## ME 225 / PHY 255:

Introduction to Fluid Dynamics

####
Department of Mechanical Engineering

University of Rochester

Fall 2018 | Douglas H. Kelley

Lectures 9:00-9:50 Monday, Wednesday, and Friday (Hutchison 140).

Recitation 14:00-15:15 Tuesday (Dewey 1101), beginning 11 September.

Required for ME majors. 4 credits, 5 contact hours. CRN 56855 (lecture) and 56861 (recitation).

#### 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).

#### Prerequisites

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

#### Materials

- 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.
- Videos that accompany the Munson text.
*Student Solutions Manual for Fundamentals of Fluid Mechanics*, on reserve at Carlson Library.- Library resources: scholarly articles, material properties, patents, standards, and more.
- Films of the National Committee for Fluid Mechanics.
*Div, Grad, Curl, and All That: An Informal Text on Vector Calculus*by H. M. Schey- F*** Yeah Fluid Dynamics

#### 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 — provided that each collaborator takes the time to fully understand the material and write a separate copy of the assignment. On exams, no outside aids are permitted unless the instructor explicitly states otherwise. 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 - 20%
- Homework is due at the start of class on dates listed below and will not be accepted late.
- Midterm exams - 40%
- Of three midterms, your lowest grade will be dropped. Midterms will take place 25 September, 23 October, and 4 December; all in Hoyt Auditorium, 6:30-8:30 pm.
- Final exam - 35%
- Cumulative. Thursday, 20 December, 08:30, Feldman Ballroom.

#### Students with Disabilities

The University of Rochester respects and welcomes students of all backgrounds and abilities. In the event you encounter any barrier(s) to full participation in this course due to the impact of disability, please contact the Office of Disability Resources. 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.

#### 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. Tau Beta Pi study sessions are also available, 7-8 pm on Tuesdays and Wednesdays in Genesee 321.

Douglas H. Kelley | Sedigheh Sheykholeslami | Victor Zhang | Suman Kumar |

10-11 am Monday | 3:30-4:30 pm Wednesday | 10-11 am Friday | 6:30-7:30 pm Tuesday |

Hopeman 218 | Carlson Library, 2nd floor | Hopeman 403 | iZone downstairs |

d.h.kelley@rochester.edu | Sedigheh.sh@rochester.edu | vyzhang@rochester.edu | skumar23@u.Rochester.edu |

Jordy Mendez | Ramon Nieves | Obed Badillo Moreno | Rebeca Toro Garza |

3:30-4:30 pm Tuesday | 10:30-11:30 am Wednesday | 12-1 pm Monday | 5-6 pm Thursday |

iZone downstairs | Carlson Library main floor | Carlson Library main floor | ME TA lounge in Hopeman |

jmendez6@u.Rochester.edu | rnieves3@u.rochester.edu | obadillo@u.Rochester.edu | etorogar@u.Rochester.edu |

#### 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. The first recitation will meet 11 September.

Date | Topic | Reading | Due |
---|---|---|---|

Wednesday, 29 August | Introduction, units of measurement, relevance of fluids, ideal gas law | 1.1-1.5 | |

Friday, 31 August | Viscosity, stress and strain, Newtonian and non-Newtonian fluids | 1.6-1.11 | |

Monday, 3 September | No class: Labor day. | ||

Wednesday, 5 September | Pressure, force multiplication, gravitational pressure head, measuring pressure | 2.1-2.7 | Reading Quiz 1 |

Friday, 7 September | Pressure on vessel walls, center of force, center of pressure | 2.8-2.10 | Homework 1 |

Monday, 10 September | Buoyant forces | 2.11 | Reading Quiz 2 |

Wednesday, 12 September | Stability, pressure variation during rigid body motion | 2.12-2.13 | |

Friday, 14 September | F=ma along streamlines, pressure head | 3.1-3.2, 3.4 | Homework 2 |

Monday, 17 September | Bernoulli's equation, stagnation pressure, Pitot tubes | 3.5-3.6 | Reading Quiz 3 |

Wednesday, 19 September | Flowmeters, F=ma across streamlines | 3.3, 3.6 | |

Friday, 21 September | Energy line, hydraulic grade line, restrictions on Bernoulli | 3.7-3.9 | Homework 3 |

Monday, 24 September | Velocity fields, Eulerian and Lagrangian methods | 4.1 | Reading Quiz 4 |

Tuesday, 25 September | 18:30-20:30, Hoyt Auditorium |
Midterm 1 | |

Wednesday, 26 September | Streamlines, pathlines, and streaklines | 4.1 | |

Friday, 28 September | Acceleration fields, material derivatives | 4.2 | |

Monday, 1 October | Systems and control volumes, Reynolds transport theorem | 4.3-4.5 | Reading Quiz 5 |

Wednesday, 3 October | Conservation of mass in control volumes | 5.1 | Homework 4 |

Friday, 5 October | Conservation of momentum in control volumes | 5.2 | |

Monday, 8 October | Conservation of angular momentum in control volumes | 5.2 | Reading Quiz 6 |

Wednesday, 10 October | Conservation of energy in control volumes | 5.3-5.4 | |

Friday, 12 October | Fluid elements, dilation, vorticity | 6.1 | Homework 5 |

Monday, 15 October | No class: fall break. | ||

Wednesday, 17 October | Gradient, divergence, curl | 6.1 | |

Friday, 19 October | Conservation of mass in differential form | 6.2 | |

Monday, 22 October | Cylindrical polar coordinates, stream functions | 6.2 | Reading Quiz 7 |

Tuesday, 23 October | 18:30-20:30, Hoyt Auditorium |
Midterm 2 | |

Wednesday, 24 October | Conservation of momentum in differential form for inviscid flow, the Bernoulli equation | 6.3-6.4 | Homework 6 |

Friday, 26 October | Irrotational flow, velocity potentials, circulation | 6.4-6.5 | |

Monday, 29 October | Superposition, flow around a cylinder, d'Almbert's paradox | 6.6 | Reading Quiz 8 |

Wednesday, 31 October | Magnus effect, general-purpose superposition | 6.6-6.7 | |

Friday, 2 November | Conservation of momentum in differential form for viscous flow, stress-deformation relationships | 6.8 | Homework 7 |

Monday, 5 November | Poiseuille flow, Couette flow | 6.9-6.11 | Reading Quiz 9 |

Wednesday, 7 November | Dimensional analysis, Buckingham Pi theorem, method of repeating variables | 7.1-7.4 | |

Friday, 9 November | Common dimensionless groups, correlation with experiments | 7.6-7.7 | Homework 8 |

Monday, 12 November | Modeling | 7.8-7.10 | Reading Quiz 10 |

Wednesday, 14 November | Laminar pipe flow, the Hagen-Poiseuille law | 6.9, 8.2 | |

Friday, 16 November | Turbulent pipe flow, fully developed flow, turbulent shear stress | 8.1-8.3 | Homework 9 |

Monday, 19 November | No class. | ||

Wednesday 21 November | No class: Thanksgiving. | ||

Monday, 26 November | Dimensional analysis of pipe flow, relative roughness, friction factor, Darcy-Weisbach equation, Moody chart, Colebrook formula | 8.4 | Reading Quiz 11 |

Wednesday, 28 November | Loss coefficients, pipe systems, Picard iteration | 8.5 | |

Friday, 30 November | Flowrate measurement | 8.6-8.7 | Homework 10 |

Monday, 3 December | Flow over immersed bodies, boundary layer characteristics and thickness | 9.1-9.2 | Reading Quiz 12 |

Tuesday, 4 December | 18:30-20:30, Hoyt Auditorium |
Midterm 3 | |

Wednesday, 5 December | Boundary layer separation, friction drag, pressure drag | 9.2-9.3 | |

Friday, 7 December | Wall shear stress, drag coefficients | 9.3 | |

Monday, 10 December | Lift, circulation | 9.4-9.5 | Reading Quiz 13 |

Wednesday, 12 December | Exam review | Homework 11 | |

Thursday, 20 December | 08:30, Feldman Ballroom |
Final exam |

#### Grading Responsibilities

Quizzes and homework are graded by the course teaching assistants, who rotate duties based on students' last names.

Assignment | Last name begins | ||||||
---|---|---|---|---|---|---|---|

A - Br | Bu - Da | De - G | H - Le | Li - N | O - To | Tr - Z | |

Homework 1 | Sedigheh | Victor | Suman | Jordy | Ramon | Obed | Rebeca |

Homework 2 | Victor | Suman | Jordy | Ramon | Obed | Rebeca | Sedigheh |

Homework 3 | Suman | Jordy | Ramon | Obed | Rebeca | Sedigheh | Victor |

Homework 4 | Jordy | Ramon | Obed | Rebeca | Sedigheh | Victor | Suman |

Homework 5 | Ramon | Obed | Rebeca | Sedigheh | Victor | Suman | Jordy |

Homework 6 | Obed | Rebeca | Sedigheh | Victor | Suman | Jordy | Ramon |

Homework 7 | Rebeca | Sedigheh | Victor | Suman | Jordy | Ramon | Obed |

Homework 8 | Sedigheh | Victor | Suman | Jordy | Ramon | Obed | Rebeca |

Homework 9 | Victor | Suman | Jordy | Ramon | Obed | Rebeca | Sedigheh |

Homework 10 | Suman | Jordy | Ramon | Obed | Rebeca | Sedigheh | Victor |

Homework 11 | Jordy | Ramon | Obed | Rebeca | Sedigheh | Victor | Suman |

Quiz 1 | Sedigheh | ||||||

Quiz 2 | Victor | ||||||

Quiz 3 | Suman | ||||||

Quiz 4 | Jordy | ||||||

Quiz 5 | Ramon | ||||||

Quiz 6 | Obed | ||||||

Quiz 7 | Rebeca | ||||||

Quiz 8 | Sedigheh | ||||||

Quiz 9 | Victor | ||||||

Quiz 10 | Suman | ||||||

Quiz 11 | Jordy | ||||||

Quiz 12 | Ramon | ||||||

Quiz 13 | Obed |