535.620.81 - Fluid Dynamics I

Expanded Course Description

This is a graduate level course. 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	The Continuum Model
2	Mass Conservation, and the Reynolds Transport Theorem
3	Euler's Equation
4	Potential Flow I
5	Tensor Algebra
6	Potential Flow II
7	Governing Equations
8	Solutions to the Navier-Stokes Equations
9	Dimensionless Groups
10	Vorticity Equation
11	Boundary Layer Theory
12	Final Exam

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 (15% of final grade)

Each week, students will participate in an online discussion forum for a total of ten (10) discussion assignments. These discussions are an opportunity to engage more deeply with the concepts, ask questions, and explore applications of fluid dynamics beyond problem sets. Prompts will vary with some focusing on theoretical interpretation, others on real-world implications, or emerging computational methods (including the strengths and limitations of large language models in fluid mechanics). Students must make their first post during the first half of the week (between Wednesday at 12:00 AM and Saturday at 11:59 PM) and respond to at least one classmate in the second half of the week (between Sunday at 12:00 AM and Tuesday at 11:59 PM). Grading will emphasize clarity of thought, depth of engagement, and respectful interaction. These discussions are intended to build community, foster critical thinking, and provide space to articulate and challenge ideas in a supportive environment.

Problem Sets (40% of final grade)
There will be nine (9) 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.

• Solutions must be clearly presented. Each step of your reasoning should be shown in an organized manner. Final answers should be clearly boxed or highlighted.
• Show all of your work. Full credit will not be given for correct answers alone—intermediate steps, derivations, and explanations are essential. A correct answer with no supporting work will receive little to no credit.
• You must justify your approach. Where relevant, explain why you chose a particular method or model, especially in multi-part or conceptual problems.
  
• Clearly list any assumptions or approximations you make. Many fluid dynamics problems involve simplifications (e.g., incompressibility, steady flow, inviscid assumptions), and part of the assignment is recognizing and stating them explicitly.
• Always include units with your final answers. Ensure dimensional consistency throughout.
• You may type or neatly handwrite your solutions, but submissions must be legible. Typed submissions (using LaTeX, Word, or similar tools) are encouraged. Illegible work may not be graded.
• You are encouraged to discuss concepts with your peers, but all submitted work must be your own. Direct copying will result in penalties as outlined in the academic honesty policy.
• Upload a single PDF document to the course LMS (Canvas) by the stated deadline. Scanned handwritten work must be combined into a single file and organized in problem order.

Project (15% of final grade)

The course includes a final project designed to give you an opportunity to apply the concepts and analysis methods covered in class to a real-world fluid system. You will select a real-world system where fluid dynamics plays an important role (e.g., air movement through HVAC ducts, drag on a vehicle, fluid mixing in a pipe). You will analyze this system using the physical principles developed throughout the course and prepare a 4–6 page report. There will be two checkpoint assignments along the way including your topic selection and a midpoint report.

Midterm and Final Exam (15% each of final grade)
The expectations for the midterm and final exam are the same as those for the problem sets with the only difference being that you may not discuss the exams with other students before the submission deadline. Additionally, you may not use generative AI tools to help you complete the exams. You may use calculators. 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. Late submissions of the midterm or final exam will not be accepted.

Grading Policy

Discussion Forum (15% of final grade)

The discussion assignment for each week will be worth ten (10) points. A rubric will be provided to describe how you will be graded. Your lowest score will be dropped when calculating your final grade for the course.

Problem Sets (40% 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.

A successful submission will follow the expectations stated above. Failure to follow those requirements may result in a loss of points.

Midterm and Final Exam (15% 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.

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 in 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.

You are strongly encouraged to type up your assignments using LaTeX or Word.

Student Generative AI (GenAI) Use

Yellow: Moderate GenAI use is permitted, with restrictions

• GenAI may not be used on exams.
• GenAI may not be used to generate text that you then turn in as your own.
• All GenAI use must be disclosed.

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. 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. Our courses are designed with a proactive approach to accessibility to minimize the need for disability disclosure and accommodation requests, but we recognize that you may need additional support. 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 EP Student Disability Services at 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 Student Conduct Code website.

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.