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MEEN315 Project Topic: Thermodynamic Model of an Exploding Water Heater Problem Overview: A typical residential electric water heater has a capacity of 55 gal

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MEEN315 Project

Topic: Thermodynamic Model of an Exploding Water Heater Problem

Overview: A typical residential electric water heater has a capacity of 55 gal. (1 gal. = 0.13368 ft3 ) and may be approximated as a semi-rigid tank. A water heater has redundant safety features to prevent overheating of the system. However, on rare occasions the active and passive safety mechanisms may fail, resulting in an explosive rupture of the tank. Two episodes of the Discover Channel program “MythBusters” experimentally tested the energetic rupture of a water heater. You can watch the second episode on YouTube at: http://www.youtube.com/watch?v=68p4ngS-yME). In this project, you will develop and analyze a thermodynamic model for the process observed in the MythBusters episode shown in the link above. This is an ‘open-ended’ project assignment that requires you to make assumptions about the system model and method of analysis. There is no single ‘correct answer’ or approach. Instead, you will be evaluated on your ability to think critically about the actual process observed, and apply what you have learned about fundamentals of thermodynamics to make realistic predictions about the exploding water heater event. Analysis Objectives: Your completed analysis should provide values for the following system/event characteristics: • The total electrical energy supplied to the system to just prior to rupture • Thermodynamic properties of the water just prior to rupture • Thermodynamic properties of the water just after rupture, and/or the water properties exiting the system after rupture • Speed and mass of the tank system just after rupture • Maximum altitude attained by the tank after rupture • Length of time the tank is airborne Common Parameters: For purposes of consistency, certain values will be assumed about the water heater and rupture event. • Water Heater Capacity: 55 gallons* • Initial (unheated) Water Condition: 14.7 psia, 75 °F • Rupture Pressure: 300 psia. *note that when a water heater tank is ‘filled’, air is trapped in at the top of the heater and in connecting lines such that actual liquid volume is around 90% of the tank capacity. Any air in the tank can be assumed as separate phase and un-mixed. Your Tasks: A project template document has been provided to help you organize each of the project tasks. Unlike most homework problems, you may find it necessary to return to early steps in process to review and revise modeling decisions. Trial-and-error is an expected part of most engineering analysis. The final project document you submit should reflect your final/best analysis. There are five tasks for this project: • Develop a system and process model- This task will require you to approximate the tank system based on common/simplified devices (tanks, piston-cylinder, etc). You will likely need a different physical model of the system before and after tank rupture*. Besides the physical components, you will need to model the process(es) that occur both before and after rupture. A complete model for including all the mechanical dynamics rupture event is quite complex. You may model the rupture using a work-energy, or mass and energy transport basis. • Identify values for any parameters needed- Besides the common parameters given above, there are many other parameter values that may be needed to complete the analysis of the problem. It is key here to assume values for material properties or dimensions (e.g. density of water, diameter of the tank) and not for the behavior of the system that we wish to predict. Note that is may be necessary to assume an efficiency or energy conversion value to solve for dynamics of the rupture event. • Develop mathematical model for properties and process- Once the system has been modeled and process types identified, the appropriate physical laws (Conservation of Mass, Conservation of Energy, F = ma, etc) should be written in terms of the parameters of your model. Equations do not need to be solved at this stage, but it should be clear that the set of equations you present are sufficient to make desired predictions about the entire water heater rupture event. • Analyze mathematical model- In this phase you solve the mathematical equations. Solution methods can be algebraic, numerical, or a combination of both approaches. • Summarize and critique results- Once results are obtained, you should consider your results and judge for reasonableness and accuracy. Are the results what you expected? Are the results reasonable? Are there other ways to compute or compare the results to judge reasonableness? Scoring: Each subtask will be scored on 10 point scale, for a total of 50 points for the project. The subtask scoring is based on three elements: completion, clarity, suitability/appropriateness • Completion: Was the task adequately developed/completed? (0-4 points) • Clarity: Was the writing/formatting/imaging for the task legible and organized? (0-3 points) • Suitability: Were the equations/results/decisions for the task appropriate for the physical situation? (0-3 points)