ES3D6 Fluid Mechanics for Mechanical Engineers

Module Leader: Dr P.J. Thomas

Module Information

Scope

This 15 CATS module is one of the third year modules for:

Core:	Optional:
Mechanical Engineering	Engineering

Aims

All Mechanical Engineers require a sound understanding of fluid mechanics. Issues involving aspects of fluid mechanics are involved in the vast majority of engineering problems. This module introduces the elementary principles and concepts and the fundamental theoretical and applied tools required for solving typical problems in mechanical engineering.

At the end of the course students should have an understanding of how broad physical principles (conservation of mass, momentum, energy) determine fluid behaviour and lead to mathematical descriptions of key features. Students should be able to utilise the results of such descriptions, together with appropriate modelling, to carry out calculations/estimations of such engineering quantities as pressure, forces (e.g. friction, drag, lift), power requirements, efficiency.

Learning Outcomes

By the end of the module the student should be able to...

Identify the importance and role of fluid mechanics within the Mechanical Engineering profession.
Students should have an understanding of how broad physical principles (consideration of mass, momentum, energy) determine fluid behaviour and lead to mathematical descriptions of key features
Students should be able to utilise the results of such descriptions, together with appropriate modelling, to carry out calculations/estimations of such engineering quantities as pressure, forces (e.g. friction, drag, lift), power requirements, efficiency.

Syllabus

1.Introduction (partly revision): Continuum hypothesis, control surface, control volume Streamlines, Newton's law of viscosity, Non-Newtonian fluids, Reynolds number, hydrostatic pressure.

2. Conservation principles: Mass conservation, momentum equation, Reynolds transport theorem, 1-D energy equation, Euler equation, Navier-Stokes equation

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. 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, 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, 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, implicit vs. explicit methods)