Course Description (from ABET course profile)
This course introduces the fundamentals of biofluid dynamics and continuum mechanics, and covers the application of these principles to a variety of biological flows. Fluid flow in physiology and biotechnology is invested at a variety of scales, ranging from subcellular to whole body.
Course Description (from your instructors’ perspective)
We will establish our foundational understanding of fluid mechanics through biomedical examples of historical significance and modern importance, of technical rigor and of clinical relevance. Due to circumstances beyond our control, the course will be taught via a mixture of “synchronous” and “asynchronous” methods, including continuous individual work and regular group interactions. The folks teaching in this class have never taught like this before. The folks learning in this class have never learned like this before. As such, while holding ourselves to high standards, we’ll also give each other a little extra leeway in our endeavors.
Class Times
“Synchronous” / “During Class” Times
Tuesdays and Thursdays, 9:30 a.m. – 11:20 a.m. EST
“Asynchronous” / “Before Class” Times
Students will be responsible for consuming “asynchronous” content sufficiently in advance of “synchronous” activities. If unsure of what constitutes “sufficiently in advance”, start early.
Instructors and Instructional Aides, Their Contact Information, and Office Hours Details
Professor Barry Belmont, belmont@umich.edu, Wed: 57pm
Professor James Grotberg, grotberg@umich.edu Mon: 35pm
CF, @umich.edu Tues: 68pm and Thurs: 68pm
JG, @umich.edu Tues: 11:30am1:00pm and Thurs: 11:30am1:00pm
JL, @umich.edu, Fri: 12pm – 4pm
GT, @umich.edu, Mon: 11am1pm and Wed: 11am1pm
RW, @umich.edu, Wed: 810am and Fri: 810am
AW, @umich.edu, Thurs: 2pm4pm, Fri: 10am12pm
Requirements
PreRequisite Classes
BIOMEDE 231, MATH 215 , and MATH 216, or equivalent(s) with a C or better.
Textbook
Munson, Young, and Okiishi’s Fundamentals of Fluid Mechanics. 8th edition. Older editions are fine, as are other formats such as ebooks. Problems will be assigned from the 8th edition of the book and the readings of the text, a required part of the class, will follow this edition.
Regular Access to the Internet
Because this class will be held “remotely” you will need consistent access to the internet (especially our Canvas page) both before and during class times.
Planned Course Topics
 Fundamentals of fluid mechanics as they relate to living systems
 Stress and strain
 Conservation of mass, momentum, and energy
 Kinematics
 Constitutive equations
 Surface tension
 Flow properties of blood
 Bioviscoelastic fluids
 Introductory dimensional analysis
 Examples from the cardiovascular, respiratory, musculoskeletal, and nervous systems, as well as examples from biotechnology devices, will be examined
Intended Teaching Objectives
 Introduce students to fluid mechanics as it relates to living systems.
 Teach the fundamental concepts of fluid mechanics, including conservation of mass, momentum, and energy.
 Instruct students to formulate and solve biofluid problems.
 Teach biofluid mechanics fundamentals within cardiovascular/ pulmonary systems.
 Introduce concepts relating to function and disease in physiology and medicine.
 Introduce students to fluidstructure interactions as they relate to pulmonary, cardiovascular, and cellular flows.
 Introduce students to the concept of nondimensionalization.
Foreseen Learner Outcomes
 Relate stress and strain or rate of strain in a continuum.
 Determine the hydrostatic forces on planar and curved surfaces.
 Construct an appropriate control volume for a given flow situation and apply conservation of mass, momentum, and energy.
 Develop ability to determine when the ideal fluid assumption is valid and apply the Bernoulli equation.
 Interpret biological fluid data and select and apply appropriate constitutive equations, including Newtonian and nonNewtonian, to analyze flow in specific fluid systems.
 Apply the conservation laws in differential form, in velocitypressure, steam function, and velocity potential formulations.
 Apply techniques of differential equations to solve biofluid mechanics problems.
 Determine dimensionless groups and relate these groups to physiological situations.
 Model flow in blood vessels ranging in size from capillaries to large arteries and veins, accounting for effects of cellular components of blood.
 Investigate interfacial tension effects in physiological flows.
 Solve engineering and biology problems with respect to biofluid mechanics.
 Interpret data from living systems and address problems in biofluid mechanics.
New This Year
 Coinstructed by two professors and their fleet of IAs!
 New Homework Walkthrough, Reading Facilitation, and Commentary assignments.
 “Flipped” and “activated” the class to account for our constraints.
Course Assessment
Assignments
Students will be assessed on their comprehension of content via the following. Each assignment is worth 100 points.
 Homework: assignments to be completed individually; 14 are assigned of which only the top 10 grades will factor into one’s final grade; there is a mixture of “required” and “flexible” homeworks such that one must do HW 1 but can do either HW 2 or 3, must do HW 4 but can either do 5 or 6, etc. as designated below
 Must complete 1 & (2  3) & 4 & (5  6) & 7 & (8  9) & 10 & (11  12) & 13 & 14
 Homework Walkthrough: once in the semester, during class time, a student will explain to a small peer group how they reasoned through their homework assignment
 Reading Facilitation: once in the semester each student will have to facilitate a discussion regarding a chapter of the book to a small group of their peers; submitting an “executive” summary at least two days in advance of the during class discussion
 Video or Article “Commentary”: once in the semester, a student must submit a “commentary” with regards to either an assigned fluid mechanics video or of a selfsubmitted biofluid mechanicsrelated scientific journal article; in either case, the student must then present that commentary to a small group during class
 NSF Video Commentaries
 Sept 17 – 1. Eulerian and Lagrangian Descriptions in Fluid Mechanics
 Oct 1 – 6. Pressure Fields and Fluid Acceleration
 Oct 15 – 2. Deformation of Continuous Media
 Oct 29 – 3. Rheological Behavior of Fluids
 Nov 12 – 7. LowReynoldsNumber Flows
 Dec 3 – 10. Fundamentals of Boundary Layers
 Article Commentaries
 Sept 24 – I. Inspiring on respiratory systems, breath, air
 Oct 8 – II. Circulating on cardiovascular systems, blood, circuits
 Oct 22 – III. Maintaining on tissues, cells, metabolics, living
 Nov 10 – IV. Excreting on digestive and renal systems, food, urine
 Nov 19 – V. And Beyond on curios, bleeding edges, assortments
 NSF Video Commentaries
 Attendance: students must attend at least half of all synchronous classes
Grade Scale
In total there are 1400 points available. We intend to use the following scale to assign final grades. If any changes are made to this scale, the class will be informed in a timely manner.
A+ ≥ 1,360 pts; A ≥ 1,300 pts; A– ≥ 1,250 pts;
B+ ≥ 1,215 pts; B ≥ 1,160 pts; B– ≥ 1,115 pts;
C+ ≥ 1,080 pts; C ≥ 1,020 pts; C– ≥ 980 pts;
D+ ≥ 940 pts; D ≥ 880 pts; D– ≥ 840 pts; ≤839 → Try Again
Course structure
The course is divided into two forms of instruction: asynchronous (“Before Class”) material that includes prerecorded lectures, examples, demonstrations, flow visualizations, videos, etc. and synchronous (“During Class”) materials that will include worked examples, class participation, and homework clarifications. All will be fully remote this semester.
Week 
Date 
Topics and their accompaniment 
Wk. 1 HW 1 by 9/6 (Sun) 
Sept 1 
An Introduction to (Bio)Fluid Mechanics BC (“Before Class”): Stay safe, stay healthy; watch video #01 DC (“During Class”): Ask any questions you have 
Sept 3 
Basic Fluid Properties BC: Read § 1.1, 1.2, 1.3, 1.4, 1.6, 1.9, 1.11; watch videos #0206 DC: Example problems; homework clarifications 

Wk. 2 HW 2 by 9/11 
Sept 8 
Fluid Statics: I. Pressure at a point BC: Read § 2.1, 2.2, 2.3, 2.4, 2.5; watch videos #0710 DC: HW 1 Walkthrough; Ch. 1 Reading Discussion 
Sept 10 
Fluid Statics: II. Pressure within a field BC: Read § 2.8, 2.9, 2.10, 2.12, 2.13; watch videos 1113 DC: Ch. 2 Reading Discussion 

Wk. 3 HW 3 by 9/18 
Sept 15 
Fluid Dynamics: I. Newton’s Second Law along a streamline BC: Read § 3.1, 3.2, 3.3; watch videos #1416 DC: HW 2 Walkthrough 
Sept 17 
Fluid Dynamics: II. The Bernoulli Equation BC: Read § 3.4, 3.5, 3.6; watch videos #17 & 18; watch NSF Video 1 DC: Video Commentaries: 1. Eulerian & Lagrangian Descriptions 

Wk. 4 HW 4 by 9/25 
Sept 22 
Fluid Kinematics: I. The Velocity Field BC: Read § 3.7, 3.8, 3.9; watch video #19 DC: HW 3 Walkthrough; Ch. 3 Reading Discussion 
Sept 24 
Fluid Kinematics: II. The Acceleration Field BC: Read § 4.1, 4.2; watch video #20 DC: Article Commentaries: I. Inspiring 

Wk. 5 HW 5 by 10/2 
Sept 29 
Fluid kinematics III. Reynolds Transport Theorem BC: Read § 4.3, 4.4, 4.5; watch video #21 DC: HW 4 Walkthrough 
Oct 1 
Fluid Kinematics: IV. Control Volume Representations BC: Watch video #22; watch NSF Video 6 DC: Video Commentaries: 6. Pressure Fields and Fluid Acceleration 

Wk. 6 HW 6 by 10/9 
Oct 6 
Control Volume Analysis: I. Conservation of Mass BC: Read § 5.1; watch video #23 DC: HW 5 Walkthrough; Ch. 4 Reading Discussion 
Oct 8 
Control Volume Analysis: II. Conservation of Linear Momentum BC: Read § 5.2, 5.3, 5.5; watch video #24 DC: Article Commentaries: II. Circulating 

Wk. 7 HW 7 by 10/16 
Oct 13 
Control Volume Analysis: III. MomentofMomentum BC: Watch video #25 DC: HW 6 Walkthrough; Ch. 5 Reading Discussion 
Oct 15 
Control Volume Analysis: IV. Application of Control Volumes BC: Watch videos #26; watch NSF Video 2 DC: Video Commentaries: 2. Deformation of Continuous Media 

Wk. 8 HW 8 by 10/23 
Oct 20 
Differential Analysis: I. Conservation of Mass and Momentum BC: Read § 6.1, 6.2, 6.3, 6.4; watch videos #2729 DC: HW 7 Walkthrough 
Oct 22 
Differential Analysis: II. Potential Flows BC: Read § 6.5, 6.6; watch videos #30 & 31 DC: Article Commentaries: III. Maintaining 

Wk. 9 HW 9 by 10/30 
Oct 27 
Differential Analysis: III. Superposition BC: Read § 6.8, 6.9, 6.10, 6.11; watch videos #32 DC: HW 8 Walkthrough; Ch. 6 Reading Discussion 
Oct 29 
Differential Analysis: IV. Viscous Flow BC: Watch videos #33 & 34; watch NSF Video 3 DC: Video Commentaries: 3. Rheological Behavior of Fluids 

Wk. 10 HW 10 by 11/6 
Nov 2 Nov 3 
Respiratory Flows: Disease and Devices (6:308:30pm) BC: Watch video #35 / DC: Open discussion, survey Go Vote! [Class off] BC: Read § 7.1, 7.2, 7.3, 7.4 / DC: Your civic duty 
Nov 5 
Dimensional Analysis: I. Buckingham Pi Theorem BC: Read § 7.5, 7.6, 7.7, 7.8, 7.9, 7.10, 7.11; watch video #36 DC: HW 9 Walkthrough; Ch. 7 Reading Discussion 

Wk. 11 HW 11 by 11/13 
Nov 10 
Dimensional Analysis: II. Determination of Pi Common Groups BC: Watch video #37 DC: HW 10 Walkthrough; Article Commentaries: IV. Excreting 
Nov 12 
Viscous Flow in Pipes: I. General Characteristics BC: Read § 8.1, 8.2, 8.3; watch video #38; watch NSF Video 7 DC: Video Commentaries: 7. LowReynoldsNumber Flows 

Wk. 12 HW 12 by 11/20 
Nov 17 
Viscous Flow in Pipes: II. Fully Developed Flow BC: Read § 8.4, 8.5, 8.6., 8.7; watch video #39 DC: HW 11 Walkthrough; Ch. 8 Reading Discussion 
Nov 19 
Viscous Flow in Pipes: III. Pipe Flow Examples BC: Watch video #40 DC: Article Commentaries: V. And Beyond 

THANKSGIVING BREAK 

Wk. 13 
Dec 1 
A Survey of Biofluid Mechanics: I. Flow at the MicroScale BC: Transition safely to remote environment; watch video #41 DC: We will cross that bridge when we get to it 
Dec 3 
A Survey of Biofluid Mechanics: II. Flow at the MacroScale BC: Watch video #42; watch NSF Video 10 DC: Video Commentary: 10. Fundamentals of Boundary Layers 

Wk. 14 HW 13 by 12/11 
Dec 8 
A Philosophy of (Bio)Fluid Mechanics BC: Review The Review Video DC: A few final words 
Wk. 15 
Dec 18 
HW 14 by 12:30pm 
Planned Asynchronous Videos
 Introduction to the class and its instructors
 Important characteristics of fluids
 Dimensions and the (in)sensible use of units in fluids
 To speak of the “mass” of fluids
 Viscosity: a sticking point
 Surface tension
 Pressure at a point
 Pressure in a field
 Pressure variation in a static field, or, Hydrostatics
 Measurement of pressure
 Hydrostatics of planar surfaces
 Hydrostatics of curved surfaces
 Pressure variation in a fluid with rigid body motion
 Newton’s Second Law of Motion along a streamline, or, Bernoulli’s equation, or, The conservation of energy
 The Second Law normal to a streamline
 Applications of Bernoulli’s equation
 Energy lines and hydraulic grade lines
 Restrictions on the use of Bernoulli’s equation
 Fluid Kinematics: I. The Velocity Field
 Fluid Kinematics: II. The Acceleration Field
 Fluid Kinematics III. Reynolds Transport Theorem
 Fluid Kinematics: IV. Control Volume Representations
 Control Volume Analysis: I. Conservation of Mass
 Control Volume Analysis: II. Conservation of Linear Momentum
 Control Volume Analysis: III. MomentofMomentum
 Control Volume Analysis: IV. Applications of Control Volumes
 Differential Analysis: I. Velocity and Acceleration Fields Revisited
 Differential Analysis: II. Continuity, Conservation of Mass
 Differential Analysis: III. Conservation of Momentum
 Inviscid Flow
 Planar Potential Flows
 Superposition of Potential Flows
 Viscous Flow
 Differential Analysis of Fluids
 Respiratory Flows: Disease and Devices
 Dimensional Analysis: I. Buckingham Pi Theorem
 Dimensional Analysis: II. Determination of Pi Common Groups
 Viscous Flow in Pipes: I. General Characteristics
 Viscous Flow in Pipes: II. Fully Developed Flow
 Viscous Flow in Pipes: III. Pipe Flow Examples
 A survey of biofluid mechanics: I. Microcirculation
 A survey of biofluid mechanics: II. Macrocirculation
Policies
Lateness
For each homework due on Fridays there will be a corresponding homework walkthrough the next Tuesday. That being the case, a deduction of one point per hour will be applied to every assignment submitted late (with lateness being measured as the rounded integer of hours displayed by Canvas as past the due date). If mitigating circumstances preclude you from submitting an assignment on time (e.g., taking care of your health, once in a lifetime opportunities, family stuff, etc.) please let the instructors know as soon as you can so that accommodations may be made.
In Sickness and in Health
If you need to take care of your physical or mental health for a period of time that precludes you from participating in the course, let us know how we can best help you, but also please do not feel compelled to tell us your health state or furnish us with physicians’ notes. If you need to take a couple days for yourself, please do so.
Our Code of Honor
Everybody in this course will be respected as full adults capable of making their own decisions. All students in the class are presumed to be decent and honorable and are bound by the College of Engineering’s Honor Code. You may collaborate with a peer or peers on homework, though you may not share answers or copy from another. You may not seek to gain an unfair advantage over your fellow students; you may not consult, look at, or possess the unpublished work of another without their permission; and you must appropriately acknowledge your use of another’s work. Any and all suspected violations of the honor policies will be reported to the Honor Council, and if guilt is established penalties may be imposed by the Honor Council and Faculty Committee on Discipline. Such penalties can include, but are not limited to, letter grade deductions and expulsion from the University.
Piazza Guidelines
Piazza will be used as a forum for posting conceptual questions, sharing helpful outside resources, and helping your fellow students. Please refrain from sharing detailed answers to homework exercises and focus on general concepts. Be polite and professional. Students will be liable for disrespectful postings.
Why it has been modified from years past
Lo! Pandemic ravages the nation! As such, we must keep our distance from each other for awhile and this class must be taught to over 100 students remotely, effectively. Recognizing that exams in this context would be both stressful and burdensome to all involved (and would be so at a time already stressful and burdensome enough), we have elected to instead have consistent homework, which will facilitate retention through practice without the pressure of more rigid examination. What’s more, the environment in which you are all meant to learn in this fine institution – i.e., one in which you are working with amongst yourselves, amongst your peers, amongst the leaders and best – ought to be retained for your education. In this class, it is hoped that this will be done as part of the Homework Walkthrough, Reading Facilitation, Commentary, and Attendance assignments as well as through regular “during class” group work, active participation, and office hours should you need/want them.
Chapter sections you are expected to read
Chapter 1. Introduction
1.1. Some Characteristics of Fluids
1.2. Dimensions, Dimensional Homogeneity, and Units
1.3. Analysis of Fluid Behavior
1.4. Measures of Fluid Mass and Weight
1.6. Viscosity
1.9. Surface Tension
1.11. Chapter Summary and Study Guide
Chapter 2. Fluid Statics
2.1. Pressure at a Point
2.2. Basic Equation for Pressure Field
2.3. Pressure Variation in a Fluid at Rest
2.4. Standard Atmosphere
2.5. Measurement of Pressure
2.8. Hydrostatic Force on a Plane Surface
2.9. Pressure Prism
2.10. Hydrostatic Force on a Curved Surface
2.12. Pressure Variation in a Fluid with RigidBody Motion
2.13. Chapter Summary and Study Guide
Chapter 3. Elementary Fluid Dynamics – The Bernoulli Equation
3.1. Newton’s Second Law
3.2. F = ma along a Streamline
3.3. F = ma Normal to a Streamline
3.4. Physical Interpretation
3.5. Static, Stagnation, Dynamic, and Total Pressure
3.6. Examples of Use of the Bernoulli Equation
3.7. The Energy Line and the Hydraulic Grade Line
3.8. Restriction on Use of the Bernoulli Equation
3.9. Chapter Summary and Study Guide
Chapter 4. Fluid Kinematics
4.1. The Velocity Field
4.2. The Acceleration Field
4.3. Control Volume and System Representations
4.4. The Reynold’s Transport Theorem
4.5. Chapter Summary and Study Guide
Chapter 5. Finite Control Volume Analysis
5.1. Conservation of Mass – The Continuity Equation
5.2. Newton’s Second Law – The Linear Momentum and MomentofMomentum Equations
5.3. First Law of Thermodynamics – The Energy Equation
5.5. Chapter Summary and Study Guide
Chapter 6. Differential Analysis of Fluid Flow
6.1. Fluid Element Kinematics
6.2. Conservation of Mass
6.3. Conservation of Linear Momentum
6.4. Inviscid Flow
6.5. Some Basic, Plane Potential Flows
6.6. Superposition of Basic, Plane Potential flows
6.8. Other Aspects of Potential Flow
6.9. Some Simple Solutions for Viscous Incompressible Fluids
6.10. Other Aspects of Differential Analysis
6.11. Chapter Summary and Study Guide
Chapter 7. Dimensional Analysis, Similitude, and Modeling
7.1. Dimensional Analysis
7.2. Buckingham Pi Theorem
7.3. Determination of Pi Terms
7.4. Some Additional Comments
7.5. Determination of Pi Terms by Inspection
7.6. Common Dimensionless Groups in Fluid Mechanics
7.7. Correlation of Experimental Data
7.8. Modeling and Similitude
7.9. Some Typical Model Studies
7.10. Similitude Based on Governing Differential Equations
7.11. Chapter Summary and Study Guide
Chapter 8. Viscous Flow in Pipes
8.1. General Characteristics of Pipe Flow
8.2. Fully Developed Laminar Flow
8.3. Fully Developed Turbulent Flow
8.4. Dimensional Analysis of Pipe Flow
8.5. Pipe Flow Examples
8.6. Pipe Flowrate Measurement
8.7. Chapter Summary and Study Guide