535.620.81 - Fluid Dynamics I

Expanded Course Description

This is a graduate level course so students are expected to have an undergraduate-level understanding of the following topics:

• Multivariable Calculus: Proficiency with line, surface, and volume integrals and a familiarity with vector calculus operations.
  
• Linear Algebra: Familiarity with matrix operations and eigenvalue problems.
  
• Differential Equations: Proficiency at solving ordinary and partial differential equations.

Course Structure

The course materials are divided into modules which can be accessed by clicking Modules on the course menu. A module will have several sections including the overview, content, readings, discussions, and assignments. You are encouraged to preview all sections of the module before starting. Most modules run for a period of seven (7) days, exceptions are noted in the Course Outline. You should regularly check the Calendar and Announcements for assignment due dates.

Course Topics

Module/Week	Topic
1	Continuum Model
2	Mass Conservation and the Reynolds Transport Theorem
3	Euler's Equation
4	Potential Flow 1
5	Tensor Algebra
6	Potential Flow 2
7	Potential Flow 3
8	Governing Equations
9	Navier-Stokes Equations
10	Solutions to the Navier-Stokes Equations
11	Dimensionless Groups
12	Vorticity Equation
13	Boundary Layer Theory

Course Goals

Students will understand the theoretical foundations and learn how to approach problems in fluid dynamics. Additionally, this course will serve as a starting point from which students can branch out to explore additional areas of study related to fluid dynamics.

Course Learning Outcomes (CLOs)

• Derive and apply conservation equations to solve problems in fluid dynamics.
• Solve potential flow problems for simple and complex flow arrangements.
• Write and manipulate algebraic and differential relationships using index notation.
• Derive, explain, and use the Navier-Stokes equations to solve tractable fluid flow problems.
• Derive and apply dimensionless groups to create non-dimensional governing equations and perform similarity analyses.

Textbooks

Required: None, course notes will be provided in the modules.
Recommended: Panton, R. L. (2013). Incompressible flow. John Wiley & Sons, Incorporated.
Recommended: Kundu, Pijush K., Ira M. Cohen, and David R. Dowling. "Fluid mechanics." Fifth edition. Waltham, MA: Academic Press, 2014.

Other Materials & Online Resources

These additional texts may be useful but are not required for the course:

• Batchelor, G. K. (2000). An introduction to fluid dynamics. Cambridge university press.
• Van Dyke, M., & Van Dyke, M. (1982). An album of fluid motion (Vol. 176). Stanford: Parabolic Press.
• National Committee for Fluid Mechanics Films (NCFMF), Shapiro. http://web.mit.edu/hml/ncfmf.html
• Aris, Rutherford. Vectors, tensors and the basic equations of fluid mechanics. Courier Corporation, 2012.
• Schlichting, H., & Gersten, K. (2016). Boundary-layer theory. Springer.

Required Software

There is no requirement for a particular software in this course. However, some problems will require the use of a computer programming language, such as MATLAB or Python. For such problems, you may choose to use whichever language you are most comfortable with.

In this class, some computer literacy skills you are expected to have include creating and submitting files in a word processing program, downloading and installing software, and using web conferencing tools and software. Additionally, you will be expected to use online search tools for academic purposes, properly cite information sources, and prepare a write-up of such findings.

Student Coursework Requirements

Modules are expected to take 7-10 hours per week to complete. This includes the reviewing lecture notes, watching video lectures, participating in the discussion forum, and completing problem sets or exams.

Your final grade will be derived from the following five categories.

Discussion Forum (10% of final grade)

In order to encourage productive conversation throughout the week you will be required to submit at least two (2) posts to the discussion forum over the course of each module. Each of the two required posts will be worth one (1) point, and each post must take place within the specified time period for the week. Simply put, the first post must be made during the first half of the week, and it must start a new conversation. The second post must be made during the second half of the week and can either respond to an existing conversation or start a new one. The topic of these posts must be related to fluids in some way. This may include (but are not limited to) a discussion about the topics covered in the module, a summary of and link to an interesting paper or news article you found, or something you observed in your daily life (e.g. summary and photograph of fluid phenomena you encountered). Additional discussion topics may also be posed for you to choose to answer. All posts are expected to remain respectful to other students. The following is a breakdown of the discussion expectation:

Period Start	Period End	Expectation	Points Awarded
Monday 12:00 AM	Thursday 11:59 PM	An insightful new post	1
Friday 12:00 AM	Sunday 11:59 PM	An insightful new post or response to an existing post	1

Problem Sets (35% of final grade)

There will be seven (7) problem sets throughout the course. These provide you with an opportunity to practice what you have learned in the lecture and prepare you for the exams. Problem sets must be turned in by the stated due date. The grade for late submissions will be reduced by ten (10) percentage points for each day late. Assignments will not be accepted four (4) or more days after the due date without prior coordination with the instructor.

Your solutions to a problem set should demonstrate your knowledge and ability to solve the given problems. Just as in your career, you will need to be able to neatly and clearly present your thoughts. This means that there should be no ambiguity in what you turn in.

• If you choose to handwrite solutions, your handwriting must be legible, and any scans must be clear (beware of blurry scans with a phone).
• Proper notation must be used. For example, do not forget to include proper vector notation, unit vectors, minus signs, closing parentheses, or units when necessary.
• You must explain and justify all steps taken on your way to a solution. This is especially important for problems asking you to show some result.
  
• Explicitly list out any assumptions you make and, if necessary, justify why you made those assumptions.
• The order of steps you take to arrive at a solution should be obvious from simply looking at your submission. Do not scatter equations across the page.
• When the problem asks for a final result, be it a number, expression, or equation, it must be boxed and only a single final result may be provided.
• Plots and sketches must be clearly labeled.
• Any code used must be submitted.

You may discuss how to solve the problems in a problem set with other students currently in the class, however any work you turn in must be original. You may not copy work from other students.

Project (15% of final grade)

There will be one project over the course of the class asking you to select a topic from a set of articles, seek out additional resources to develop an overall comprehension of the topic, and then prepare a write-up describing your chosen topic. You may not use AI tools to generate the text in your write-up. Your write-up is expected to be your own original work, well-written, and focused on a fluids-related topic.

Midterm and Final Exam (20% each of final grade)

The midterm and final exam will be similar to the problem sets. Both will be take-home exams where you are free to use any materials from this course. You may not use outside materials, textbooks, people, or the internet to help you complete the exams. You may not discuss the exams with other students before the submission deadline and you may not use generative AI tools to help you complete the exams. You are free to use calculators. Late submissions of the midterm or final exam will not be accepted.

Grading Policy

Discussion Forum (10% of final grade)

To earn a point for your posts to the discussion forum your post should be (i) submitted on time, (ii) relevant to fluid dynamics, and (iii) offer insight, show evidence of critical thinking, ask substantive questions, provide a meaningful summary of a linked-to resource or photograph, or critically address a posed question. Late posts will not be accepted.

Problem Sets (35% of final grade)

Problem sets must be turned in by the stated due date. The grade for late submissions will be reduced by ten (10) percentage points for each day late. Assignments will not be accepted four (4) or more days after the due date without prior coordination with the instructor.

Each problem will be worth a set number of points, roughly corresponding to the length of the problem. Each problem set will be weighted equally in computing your final grade.

A successful submission will use the correct approach, clearly and explicitly explain all steps along the way, arrive at the correct intermediate and final results, and be both neat and legible. Note that this may include a combination of equations, words, and sketches or graphs to achieve. Additional points may be deducted if your solution is unclear, skips steps, uses improper notation, or does not justify the steps taken.

Midterm and Final Exam (20% each of final grade)

Late submissions of the midterm or final exam will not be accepted. Both exams will consist of problems similar to those found on the problem sets and will be graded in a similar way.

Additional points may be deducted if your solution is unclear, skips steps, uses improper notation, or does not justify the steps taken.

Project (15% of final grade)

The course project must be turned in by the stated due date. The grade for late submissions will be reduced by ten (10) percentage points for each day late.

A rubric will be provided that describes the grading scheme for the course project.

Final Grade

EP uses a +/- grading system (see “Grading System”, Graduate Programs catalog, p. 10).

Score Range	Letter Grade
100-97	= A+
96-93	= A
92-90	= A−
89-87	= B+
86-83	= B
82-80	= B−
79-77	= C+
76-73	= C
72-70	= C−
69-67	= D+
66-63	= D
<63	= F

Course Policies

All assignments are released and due on Eastern Time.

Each assignment, unless otherwise noted in the course module, should be submitted electronically via the assignment submission link within the module in which it is due.

AI tools may not be used to generate any text that is submitted for any assignment.

You are encouraged, but not required, to type up your assignments using a tool like LaTeX or Word.

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. 

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. 
 
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.