Undergraduate Course: Fluid Mechanics (Mechanical) 4 (MECE10004)
|School||School of Engineering
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 10 (Year 4 Undergraduate)
||Availability||Available to all students
|Summary||The course presents the classical 3D differential form of the fluid mechanics equations and some canonical solutions, including potential flow, incompressible laminar and turbulent flow, and boundary layer flow.
The following list of lectures is only indicative and should be considered an example of delivery of the course.
Introduction and Recap
L1. Introduction to the course.
L2. Mathematical methods for fluid mechanics: revision of vector total and partial derivatives, application to fluid mechanics, introduction to Einstein notation and application to differential operations, revision of vector calculus (gradient, divergence, Stokes and Green¿s theorem), complex variable calculus and Fourier and Laplace transforms.
Governing Equations of Fluids (4 lectures)
L3. Derivation of the continuity equation.
L4. Definition of the stresses and of the strain rate tensor; derivation of the momentum Cauchy equation.
L5. Constitutive equation for Newtonian fluids, derivation of the Navier-Stokes Equation.
L6. Derivation of the nondimensional form of the Navier-Stokes equation.
Potential flow (3 lectures)
L7. The basics of potential flow: introduction of vorticity and the velocity potential and derivation of the conservation laws governing incompressible irrotational flow, including Bernoulli's law.
L8. The building blocks of potential flow: introduction to the elementary solutions to the Laplace equation, the principle of linear superposition and application to explain applied fluid dynamics problems.
L9. Forces on objects in potential flow: flow past a Rankine oval and a circle, flow past a rotating circle and the Magnus effect, Kelvin¿s circulation and Kutta-Joukowsky theorems, drag and d'Alembert's paradox.
L10. Example of solutions of the Navier-Stokes equations for simple boundary conditions: the Couette and the Pouiselle flows.
Turbulent Flow (5 lectures)
L11. Phenomenology of turbulent flow, Reynolds-averaged Navier-Stokes equation.
L12. Reynolds stress tensor, wall scales, Boussinesq hypothesis, turbulent viscosity.
L13. The universal Law of the wall, taxonomy of wall bounded flow.
L14. Moody diagram, k-type and d-type roughness.
L15. Review of turbulent flow.
Boundary Layer (2 lectures)
L16. Phenomenology and taxonomy of boundary layer flow, von Karman integral of the boundary layer and definition of the displacement and momentum thickness.
L17. Derivation of the boundary layer equations, summary of results of the Blasius solution of the laminar boundary layer equations, and summary of results of the solutions of the power law for turbulent flow.
Waves (3 lectures)
L19. Surface gravity waves: derivation of free surface boundary conditions, linearisation and solutions using separation of scales, properties of linear wave theory including propagation, dispersion, orbits, wave forces.
L19. Internal gravity waves: derivation of the governing equations from the vorticity equation, linearisation and solutions, properties of linear wave theory including propagation, dispersion, orbits.
L20. Capillary waves: derivation of boundary conditions, linearisation and solutions, properties including dispersion compared to surface waves.
Tutorial classes (11 classes)
T1. Mathematics revision
T2. Navier-Stokes Equation
T4. Potential Flow 1
T5. Mock Exam
T6. Potential Flow 2
T7. Laminar Flow
T8. Turbulent Flow
T9. Boundary Layer
AHEP outcomes: SM1m, SM2m, SM3m, SM5m, SM6m, EA1m, EA2m, P1, G1, G2.
Entry Requirements (not applicable to Visiting Students)
||Other requirements|| None
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2018/19, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 20,
Seminar/Tutorial Hours 10,
Formative Assessment Hours 1,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Final Examination 100%
||Hours & Minutes
|Main Exam Diet S1 (December)||Fluid Mechanics (Mechanical) 4||2:00|
|Resit Exam Diet (August)||2:00|
On completion of this course, the student will be able to:
- Demonstrate and work with knowledge that covers and integrates most of the principal areas, features, boundaries, terminology and conventions of fluid dynamics.
- Demonstrate and work with critical understanding of the principal theories, concepts and principles of fluid dynamics.
- Apply knowledge and understanding in using techniques and practices that are at the forefront of analytical fluid dynamics.
|Kundu et al., Fluid Mechanics, 6th Edition, 2016|
White, Fluid Mechanics, 7th Edition, 2009
|Course organiser||Dr Ignazio Maria Viola
Tel: (0131 6)50 5622
|Course secretary||Mr James Foster
Tel: (0131 6)51 3562