CEE 6580 Intermediate Fluid Mechanics

3 credits, Spring semester.

Textbook: Class notes will be provided consisting of notes prepared by the instructor, plus some material from: Nunn, Robert H., 1989, "Intermediate Fluid Mechanics," Hemisphere Publishing Corporation, N.Y. (referred to as the Textbook).

Other References: NCFMF, "Illustrated Experiments in Fluid Mechanics," National Committee for Fluid Mechanics Films, the MIT press, Cambridge, Massachusetts, 1972 [Held in reserve at the Merril Library].

Coordinator: Gilberto Urroz, EC 219, 797-3379, UWRL 240, 797-3204

Other Information:

• Two 75-min. or 3 55-min class sessions/week
• One 2-4 hour laboratory session/week
• Office hours TBA
• One assignment per week, due on Mondays

Objectives:
General: To learn basic concepts of ideal and viscous flow motion, and survey mathematical techniques used in the solution of fluid mechanics problems.

Particular:

1. Study fundamental concepts of fluid flow description.
2. Study the concepts of ideal or potential flows, velocity potential, stream functions, vorticity and circulation. Study two-dimensional potential flows and introduce complex variables to their analysis.
3. Review the basic concepts of dimensional analysis and their applications to fluid mechanics.
4. Develop the Navier-Stokes equations and study exact solutions in simple configurations.
5. Study the concept of boundary layers and its mathematical treatment; develop velocity distributions and compute viscous drag in laminar and turbulent boundary layers.
6. Study the basic concepts and mathematical treatment of turbulent flow; develop turbulent flow equations and study models of apparent stresses; study velocity distributions for turbulent flows.

 Topics: Textbook Class hours

1. Introduction Ch. 1/notes 1.0
2. Forces and Motions in Ideal Flows Ch. 2/notes 2.0
3. Tools for Use in Ideal Fluid Flows Ch. 3/notes 2.0
4. Analysis of Ideal Fluid Flows Ch. 4/Epilogue 3.5
5. Some Extension to the Method of Analysis of Ideal Fluid Flows Ch. 5/notes 2.5
6. Dimensional Analysis and Similitude notes 1.0
7. Fundamental Concepts and Governing Relationships in Viscous Flows Ch. 10 2.5
8. Exact Solutions to the Navier-Stokes Equations Ch. 11/Epilogue 4.5
9. The Boundary Layer Ch. 12 3.0
10. Turbulent Flows Ch. 13 5.0

Exams 3.0

Total 30.0

Program:

1.0. Introduction: Solid, liquid, gases, vapors. Systems and control volumes. The continuum. Mathematical tools. Pressure in fluids in equilibrium.

2.0. Forces and Motions in Ideal Flows: Lagrangian and Eulerian descriptions. Material derivative and fluid acceleration. Flowlines: pathline, streamline, streakline. Forces on a fluid particle. Euler equation. Bernoulli equation (I).

3.0. Tools for Use in Ideal Fluid Flows: Rotational and irrotational flows: vorticity, circulation, velocity potential. Bernoulli equation (II). Stream function. Irrotational continuous flows.

4.0. Analysis of Ideal Fluid Flows: Useful flows: uniform, source/sink, vortex, doublet. Circular cylinder in uniform flow. Numerical solutions.

5.0. Some Extensions to the Method of Analysis of Ideal Fluid Flows: Complex variables. Complex velocity potential. Distributed singularities.

6.0. Dimensional Analysis: Dimensional homogeneity. Buckinghamís P theorem. Dimensionless parameters. Design of experiments. Important dimensionless groups in fluid mechanics. Generation of dimensionless governing equations.

7.0. Fundamental Concepts and Governing Relationships in Viscous Flows: Viscosity. Surface forces. Constitutive equations for isotropic fluids. Navier-Stokes equations.

8.0. Exact Solutions to the Navier-Stokes Equations: No-slip boundary condition. Fully-developed flows. Unsteady flow solutions. Numerical solutions.

9.0. The Boundary Layer: Boundary layer equations. Boundary layer separation. Laminar boundary layer on a flat plate. Approximate methods.

10.0. Turbulent Flows: Laminar instability and transition to turbulence. Average values and fluctuating quantities. Momentum transport via turbulence. Models for apparent stresses. Turbulent flow in pipes. Flat plate boundary layer flows. Flows with pressure gradients: form drag. Velocity distributions in open channels. The k-e model.

Teaching aids:

Films from the collection of the National Committee for Fluid Mechanics Films (NCFMF) and the Iowa Institute of Hydraulic Research (*):

1. Rheological behavior of fluids.
2. Surface tension in fluid mechanics.
3. Eulerian and Lagrangian descriptions in fluid mechanics.
4. Flow visualization.
5. Pressure fields and fluid accelerations.
6. Vorticity (I & II).
7. Fluid motion in a gravitational field (*).
8. Waves in fluids.
9. Stratified flow.
10. Secondary flow.
11. Low Reynolds number flows.
12. Fundamentals of boundary layers.
13. Boundary layer control.
14. Flow instabilities.
15. Turbulence.
16. Compressible flow.
17. Magnetohydrodynamics.

Notes:

1. Films will be presented in the laboratory meetings. The examinations may contain questions related to these films.
2. Two mid-term examinations and one final examination will be given as indicated in the attached schedule.