ME 225 / PHY 255:
Introduction to Fluid Dynamics
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.
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.
- Required: A Brief Introduction to Fluid Mechanics by D. F. Young, B. R. Munson, T. H. Okiishi, and W. W. Huebsch; or an equivalent fluids text.
- Burst lectures (see below)
- Videos that accompany the Munson text.
- Student Solutions Manual for Fundamentals of Fluid Mechanics, on reserve at Carlson Library.
- F*** Yeah Fluid Dynamics
- Films of the National Committee for Fluid Mechanics.
- Library resources: scholarly articles, material properties, patents, standards, and more.
- A Student's Guide to Vectors and Tensors by Dan Fleisch, and his video, What's a tensor?
- Div, Grad, Curl, and All That: An Informal Text on Vector Calculus by H. M. Schey
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 Chegg.com 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.
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.
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|
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