AE2010_ExtraCreditProblems

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Georgia Institute Of Technology *

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2010

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Mechanical Engineering

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Apr 3, 2024

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Problem 1: Flight Conditions of Fireworks Many thermodynamics nerds and music enthusiasts alike agree that the Golden Age of 2000’s music was Katy Perry’s hit song, Firework. To celebrate this, Katy Perry herself shot off a firework that soars through the Earth’s atmosphere at a steady rate of 264ft/second, starting from sea level. Using the following property equations below, answer the following, where h is in feet. Answer in standard imperial units! T (h(ft)) = 20 -6h °C Part a: Reynold’s Number Determine the starting Reynold’s number of the firework if it has a characteristic length of .615m and an airspeed of 180 ft/s. Assume 1 meter is equivalent to 3.28 ft. Answer: _____________ Part b: Laminar and Turbulent Flow with Kinematics Determine if the firework will transition from laminar to turbulent or turbulent to laminar subject to Part A’s condition and a maximum altitude of 10000 ft, if the transition Reynold’s number is 1.3 x 10 6 . If it does transition, find the time until the transition occurs. Answer: _____________
Part c: Now it’s your Turn to Plot Plot the momentum boundary layer thickness as a function of altitude on the axes below. Label your axes properly. Part d: Bad Blood (Taylor’s Version) Being jealous of Katy Perry’s chart breaking single and the usage of imperial units, Taylor Swift fires a gun at the firework. Her aim is all too well, and hits the firework when the firework reaches an altitude of 8000 ft, causing it to explode. If we assume the Reynolds number at the end is the same as the beginning, determine the final airspeed of the firework before it collides with the bullet. Answer: _____________
Problem 2: Abby Lee Miller’s New Wheelchair After finishing the weekly pyramid, Abby calls the girls over to show off her new surprise. Her wheelchair is now equipped with a piston-cylinder device that stores R-134a initially at 1 bar and zero degrees Celsius. Abby Lee Miller then announces that only one solo will be given for the next competition, and it will go to the person who can find the net amount of work done and the thermal efficiency as the fluid moves through the following cycle. 1. Compressed to 1.500 bar isentropically 2. Heated by 60 kJ/kg isobarically 3. Expanded to 1 bar isentropically 4. Cooled to 0 degrees Celsuis isobarically. Jill, the mother of my little Kendall, provides the girls a sheet that has the thermodynamic properties of R-134a located on the next page. (It took Maddie Ziegler, Abby’s favorite dancer, 15 minutes to solve this problem. Can you beat her and earn your solo?)
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Problem 3: Is it Tricky… or are you just…dumb? You’re sitting in Dr. Lau’s class on a typical day. In the midst of off-topic conservations, constant giggling, “heat” on the board, sarcastic roasts from the professor, and the occasional effort to progress on the packet, you decide to play around with your isothermal nozzles. You decide to blow hot air into each nozzle with different conditions. For Isothermal Nozzle 1, the air enters at 350 kPa, 51m/s, and 201 ° C and leaves at 101 kPa and 203 m/s. For Isothermal Nozzle 2, the air enters at 330 kPa, 60m/s, and 150 ° C and leaves at 120 kPa and 219 m/s. Part a: Mass Flow and Exit Area Compare the mass flow rate through each nozzle, and determine from the info which nozzle has a higher exit area, if the inlet area is 101 cubic centimeters. Justify why. Assume air is an ideal gas with a molar mass of 28.8 g/mol. Answer: _____________ Part b: It’s Thermo Dog! You had a jar of peanut butter for lunch, and all this blowing hot air makes the room smell like it. From out of nowhere, Thermo dog meekly makes her way into the room, carrying a flow separation device that operates at a steady state on her back. The air from the room (79% Nitrogen, 20% Oxygen, 1 % Argon by moles) enters at 28 ° C and 1 atm. The elements are separated, leaving in three separate streams. During this process, both the temperature and pressure of the gas are kept constant. Find the velocity of each stream if the device processes 1kg of incoming air per second and all openings are .600 cubic meters in area. Assume all gasses behave as ideal gasses. Answer: _____________
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