Midterm+Project+2023

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Dec 6, 2023

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155:501 Advanced Transport Phenomena | Midterm Project (100 points) Due Sunday November 5 at 1pm on Canvas in Module 9. You should work on the project alone and not discuss the project with anyone else. Your submission is governed by Rutgers policies of academic integrity. All the work you present must be your own. The project is open-book and you are free to use resources in the form of textbooks or the internet. However, any resources you use must be cited. If you look something up in a textbook or on a webpage then the textbook (and page number) or webpage must be cited in your project. Any copied text must be placed within quotations and appropriately cited. Paraphrased text must also be appropriately cited. Discussing the project with any other person will be a serious breach of the Rutgers academic integrity policy. The Graduate School takes cheating and copying extremely seriously and consequences for cheating include getting a F for the class and suspension from Rutgers. Before you consider discussing the project with someone else or cheating or copying, please consider if it is worth the consequences that you may have to face. Please submit a single pdf or word file for your solution. Question: You are given the following configuration for a hydro-pneumatic piston. At t=0, the vessel contains mercury only with an initial height of h 0 =0.25m. At t=0, the piston is at the bottom of the vessel. At t>0, a stream of nitrogen is directed towards the bottom of the piston. The nitrogen enters the bottom of the piston through a round duct with a constant mass flux of ´ m a =2x10 -3 kg/hr. The piston has a density of ρ p =7500kg/m 3 and moves without significant friction losses. The mercury has a density of ρ Hg =13620kg/m 3 .
Part A) (40 Points) Starting from a general mass balance around a control volume, derive the differential equation that describes the rate of change of the height of mercury in the vessel. Part B) (20 Points) Scaling up or down is critical for sizing of effective hydro-pneumatic pistons. Conduct a sensitivity analysis for the height, h, as a function of the aspect ratio d/D. You may vary the aspect ratio between 0.1 and 0.001. Part C) (40 Points) An engineer plans to change the round duct used for flowing nitrogen to a rectangular duct. The engineer considers ducts with aspect ratio of 1,2 and 3. Assuming all ducts (round and rectangular) are smooth with cross-sectional area of 0.1m 2 , calculate the pressure drop per unit length for each case. Compare the pressure drop per unit length for the different cases.
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