Midterm+Project+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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