Introductory description

ES3D6-15 Fundamental Fluid Mechanics for Mechanical Engineers

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

1. Introduction (mostly brief revision from fluid dynamics part of ES2C5 module): Continuum
   hypothesis, control surface, control volume, Streamlines, Newton's law of viscosity, Non-
   Newtonian fluids, Reynolds number, hydrostatic pressure.
2. Conservation principles (in integral and differential form): Mass conservation, momentum
   equation, Reynolds transport theorem, 1-D energy equation, Euler equation, Navier-Stokes
   equation & its non-dimensionalization.
3. Bernoulli equation: Derivation, limitations, physical interpretation, Flow-measuring devices.
4. Stream function: Continuity equation - existence of stream function to describe flow field;
   relationship to streamlines.
5. Ideal flow: Assumptions, definition of vorticity, velocity potential. Rotational vs. Irrotational
   flow, Potential flow theory: mathematical description of incompressible, inviscid, irrotational
   flow - Laplace equation. Fundamental solution to Laplace equation, linear superposition,
   modelling of bodies in ideal flow (Rankine bodies). Cylinder in uniform flow, cylinder with
   circulation in uniform flow, Magnus effect: circulation and lift, Helmholtz vortex theorems,
   Principle of lifting aerofoils, Kutta-Joukowski- theorem.
6. Internal viscous flows: Laminar and turbulent pipe flows. Application of laminar flow – Darcy’s
   law, Velocity profiles, shear stress, wall friction, pressure gradient. Effect of wall roughness; Moody chart.
7. Boundary-layer flows: Limitations of ideal flow - concept of viscous boundary layer. Momentum-integral equation, displacement and momentum thickness. Laminar and turbulent boundary layers; velocity profiles, skin-friction drag. Modelling of slender-body drag.
8. Transition, Turbulence, Kolmogorov’s theory of turbulence and energy spectrum/energy cascade (very brief introduction only), separation and wakes: Mechanisms for boundary-layer transition. Separation and wake drag; aerofoil stall. Drag coefficients for bluff bodies; dynamic similarity. Strategies for drag reduction.
9. Compressible flows: flow regimes (subsonic, transonic, supersonic, ultrasonic flows), Mach number, oblique shock waves and expansion fans, area-velocity relation, Laval nozzle.
10. Rotating flows: Coriolis force, effects of Coriolis force (Taylor-curtains, Taylor-Proudman theorem).
11. Computational methods: Partial differential equations (classification scheme: elliptic, parabolic, hyperpolic). Solution strategies (finite differences, finite volumes, finite elements, method of characteristics), illustrate basic principle of finite-difference method in an example.

Learning outcomes

By the end of the module, students should be able to:

• Critically evaluate the importance and role of fluid mechanics within the Mechanical Engineering profession, consolidate and advance existing knowledge of fluidic systems;
• Communicate how broad physical principles (consideration of mass, momentum, energy) are applied in the solution of complex fluidic problems;
• Determine fluid behaviour in complex situations, and devise mathematical descriptions to communicate key features;
• Distinguish between differing fluid based phenomena and demonstrate ability to abstract solutions;
• Devise appropriate modelling and carry out calculations/estimations of such engineering quantities as pressure, forces [e.g. friction, drag, lift, power requirements, efficiency.];
• Apply complex numerical skills to the solution of fluid mechanics problems.

Indicative reading list

The main recommended textbook option are:
(1) Potter, M.C., Wiggert, D.C., Ramadan, B.H., 2017, Mechanics of Fluids (5th Edition),
Cengage Learning, Stamford. ISBN 978-1-305-63761-0.
(2) White, F.M., 2016, Fluid Mechanics (8th Edition), McGraw-Hill, New York. ISBN
9789814720175.
(3) Douglas, J.F., Gasiorek, J.M., Swaffield, J.A., Jack, L.B., 2011, Fluid Mechanics (6th Edition,
or latest edition whenever new editions become available), Prentice Hall, Pearson
Education Limited, Harlow, UK.

Subject specific skills

1. Ability to conceive, make and realise a component, product, system or process
2. Ability to develop economically viable and ethically sound sustainable solutions
3. Ability to be pragmatic, taking a systematic approach and the logical and practical steps necessary for, often complex, concepts to become reality
4. Ability to seek to achieve sustainable solutions to problems and have strategies for being creative and innovative
5. Ability to be risk, cost and value-conscious, and aware of their ethical, social, cultural, environmental, health and safety, and wider professional engineering responsibilities

Transferable skills

1. Numeracy: apply mathematical and computational methods to communicate parameters, model and optimize solutions
2. Apply problem solving skills, information retrieval, and the effective use of general IT facilities
3. Communicate (written and oral; to technical and non-technical audiences) and work with others
4. Plan self-learning and improve performance, as the foundation for lifelong learning/CPD
5. Exercise initiative and personal responsibility, including time management, which may be as a team member or leader
6. Awareness of the nature of business and enterprise in the creation of economic and social value
7. Overcome difficulties by employing skills, knowledge and understanding in a flexible manner
8. Ability to formulate and operate within appropriate codes of conduct, when faced with an ethical issue
9. Appreciation of the global dimensions of engineering, commerce and communication
10. Be professional in their outlook, be capable of team working, be effective communicators, and be able to exercise responsibility and sound management approaches.