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DRPS : Course Catalogue : School of Engineering : Mechanical

Undergraduate Course: Fluid Mechanics (Mechanical) 4 (MECE10004)

Course Outline
SchoolSchool of Engineering CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryA general form of the Navier-Stokes equation is derived with a focus on the physical interpretation of the mathematical model. This equation is used to derive simplified models for bidimensional incompressible flows, including potential flow and boundary layer flow. The fundamentals of turbulent flow, including basic turbulent statistics, are presented.
Course description The following list of lectures is only indicative and should be considered an example of delivery of the course.

Introduction and Math 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
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. Exact and integral solutions of the Navier-Stokes equation.
L7. Derivation of the nondimensional form of the Navier-Stokes equation.

Potential flow
L8. 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.
L9. 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.
L10. Forces on objects in potential flow: flow past a rotating circle, the Magnus effect and the d'Alembert's paradox, Kelvin¿s circulation theorem and Kutta-Joukowsky¿s theorem.
L11. How to reconcile potential flow with rotational flow: the link between circulation and vorticity, bound circulation and free vortices.
L12. Introduction to thin airfoil theory: key assumptions and basic results.

Turbulent Flow
L13. Phenomenology of turbulent flow, Reynolds-averaged Navier-Stokes equation.
L14. Reynolds stress tensor, wall scales, Boussinesq hypothesis, turbulent viscosity.
L15. Derivation of the universal law of the wall and taxonomy of wall bounded flow.
L16. Moody diagram, k-type and d-type roughness.

Boundary Layer
L17. Phenomenology and taxonomy of boundary layer flow, von Karman integral of the boundary layer and definition of the displacement and momentum thickness.
L18. 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.

Turbulent Statistics
L19. The statistical approach: ensemble, moments, stationarity and homogeneity.
L20. Correlations, integral scale, spectra, Kolmogorov¿s scales.

Tutorial classes
T1. Mathematics revision
T2. Navier-Stokes equation
T3. Navier-Stokes equation
T4. Potential flow
T5. Potential flow
T6. Mock exam
T7. Turbulent flow
T8. Turbulent flow
T9. Boundary layer
T10. Turbulent statistics

AHEP outcomes: SM1m, SM2m, SM3m, SM5m, SM6m, EA1m, EA2m, P1, G1, G2.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Co-requisites
Prohibited Combinations Other requirements None
Information for Visiting Students
High Demand Course? Yes
Course Delivery Information
Academic year 2024/25, Available to all students (SV1) Quota:  None
Course Start Semester 1
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( 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 65 )
Assessment (Further Info) Written Exam 100 %, Coursework 0 %, Practical Exam 0 %
Additional Information (Assessment) Final Examination 100%
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S1 (December)2:00
Resit Exam Diet (August)2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Demonstrate and work with knowledge that covers and integrates most of the principal areas, features, boundaries, terminology and conventions of fluid dynamics.
  2. Demonstrate and work with critical understanding of the principal theories, concepts and principles of fluid dynamics.
  3. Apply knowledge and understanding in using techniques and practices that are at the forefront of analytical fluid dynamics.
Reading List
Kundu et al., Fluid Mechanics, 6th Edition, 2016
White, Fluid Mechanics, 7th Edition, 2009

Additional Information
Course URL
Graduate Attributes and Skills Not entered
Course organiserDr Brian Peterson
Tel: (0131 6)50 5572
Course secretaryMiss Catherine Davidson
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