterior temperatures of 22 and 5 C respectively and compute the volume of air infiltration. Report your answer in m 3. Next, assume the 5 C air must be heated to 22 C by the residential heating system and compute the energy required to do so. Report your answer in kj. For a worst case scenario, assume that the residential heating system is direct electrical and that the local electricity cost is $0.1026/kW-hr to compute the energy cost in $. Assume a total of three trips (in or out) each day, for eight months of the year to determine the annual energy cost. Were your parents right? Paul E. Sojka, August 2016

12 SP11 Due by 4:30 pm EST on Monday 13 February 2016 to your division Gradescope site Lake Superior is the largest freshwater lake in the world, by surface area and the third largest by volume. It s maximum depth is 406 m (1333 ft). At depths greater than 200 m the water temperature is a nearly constant throughout the year with a value of 4 C. The surface water temperature varies between 0 and 13 C. What are the water specific internal energy and specific enthalpy at the lake surface when its temperature is 13 C? Report your answers in kj/kg. What are the water specific internal energy and specific enthalpy at the lake maximum depth. Report your answers in kj/kg. Paul E. Sojka, August 2016

13 SP12 Due by 4:30 pm EST on Monday 13 February to your division Gradescope site An unknown ideal gas with a molecular weight of 41 g/mol undergoes a polytropic process with n=1.25. The initial temperature is 200 ºC and the initial pressure 2.1 bar. The specific volume increases by a factor of 3. What is the gas final temperature? Report your answer in ºC. What is the gas final pressure? Report your answer in bar. What is the corresponding specific work interaction? Report your answer in kj/kg. Paul E. Sojka, August 2016

14 SP13-Due by 4:30 pm EST on Monday 13 February to your division Gradescope site A heat gun for removing paint from solid surfaces has inlet air at room temperature (20 ºC) and outlet air at either 400 or º530C. What are the changes in air specific enthalpies and specific internal energies? Report your answers in kj/kg. Paul E. Sojka, August 2016

15 SP14 Due by 4:30 pm EST on Friday 17 February 2017 to your division Gradescope site Houses need to breathe, just like most living creatures. This is called ventilation and is crucial in the attic and the under-eave soffits (see red arrows below). The EnergyStar page provided by the US government gives the following attic ventilation guidelines. Natural Attic Ventilation At first it may seem odd to add insulation for warmth and then purposely allow cold air to enter the attic through vents, but this combination is the key to a durable and energy-efficient home. Here's why: in the winter, allowing a natural flow of outdoor air to ventilate the attic helps keep it cold, which reduces the potential for ice damming (snow that melts off a roof from an attic that is too warm and then re-freezes at the gutters, causing an ice dam that can damage the roof). Proper insulation and air sealing also keeps attics cold in winter by blocking the entry of heat and moist air from below. In the summer, natural air flow in a well-vented attic moves super-heated air out of the attic, protecting roof shingles and removing moisture. The insulation will resist heat transfer into the house. Paul E. Sojka, February 2017

16 Furthermore, from the FHA The U.S. FHA (Federal Housing Administration) recommends a minimum of at least 1 square foot of attic ventilation (both intake and exhaust) for every 300 square feet of attic space.. Now consider an attic that is 25 feet wide and 15 feet long. What is the recommended ventilation area if the FHA guideline is followed? What if the FHA guideline is doubled? Report your answer in ft 2. You purchase a ridge vent to install on your 14 foot long roof ridge. It provides 18 in 2 ( ) of ventilation per lineal foot of vent. Will this be enough to meet FHA guidelines? You also need to provide soffit vents. You purchase soffits that provide 5 in 2 of ventilation are per lineal foot. You have 15 lineal feet of soffit on both sides either side of the attic. Will you have enough ventilation area to meet the FHA recommendation? The outside temperature and pressure are 31.8 F and in Hg, and the air speed through the ventilation areas (soffit and ridge) is 2.2 ft/s. What is the air mass flow rate through the attic? Transform ft 2 and in 2 to m 2, ft/s to m/s, and find the air density in kg/m 3. Report your mass flow rate in kg/s. Paul E. Sojka, February 2017

17 SP15 Due by 4:30 pm EST on Friday 17 February 2017 to your division Gradescope site Residential fireplaces in the US typically have flues that are 21.5 x 33 cm. For a typical wood fire the incoming air temperature is 25 C while the hot air going up the chimney is at 400 C. The hot air velocity is computed using V = C 2 g H( T hot T cold T hot ) where C = 0.65, g = 9.8 m/s 2, H is the chimney height (taken to be 5 m in this case), and Tcold and Thot are in Kelvin. What is the air velocity up the flue? Report your answer in m/s. Compute the heat transfer rate from the fire to the air. Report your answer in kw. Paul E. Sojka, February 2017

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19 SP16 Due by 4:30 pm EST on Friday 24 February to your division Gradescope site A water supply system leading up to and through a shower head consists of a hot water feed (T = 55 C), a cold water feed (T = 15 C), a mixer, and the shower head itself. The hot and cold water feed lines are Cu tubing having an inside diameter of 18.9 mm, as is the mixer outlet line that runs to the shower head. The shower head has 34 holes having diameters of 2.5 mm. The manufacturer indicates the shower flows 9.6 liters/min at a supply pressure of 550 kpa (that s above atmospheric pressure). What is the water temperature[degc] when the mixer is set to pass 75% hot and 25% cold water? What are the cold and hot water velocities at that condition[m/s]? The mixer outlet water velocity[m/s]? The velocity of jets leaving the shower head[m/s]? Suppose there was heat transfer, 100 W, from the mixing water through the mixer body and into the surrounding wall. Compute the new water temperature[degc] at the shower head. Paul E. Sojka, February 2017

20 SP17 Due by 4:30 pm EST on Friday 24 February to your division Gradescope site Gear pumps are used when higher pressure liquids are desired. Note that positive displacement gear pumps produce flow, not a pressure rise. The pressure rise is the result of a restriction at, or downstream of, the pump exit. This understanding leads the following: when operating with water and a pressure difference of 7 bar, a pump operating at 1750 rpm will flow about 26 litres/min (LPM) and require a little over 1.1 hp (~0.843 kw). From the example above, you are to compute the flow rate (litres/min) and power (transform to kw) for oil being pumped at 900 rpm while supplying 10 bar pressure. Also compute the pump efficiency, defined as the increase in oil energy divided by the required power. Paul E. Sojka, August 2016

21 SP18 Due by 4:30 pm EST on Friday 24 February to your division Gradescope site 1 kg/s of air at 35 C and 1 bar enters a duct. A 10 g/s water spray (20 C, sat liq) enters the duct parallel to the air. At the duct exit all the water has evaporated so is a saturated vapor. What is the new air (and water) temperature[degc]? Assume there is no stray heat transfer. Paul E. Sojka, August 2016

22 SP19 Due by 4:30 pm EST on Friday 3 MARCH to your division Gradescope site Geothermal sources for electrical power generation have obvious advantages, the most important one being a nearly inexhaustible energy supply. The schematic for a flash system is shown below. A low quality saturated liquid-vapor mixture of steam is supplied by the extraction well, then passed through the throttling valve to raise its quality. Saturated liquid collects at the bottom of the dryer separator and is returned to its original below-ground depth by the injection well. The saturated vapor continues to the turbine. The saturated vapor expands through the turbine before entering a condenser. The resulting condensate is also returned via the injection well. State p, MPa T, C x, if applicable m, kg/s pipe dia, m Use the table data to determine the mass flow rates of saturated vapor and saturated liquid exiting the Dryer-separator, the shaft power supplied by the turbine[kw], and the rate of steam heat rejection while in the condenser[kw]. The water mixture is supplied by the extraction well at a rate of 165 kg/s. If the water/steam velocity is to be 100 m/s everywhere above ground, what pipe diameters are required at states 1 through 5. Paul E. Sojka, August 2016

23 SP20 Due by 4:30 pm EST on Friday 3 March to your division Gradescope site Concentrated solar power driven electricity generation is popular in areas where fuel sources are either absent or highly expensive. Such systems can be very large, like the ~650 MW plant recently commissioned in Tamil Nadu, or much smaller village-scale units. Regardless of scale, the best one can expect from direct solar radiation is about 1300 W/m 2. Assume a 1 m 2 collector and that the units uses water as the working fluid. For safety reasons the peak pressure must be less than 5 bar (75 psia). Assume a surroundings temperature of 35 C and a mass flow rate of 0.3 g/sec. Water exists the condenser as a saturated liquid. What is the minimum condenser temperature? Assume 75% of the collected sunlight is deposited in the water while it s flowing through the boiler. If the steam exits the turbine at the minimum condenser temperature and with a quality of 100%, what is the turbine output power (in W)? What is the pump power necessary to run the system (in W)? What is the system thermal efficiency? Paul E. Sojka, August 2016

24 SP22a Due by 4:30 pm EST on Friday 10 March to your division Gradescope site A heat pump cycle has 20 bar NH3 saturated vapor enter the condenser and saturated liquid exit. The evaporator operates at 5 bar; two-phase mixtures enter and exit. Compute the coefficient of performance if all the processes are reversible. What is the condenser specific heat transfer[kj/kg]? SP-22b- Due by 4:30 pm EST on Friday 10 March to your division Gradescope site A Carnot vapor power cycle uses water as its working fluid. The boiler pressure is 150 bar; saturated liquid enters and saturated vapor exits. The condenser pressure is 0.1 bar, with 2- phase mixtures entering and exiting. Calculate the thermal efficiency. What is the specific heat transfer for water passing through the boiler[kj/kg]. Paul E. Sojka, February 2017

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26 SP22a Due by 4:30 pm EST on Friday 10 March to your division Gradescope site A heat pump cycle has 20 bar NH3 saturated vapor enter the condenser and saturated liquid exit. The evaporator operates at 5 bar; two-phase mixtures enter and exit. Compute the coefficient of performance if all the processes are reversible. What is the condenser specific heat transfer[kj/kg]? SP-22b- Due by 4:30 pm EST on Friday 10 March to your division Gradescope site A Carnot vapor power cycle uses water as its working fluid. The boiler pressure is 150 bar; saturated liquid enters and saturated vapor exits. The condenser pressure is 0.1 bar, with 2- phase mixtures entering and exiting. Calculate the thermal efficiency. What is the specific heat transfer for water passing through the boiler[kj/kg]? Paul E. Sojka, February 2017

27 SP23 Due by 4:30 pm EST on Friday 10 March to your division Gradescope site In a real heat pump, the condenser temperature is not constant because a superheated vapor enters. This renders the Carnot expression inaccurate. Be that as it may, the Carnot expression will still serve as an upper bound on the cycle thermal efficiency, as long as we can find an effective upper T. We ll do that by choosing that effective T to lie between that of the condenser outlet and condenser inlet. Choose a value and use it to compute the coefficient of performance using the Carnot expression. Use NH3 as the working fluid with an evaporator temperature corresponding to 5 bar. The condenser exit temperature corresponds to 20 bar. The compressor exit temperature is 10 C above the condenser exit temperature. Paul E. Sojka, August 2016

28 SP24 Due by 4:30 pm EST on Friday 10 March to your division Gradescope site Return to SP22a. Calculate the entropy for each of the four states. Which component has the largest entropy increase? Are they all positive? If not, does this concern you? Why or why not? Paul E. Sojka, August 2016

29 SP25 Due by 4:30 pm ES T on Friday 24 March to your division Gradescope site Use tabular data to compute the specific entropy change for water as it s compressed isothermally from 1 bar and 20 C to 100 bar and 20 C. Report your answer in kj/kg-k. What is the corresponding specific entropy change if the water is modeled as incompressible? Report your answer in kj/kg-k. Paul E. Sojka, March 2017

30 SP26 Due by 4:30 pm ES T on Friday 24 March to your division Gradescope site The Ericsson cycle has been proposed for internal combustion (IC) engine use. The working fluid is an ideal gas, in this case air. The air p- diagram and data at each state are provided in the table below. State T, C p, bar Determine the air specific entropy change all four processes. Report your answers in kj/kg-k. Repeat the calculations for CO 2 as the working fluid, assuming it s always an ideal gas. Again report your answers in kj/kg-k. Paul E. Sojka, August 2016

31 SP27 Due by 4:30 pm EST on Friday 31 March to your division Gradescope site 0.75 kg of R134a having an initial quality of 0.1 and pressure of 2.0 bar resides in a pistoncylinder device. The R134a surrounds an electrical heating element. A current of VDC flows through the element such that the final R134a quality is 0.9. What is the R134a reversible heat transfer? Report your answer in kj/k. Calculate the time that the electrical heating element is turned on. Report your answer in min. Would the time for current flow be more or less if the heat transfer were irreversible? Justify your answer using basic equation(s). Paul E. Sojka, March 2017

32 SP28 Due by 4:30 pm EST on Friday 31 March to your division Gradescope site NH3 enters a compressor at 0.6 bar and x=1.0, then exits at 3.5 bar and 80C. If the process is adiabatic, compute the required specific shaft work. Report your answer in kj/kg. Also compute the specific entropy generation. Report your answer in kj/kg-k. Paul E. Sojka, March 2017

33 SP29-Due by 4:30 pm EST on Friday 31 March to your division Gradescope site A compressor, condenser, throttling valve, and evaporator are strung together to make a refrigeration system. The working fluid is R134a, with data at each state provided in the table below. The R134a mass flow rate is 2 kg/s. Assume the heat transfer out of the condenser occurs at a temperature of 40degC. 3 Condenser 2 Throttling Valve Compressor 4 Evaporator 1 State x p, bar T,, m 3 /kg u, kj/kg h, kj/kg s, kj/kg-k C n/a (a) Compute the compressor power. Report your answer in kw. (b) Find the evaporator and condenser heat transfer rates. Report your answers in kw. (c) Determine the entropy production rate for each component. Report your answer in kw/k. Paul E. Sojka, March 2017

34 SP30 Due by 4:30 pm EST on Friday 7 April to your division Gradescope site Steam enters a turbine at 600 C and 40 bars. The turbine is well insulated and sufficiently well-designed that the steam undergoes a reversible process before exiting at 0.5 bar. Compute the turbine specific work. Report your answer in kj/kg. Paul E. Sojka, March 2017

35 SP31 Due by 4:30 pm EST on Friday 7 April to your division Gradescope site Repeat SP30 assuming the turbine has an isentropic efficiency of 90%. Paul E. Sojka, March 2017

36 SP32-Due by 4:30 pm EST on Friday 7 April to your division Gradescope site Unlike steam power cycles with their pumps, gas power cycles use compressors to raise the pressure of the working fluid. Compute the specific power work[kj/kg] required for the air to be compressed from 310 K and 1.1 bar to 11 bar if the compressor is well insulated and the air undergoes a reversible process. Repeat the calculation for a system where the overall compression ratio of 10:1 is achieved in equal steps by two identical compressors. The air temperature is dropped to 400 K between the two compressors. Finally, calculate the minimum compressor work[kj/kg] required for this overall pressure ratio (use a single compressor) and indicate what thermodynamic process is required. Paul E. Sojka, March 2017

37 SP33 Due by 4:30 pm EST on Monday 17 April to your division Gradescope site A recent article in Entropy discusses how to optimizee the design of an organic Rankine cycle power plant. The power plant is called an organic Rankine cycle because the working fluid isn t water. In this case, it s R134a. The power plant hardware diagram is shown in the figure below.. A T-s diagram follows. Paul E. Sojka, March 2017

38 Use the T-s diagram to answer the following questions: a) Is the water R134a flow through the pump isentropic? How about the waterr134a flow through the turbine? b) Is the temperature surrounding the R134a when it flows through the evaporator constant? Regardless, choose a temperature at which evaporator heat transfer occurs. c) Is the temperature surrounding the R134a when it flows through the condenser constant? Again, choose a value for it. d) How will you model the R134a thermodynamic paths as it flows through the evaporator? Through the condenser? e) Assume the R134a is incompressible through the pump, that the pump inlet pressure is 5 bar, and that the pump exit pressure is 15 bar. Estimate the specific shaft power required to run an ideal pump. Report your answer in kj/kg. If the pump isentropic efficiency is 80%, what is the actual specific pump work required? Again, report your answer in kj/kg. f) If the turbine inlet temperature is 80 C and its isentropic efficiency 80%, what specific work does it produce? Report your answer in kj/kg. g) Now calculate the overall cycle efficiency. Paul E. Sojka, March 2017

39 SP34 Due by 4:30 pm EST on Monday 17 April to your division Gradescope site Modify the cycle described in SP33 by adding reheat and a second stage of expansion through inclusion of a second turbine. The turbine isentropic efficiencies will both be 80%, the steam exits the first stage at 9 bar, and the reheat temperature the same as the original turbine inlet temperature. Calculate the efficiency of the modified cycle. Paul E. Sojka, April 2017

40 SP35 Due by 4:30 pm EST on Monday 17 April to your division Gradescope site A Purdue e-pub from the 2008 International Refrigeration and Air Conditioning Conference discussed the utility of several working fluids for use in in high-performance lap top vapor compression cooling systems. The issue of flammability eliminated many of the hydrocarbon refrigerants (such as C 3 H 8 ) while toxicity eliminated some inorganic compounds (NH 3 is an example). The most environmentally friendly choice, H 2 O, has too high of a flow rate. This left only a few of the newer, less environmentally invasive, products. R134a is one option. The cycle you will analyze has an evaporator temperature of 55C, a condenser temperature of 90C, and must produce 50 W of cooling. Assume that the compressor inlet state is a saturated vapor and that the throttle inlet state is saturated liquid. Assume the compressor is isentropic and isentropic exit enthalpy is kj/kg. Compute the compressor power required to run this device, and report your answer in W. How does that value compare to the power supplied by a typical AC charger (45 to 60 W)? Is compressor efficiency, and that of the electrical motor driving it important? Consider where any waste compressor and motor power goes when formulating your answer. Paul E. Sojka, April 2017

41 SP36 Due by 4:30 pm EST on Friday 21 April to your division Gradescope site The T-s diagram for a vapor compression heat pump is shown below. Extract s data from it and estimate the specific entropy generation for the adiabatic throttle and compressor. T [K] R134a bar bar bar kj/kg bar s [kj/kg-k] [A little foresight when estimating T1, T2 and T3 will be very beneficial. You will want enthalpies for all four states in a minute, so you ought to choose your temperatures so that the corresponding saturation pressures are even numbers and included in the R134a saturation tables.]. Use the corresponding enthalpies, h 1, h 2, h 3 and h 4, compute the heat pump coefficient of performance. Paul E. Sojka, March 2017

42 SP37 Due by 4:30 pm EST on Friday 21 April to your division Gradescope site The Fate of the Furious opened recently to bad reviews and great ticket sales. While the acting and story line may have been good or bad, one excellent feature was the introduction of the 2017 Dodge Demon sports car. The new Demon is unique in that the 6.2 l 8-cylinder engine (compression ratio of 9.5:1) produces 717 ft-lbf of torque (@4500 rpm) and 808 hp (@6300 rpm) on 91 octane pump gas. If you happened to have some 100 octane gas lying around (typically used for piston aircraft engines) the engine will produce 770 ft-lbf of torque and 840 hp. This engine is a four-stroke engine. The largest factor in this is the 2.7 l supercharger which boosts engine intake pressure to 14.5 psig. The second largest factor is intercooling of the supercharger exhaust air before it enters the engine intake passages. This drops the engine inlet temperature back to 100 F. Nonetheless, the engine thermodynamic cycle can still be approximated as an Otto cycle. Your task is to assume the maximum cycle temperature is and reproduce the manufacturers stated performance specifications for rated power of rpm. Report the max cycle temperature in Rankine. You should also compute the engine brake mean effective pressure[psia].

43 SP38 Due by 4:30 pm EST on Friday 28 April to your division Gradescope site The Brayton cycle describes any gas power system where heat transfer occurs at constant pressure. An example is collecting solar radiation to heat pressurized air that then moves through a turbine, a cooler, and a compressor before returning to the heater. One such system is the upper-critical CO2 unit being studied at Sandia National Laboratories in Albuquerque. In its simplest configuration 8 MPa CO2 at 27 C is compressed to 20 MPa before being heated to 650 C by the focused solar radiation. A turbine expands the air CO2 to back to 8 MPa where it passes through a cooler that returns it to 300 K. Start by assuming adiabatic and reversible rotating machinery and calculate the cycle thermal efficiency. Then assume 200 MW of solar power are supplied and compute the CO2 mass flow rate[kg/s]. Finally, determine the net power out[mw]. The compressor and turbine do not allow reversible operation. Instead, the actual turbine exhaust temperature is 800 K, while the actual compressor outlet temperature is 380 K. Compute the new cycle thermal efficiency, the new net power produced (given the same 200 MW of solar power input), and the new CO2 mass flow rate[kg/s]. Finally, calculate the entropy generation [MW/K] for the compressor and the turbine. Paul E. Sojka, March 2017

44 SP39 Due by 4:30 pm EST on Friday 28 April to your division Gradescope site The solar-powered Brayton cycle described in SP38 is modified to include reheat and compressor staging. When that is done, it takes the form shown in the following figure.. Calculate the cycle thermal efficiency for this new configuration. Paul E. Sojka, April 2017

45 SP40 Due by 4:30 pm EST on Friday 28 April to your division Gradescope site Rolls-Royce makes a host of gas turbine engines, one of which is shown below. This twospool design uses the high pressure turbine to drive the high pressure compressor and the low pressure turbine to drive the low pressure compressor and fan. Use operating conditions given in the figure to determine the cycle thermal efficiency. In this case, the net work is a combination of the work of the fan, compressor, and turbine as well as the kinetic energy of air at the nozzle exit. The velocity of the flow at the nozzle exit is 375 m/s. Paul E. Sojka, April 2017