ME 225 / PHY 255:
Introduction to Fluid Dynamics

U of R shield Department of Mechanical Engineering
University of Rochester
Fall 2021 | Douglas H. Kelley

Lectures 9:00-9:50 Monday, Wednesday, and Friday (Meliora 221 and Zoom meeting 984 5790 3544).
Two workshop sections: Mondays 16:50-18:05 (Dewey 2110E) and Thursdays 14:00-15:15 (Gavett 301), beginning 30 August. Required for ME majors. 4 credits, 5 contact hours.

Course Goals

This is a first course in fluid dynamics, considering phenomena relevant to fluids (liquid, gases, and plasmas), whether stagnant or flowing. In particular, we will consider fluid properties, fluid statics, kinematics of moving fluids, the Bernoulli equation and applications, control volume analysis, differential analysis of fluid flow, inviscid flow, plane potential flow, viscous flow, the Navier-Stokes equation, dimensional analysis, similitude, empirical analysis of pipe flows, flow over immersed bodies, boundary layers, lift, and drag. Successful students in this course will also gain an ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics (ABET Student Outcome 1).


MTH 165, MTH 164, PHY 121, ME 120 , ME 123.


Sharing material generated for this course by the instructor is prohibited.

Assignments & Grading

All assignments and activities associated with this course must be performed in accordance with the University of Rochester's Academic Honesty Policy. In this course, students are allowed to collaborate on homework and design problems — provided that each collaborator takes the time to fully understand the material and write a separate copy of the assignment. On quizzes and exams, neither collaboration nor outside aids are permitted unless the instructor explicitly states otherwise. Services like are uniformly prohibited. Students must write and sign the Honor Pledge on all exams: “I affirm that I will not give or receive any unauthorized help on this exam, and that all work will be my own.” Facilitating dishonesty is dishonesty. Procrastination is a major source of dishonesty, so start assignments early and keep yourself organized.

Reading Quizzes - 5%
Each Monday meeting will begin with a reading quiz consisting of three short questions taken directly from the text.
Homework - 15%
Homework is to be submitted via GradeScope, due 15 minutes before each Friday meeting. Late submissions will not be accepted.
Design problems - 15%
Design problems are to be submitted via GradeScope, due 15 minutes before class begins on the dates listed below. Late submissions will not be accepted.
Midterm exams - 35%
Of three midterms, your lowest grade (by percentage) will be dropped. Midterms will take place in person and will be scheduled during the evening to allow additional time. Dates below are tentative and will be discussed in class soon after the semester begins, with the goal of minimizing schedule conflicts. If you know you will be unable to participate in person, please contact the instructor immediately.
Final exam - 30%
Cumulative. Date, time, and location to be specified by the registrar. In person. If you know you will be unable to participate in person, please contact the instructor at least a week beforehand.
All assignments will be graded using GradeScope, and regrade requests will be handled through the GradeScope interface. Each student's work will be graded by different people as the course proceeds.

Feedback & Availability

I will distribute evaluations periodically to collect feedback. Announcements will occasionally be made by email. I typically check email frequently but cannot guarantee immediate response at all times. Quick questions can be effectively and efficiently addressed by email, but for in-depth questions a face-to-face discussion usually works better, so consider requesting a meeting. Or, when classes are in session, come to regular office hours with the professor or teaching assistants; times are listed below.

Douglas H. Kelley
Douglas H. Kelley
time TBD
Hopeman 218 or Zoom
Omar Hamad
Omar Hamad
time TBD
location TBD
Michael Harnish
Michael Harnish
time TBD
location TBD
Dung Nguyen
Dung Nguyen
time TBD
location TBD
Ethan Peltier
Ethan Peltier
time TBD
location TBD
Helena Schreder
Helena Schreder
time TBD
location TBD
Yuqi Sun
Yuqi Sun
time TBD
location TBD

Course Schedule

This schedule may evolve as the course progresses. Reading assignments specified as section numbers below come from the fifth edition of Munson's text. Burst lectures lectures are offered to help you prepare for each meeting of the class. Each meeting of the class will be recorded and posted below. Burst lectures and recordings are accessible to ME 225 students and staff but not to the general public, nor the entire University of Rochester. Students may appear in recordings, for example, when interacting with the instructor. Neither burst lectures nor meeting recordings should be understood as a substitute for participation! Homework and design problems are submitted via GradeScope and due 15 minutes before the day's meeting begins. In the schedule below, workshops and exams are shown in italics; other meetings are not.

Date Topic & recording Reading & burst lectures Due
Wednesday, 25 August Introduction, units of measurement, relevance of fluids, ideal gas law 1.1-1.5 • Fluids, Density, and Modulus; Surface Tension
Friday, 27 August Viscosity, stress and strain, Newtonian and non-Newtonian fluids 1.6-1.11 • Viscosity Bonus: Beliefs & Goals
Monday, 30 August Pressure, force multiplication, gravitational pressure head, measuring pressure 2.1-2.7 • Isotropy of Pressure; Measuring Pressure Reading Quiz 1
Monday, 30 August Workshop 1
Wednesday, 1 September Pressure on vessel walls, center of force, center of pressure 2.8-2.10 • Pressure Variation with Position; Pressure Variation with Position: Implications; Hydrostatic Forces on a Vertical Surface; Pressure Forces and Centroids; Example: Underwater Gate
Wednesday, 1 September Workshop 1
Friday, 3 September Buoyant forces 2.11 • Buoyant Forces Homework 1
Monday, 6 September No class: Labor day.
Wednesday, 8 September Stability, pressure variation during rigid body motion 2.12-2.13
Wednesday, 8 September Workshop 2
Friday, 10 September F=ma along streamlines, pressure head 3.1-3.2, 3.4 • Newtons 2nd Law Along Streamlines Homework 2
Monday, 13 September Bernoulli's equation, stagnation pressure, Pitot tubes 3.5-3.6 • Volume Flow Rate; Pitot Tubes & Venturi Meters Reading Quiz 2
Monday, 13 September Workshop 2
Wednesday, 15 September Flowmeters, F=ma across streamlines 3.3, 3.6 • Newtons 2nd Law Across Streamlines Typo alert: from 8:00 onward, 1/2*ρV2/R should be ρV2/R; Example: Flow around a Bend
Wednesday, 15 September Workshop: Practice midterm
Friday, 17 September Energy line, hydraulic grade line, restrictions on Bernoulli 3.7-3.9 • Heads, Energy Lines, & Grade Lines Homework 3
Monday, 20 September Velocity fields, Eulerian and Lagrangian methods 4.1 • Eulerian and Lagrangian Methods; Example: Exhaust Temperature Reading Quiz 3
Monday, 20 September Workshop: Practice midterm
Tuesday, 21 September Time and location to be determined. Midterm 1 (tentative)
Wednesday, 22 September Streamlines, pathlines, and streaklines 4.1 • Streaklines, Pathlines, and Streamlines
Wednesday, 22 September Workshop: Midterm solutions
Friday, 24 September Acceleration fields, material derivatives 4.2 • Acceleration Fields and the Material Derivative Homework 4
Monday, 27 September Systems and control volumes, Reynolds transport theorem 4.3-4.5 • Reynolds Transport Theorem; Example: Two-Layer Fluid System Reading Quiz 4
Monday, 27 September Workshop: Midterm solutions
Wednesday, 29 September Conservation of mass in control volumes 5.1 • Conservation of Mass; Example: Wind through a Garage
Wednesday, 29 September Workshop 3
Friday, 1 October Conservation of momentum in control volumes 5.2 • Conservation of Linear Momentum; Example: Anchoring a Nozzle Homework 5
Monday, 4 October Conservation of angular momentum in control volumes 5.2 • Conservation of Angular Momentum; Example: Spinning Yard Sprinkler Reading Quiz 5
Monday, 4 October Workshop 3
Wednesday, 6 October Conservation of energy in control volumes 5.3-5.4 • Conservation of Energy; Example: Loss in a Valve
Wednesday, 6 October No workshop.
Friday, 8 October Fluid elements, dilation, vorticity 6.1 Homework 6
Monday, 11 October No class: fall break.
Wednesday, 13 October Gradient, divergence, curl 6.1 • Gradients; Divergence and Curl Typo alert: at about 2:45, du/dy should be dv/dy.
Wednesday, 13 October Workshop: Practice midterm
Friday, 15 October Cylindrical polar coordinates, circulation 6.2 • Cylindrical polar coordinates and circulation Homework 7
Monday, 18 October Conservation of mass in differential form 6.2 • Conservation of Mass Reading Quiz 6
Monday, 18 October Workshop: Practice midterm
Tuesday, 19 October Time and location to be determined. Midterm 2 (tentative)
Wednesday, 20 October Conservation of momentum in differential form for viscous flow, stress-deformation relationships, the Navier-Stokes equation 6.3, 6.8 • Momentum Equation Typo alert: at about 12:45, stress terms τxy etc. should contain pluses, not minuses.
Wednesday, 20 October Workshop: Midterm solutions
Friday, 22 October Poiseuille flow, Couette flow 6.9 • Poiseuille Flow Typo at 0:45: total derivative should be written D/Dt, not as partial derivative. Homework 8
Monday, 25 October Stream functions 6.2 • ; Stream Functions Typo alert: at 14:34, the expression should be dq = u dy - v dx (not +), consistent with the drawing at left. Example: Stream Function from Velocity Reading Quiz 7
Monday, 25 October Workshop: Midterm solutions
Wednesday, 27 October Velocity potentials, potential flow 6.4 • Velocity Potentials; Potential Flow; Example: Velocity Potential from Stream Function
Wednesday, 27 October Workshop 4
Friday, 29 October Sinks, sources, doublets, and irrotational vortices 6.5 • Sinks and Sources; Irrotational Vortices Homework 9
Monday, 1 November Superposition, potential flow around a cylinder 6.5, 6.7 • Potential Flow around a Cylinder Reading Quiz 8
Monday, 1 November Workshop 4
Wednesday, 3 November Pressure in potential flow, d'Almbert's paradox 6.6 • Pressure in Potential Flow
Wednesday, 3 November Workshop 5
Friday, 5 November Magnus effect 6.6 Homework 10
Monday, 8 November Dimensional analysis, Buckingham Pi theorem, method of repeating variables 7.1-7.4 • Buckingham Pi Theorem; Example: Constructing Pi Terms Reading Quiz 9
Monday, 8 November Workshop 5
Wednesday, 10 November Common dimensionless groups, correlation with experiments 7.6-7.7
Wednesday, 10 November Workshop 6
Friday, 12 November Modeling 7.8-7.10 Homework 11
Monday, 15 November Laminar pipe flow, the Hagen-Poiseuille law 6.9, 8.2 • Laminar Pipe Flow; Characteristics of Laminar Pipe Flow Typo alert: At 3:44, I dropped a factor of 2, but the final expression for Q is correct. Reading Quiz 10
Monday, 15 November Workshop 6
Wednesday, 17 November Turbulent pipe flow, fully developed flow, turbulent shear stress 8.1-8.3 • Turbulent Pipe Flow
Friday, 19 November Dimensional analysis of pipe flow, relative roughness, friction factor, Darcy-Weisbach equation, Moody chart, Colebrook formula 8.4 • Major Losses Typo alert: at 13:10, the friction factor for laminar pipe flow should be f = 64/Re, not f = 32/Re. Homework 12
Monday, 22 November No class.
Wednesday, 24 November No class.
Friday, 26 November No class: Thanksgiving break.
Monday, 29 November Loss coefficients, pipe systems, Picard iteration, flowrate measurement 8.5-8.7 • Minor Losses; Example: Water Supply Pipe; Example: New Duct for Fume Hood Typo alert: Starting at 12:20, all values of f are written with an incorrect extra zero. The correct values are f = 0.019 and f = 0.022. Example: Three Connected Tanks Reading Quiz 11
Monday, 29 November Workshop: Practice midterm
Wednesday, 1 December Flow over immersed bodies, boundary layer characteristics and thickness 9.1-9.2 • Boundary Layers
Wednesday, 1 December Workshop: Practice midterm
Thursday, 2 December Time and location to be determined. Midterm 3 (tentative)
Friday, 3 December Boundary layer separation, friction drag, pressure drag 9.2-9.3 • Lift and Drag; Example: Drag Force Homework 13
Monday, 6 December Wall shear stress, drag coefficients 9.3 • Example: Wind Pressure on a Building
Monday, 6 December Workshop: Midterm solutions
Wednesday, 8 December Lift, circulation 9.4-9.5
Monday, 8 December Workshop: Midterm solutions

Accessibility Accommodations

The University of Rochester respects and welcomes students of all backgrounds and abilities. The University employs professional staff committed to assisting students with disabilities in the classroom, residence halls, libraries, and elsewhere on campus. In the event you encounter any barriers to full participation in this course due to the impact of a disability, please contact the Office of Disability Resources (, 585-276-5075). The access coordinators in the Office of Disability Resources can meet with you to discuss the barriers you are experiencing and explain the eligibility process for establishing academic accommodations. It is a personal decision to disclose the existence of a disability and to request an accommodation. A decision not to disclose will be respected. Students who request an accommodation must provide appropriate documentation to the Disability Coordinator. The University remains flexible regarding the types of reasonable accommodations that can be made. Students with disabilities are invited to offer suggestions for accommodations.

Title IX

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