M E 521, Fall 2017
Foundations of Fluid Mechanics I

Prepared by Professor J. M. Cimbala, Department of Mechanical and Nuclear Engineering at The Pennsylvania State University
Latest revision, 08 November 2017

[Equations]
[Exams]
[Grades]
[Instructor]
[References]
[Syllabus]
[TA]
[Textbook]
[Videos]
Week
Dates
Lecture material
Homework
Exams
Week 1
08/22-08/26
Chapters 1 and 2 - Introduction: notation; review; vectors and tensors; tensor notation; eigenvalues and principal axes
HW Info
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Week 2
08/29-09/024
Chapter 3 - Kinematics: Lagrangian vs. Eulerian descriptions, material derivative, motion of fluid particles, streamlines, stress and strain, vorticity, circulation, stream function; cylindrical and polar coordinates
HW 1
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Week 3
09/05-09/09
Chapter 4 - Conservation Laws: Reynolds transport theorem; control volume integrals; stress tensor; constitutive equations
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Week 4
09/12-09/16
Chapter 4 - Conservation Laws (continued): differential equations for conservation of mass, momentum, and energy
HW 2
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Week 5
09/19-09/23
Chapter 4 - Mechanical energy equation, viscous dissipation, various forms of the energy equation; Bernoulli equation; buoyancy
HW 3
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Week 6
09/26-09/30
Chapter 5 - Vorticity Dynamics: Kelvin’s circulation theorem; interaction of vortices
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Exam 1
Week 7
10/03-10/07
Chapter 5 - Interaction of vortices (continued); the vorticity equation; production of vorticity
Matlab_simple_example_2_variables.m
Matlab_simple_example_2_variables_PLOT.JPG
HW 4
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Week 8
10/10-10/14
Chapter 7 - Irrotational Flow: complex variables; elementary flows; superposition; images; conformal mapping; numerical solutions
Smithsonian video - Line vortex with bubbles in the ocean (sent by Christine Truong)
HW 5
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Week 9
10/17-10/21
Chapters 7 and 14 - Irrotational Flow (continued): application to aerodynamics; axisymmetric flows; 3-D flows
Zhukhovsky_Transformation_circle_to_airfoil.xlsx
HW 6
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Week 10
10/24-10/28
Chapter 14 - Aerodynamics and irrotational 3D Flow (continued) - lift, induced drag, trailing vortices; fish, birds, insects, and sailboat propulsion
Begin Chapter 9 - Laminar Flow Solutions
YouTube video: cool trailing vortices in a cloud.
YouTube video: Simulations of swimming fish "
YouTube video: Bee flight in slow motion
HW 7
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Week 11
10/31-11/04
Chapter 9 - Laminar Flow Solutions: diffusion; exact analytical solutions; similarity solutions
HW 8
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Week 12
11/07-11/12
Chapter 9 - Laminar Flow Solutions (continued): similarity solutions using the Runge-Kutta technique; begin creeping flow
R_K_for_Stagnation_pt_Matlab.m
Yates_microorganisms_article_27854249.pdf
YouTube: Nematodes swimming at very low Re
YouTube: Spirillum Volutans at very low Re
avi: Spirillum Volutans bacteria at very low Re
avi: Sperm cells swimming at very low Re
YouTube: NSF Fluid Mech. film on low Re flow (by G. I. Taylor!)
picture: Boy playing in pool of plastic balls
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Exam 2
Week 13
11/14-11/18
Chapters 9 and 6 - Creeping flow (continued); introduction to CFD; introduction to compressible flow
HW 9

See our Canvas website for downloading instructions for STAR-CCM.
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For Windows machines
For Linux machines
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Fall Break
11/21-11/25
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Week 14
11/28-12/02
Chapter 10 - Laminar Boundary Layers: introduction to the boundary layer approximation; Blasius flat plate
R_K_for_Blasius_BL.m
HW 10
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Week 15
12/05-12/09
Chapter 10 - Laminar Boundary Layers (continued): Falkner-Skan flow; separation; cylinders and spheres; free shear flows
OPTIONAL HW 11
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Finals Week
12/12-12/16
The final exam is scheduled for: Monday Dec. 11, 4:40-6:30 pm, 7 Business Building
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Final Exam