[A draft of the syllabus for the Fall 2020 semester. Not to be relied on during the semester!]

Introductory (bio)fluid mechanics, Fall 2020

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. – 11:30 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,
Professor James Grotberg,


Pre-Requisite Classes

BIOMEDE 231, MATH 215 , and MATH 216, or equivalent(s) with a C or better.


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

  1. Fundamentals of fluid mechanics as they relate to living systems
  2. Stress and strain
  3. Conservation of mass, momentum, and energy
  4. Kinematics
  5. Constitutive equations
  6. Surface tension
  7. Flow properties of blood
  8. Bioviscoelastic fluids
  9. Introductory dimensional analysis
  10. Examples from the cardiovascular, respiratory, musculoskeletal, and nervous systems, as well as examples from biotechnology devices, will be examined

Intended Teaching Objectives

  1. Introduce students to fluid mechanics as it relates to living systems.
  2. Teach the fundamental concepts of fluid mechanics, including conservation of mass, momentum, and energy.
  3. Instruct students to formulate and solve biofluid problems.
  4. Teach biofluid mechanics fundamentals within cardiovascular/ pulmonary systems.
  5. Introduce concepts relating to function and disease in physiology and medicine.
  6. Introduce students to fluid-structure interactions as they relate to pulmonary, cardiovascular, and cellular flows.
  7. Introduce students to the concept of non-dimensionalization.

Foreseen Learner Outcomes

  1. Relate stress and strain or rate of strain in a continuum.
  2. Determine the hydrostatic forces on planar and curved surfaces.
  3. Construct an appropriate control volume for a given flow situation and apply conservation of mass, momentum, and energy.
  4. Develop ability to determine when the ideal fluid assumption is valid and apply the Bernoulli equation.
  5. Interpret biological fluid data and select and apply appropriate constitutive equations, including Newtonian and non-Newtonian, to analyze flow in specific fluid systems.
  6. Apply the conservation laws in differential form, in velocity-pressure, steam function, and velocity potential formulations.
  7. Apply techniques of differential equations to solve biofluid mechanics problems.
  8. Determine dimensionless groups and relate these groups to physiological situations.
  9. Model flow in blood vessels ranging in size from capillaries to large arteries and veins, accounting for effects of cellular components of blood.
  10. Investigate interfacial tension effects in physiological flows.
  11. Solve engineering and biology problems with respect to biofluid mechanics.
  12. Interpret data from living systems and address problems in biofluid mechanics.

New This Year

  • Co-instructed 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


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 self-submitted biofluid mechanics-related 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. Low-Reynolds-Number 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
  • 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 pre-recorded 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.



Topics and their accompaniment 

Wk. 1

HW 1 by 9/6

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, 1.11; watch videos #02-06

DC: Example problems; homework clarifications

Wk. 2

HW 2 by 9/12

Sept 8

Fluid statics: I. Pressure at a point

BC: Read § 2.1, 2.2, 2.3, 2.4, 2.5; watch videos #07-10

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 11-13

DC: Ch. 2 Reading Discussion

Wk. 3

HW 3 by 9/19

Sept 15

Fluid dynamics: I. Newton’s Second Law along a streamline

BC: Read § 3.1, 3.2, 3.3; watch videos #14-16

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 9/26

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 10/3

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 10/10

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, 5.5; watch video #24

DC: Article Commentaries: II. Circulating

Wk. 7

HW 7 by 10/17

Oct 13

Control Volume Analysis: III. Moment-of-Momentum

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 10/24

Oct 20

Differential Analysis: I. Conservation of Mass and Momentum 

BC: Read § 6.1, 6.2, 6.3, 6.4; watch videos #27-29

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 10/31

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 11/7

Nov 3

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; watch video #35

DC: HW 9 Walkthrough; Ch. 7 Reading Discussion

Wk. 11

HW 11 by 11/14

Nov 10

Dimensional Analysis: II. Determination of Pi Common Groups

BC: Watch video #36

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 #37; watch NSF Video 7

DC: Video Commentaries: 7. Low-Reynolds-Number Flows

Wk. 12

HW 12 by 11/19

Nov 17

Viscous Flow in Pipes: II. Fully Developed Flow

BC: Read § 8.4, 8.5, 8.7; watch video #38

DC: HW 11 Walkthrough; Ch. 8 Reading Discussion

Nov 19

Viscous Flow in Pipes: III. Pipe Flow Examples

BC: Watch video #39

DC: Article Commentaries: V. And Beyond


Wk. 13

HW 13 by 12/5

Dec 1

A Survey of Biofluid Mechanics: I. Flow at the Micro-Scale

BC: Transition safely to remote environment; watch video #40

DC: We will cross that bridge when we get to it

Dec 3

A Survey of Biofluid Mechanics: II. Flow at the Macro-Scale

BC: Watch video #41; watch NSF Video 10

DC: Video Commentary: 10. Fundamentals of Boundary Layers

Wk. 14

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

  1. Introduction to the class and its instructors
  2. Important characteristics of fluids
  3. Dimensions and the (in)sensible use of units in fluids
  4. To speak of the “mass” of fluids
  5. Viscosity: a sticking point
  6. Surface tension
  7. Pressure at a point
  8. Pressure in a field
  9. Pressure variation in a static field, or, Hydrostatics
  10. Measurement of pressure
  11. Hydrostatics of planar surfaces
  12. Hydrostatics of curved surfaces
  13. Pressure variation in a fluid with rigid body motion
  14. Newton’s Second Law of Motion along a streamline, or, Bernoulli’s equation, or, The conservation of energy
  15. The Second Law normal to a streamline
  16. Applications of Bernoulli’s equation
  17. Energy lines and hydraulic grade lines
  18. Restrictions on the use of Bernoulli’s equation
  19. Fluid Kinematics: I. The Velocity Field 
  20. Fluid Kinematics: II. The Acceleration Field 
  21. Fluid Kinematics III. Reynolds Transport Theorem 
  22. Fluid Kinematics: IV. Control Volume Representations 
  23. Control Volume Analysis: I. Conservation of Mass 
  24. Control Volume Analysis: II. Conservation of Linear Momentum
  25. Control Volume Analysis: III. Moment-of-Momentum
  26. Control Volume Analysis: IV. Applications of Control Volumes
  27. Differential Analysis: I. Velocity and Acceleration Fields Revisited
  28. Differential Analysis: II. Continuity, Conservation of Mass
  29. Differential Analysis: III. Conservation of Momentum
  30. Inviscid Flow
  31. Planar Potential Flows
  32. Superposition of Potential Flows
  33. Viscous Flow
  34. Differential Analysis of Fluids
  35. Dimensional Analysis: I. Buckingham Pi Theorem 
  36. Dimensional Analysis: II. Determination of Pi Common Groups 
  37. Viscous Flow in Pipes: I. General Characteristics 
  38. Viscous Flow in Pipes: II. Fully Developed Flow 
  39. Viscous Flow in Pipes: III. Pipe Flow Examples
  40. A survey of biofluid mechanics: I. Microcirculation
  41. A survey of biofluid mechanics: II. Macrocirculation



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. HOMEWORK COLLABORATION. 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 the Course 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 yourself, 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.