# Study-Unit Description

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CODE PHY3225

TITLE Fluid Mechanics

LEVEL 03 - Years 2, 3, 4 in Modular Undergraduate Course

ECTS CREDITS 4

DEPARTMENT Physics

DESCRIPTION This study-unit provides a broad introduction to fluid mechanics. It is composed of (i) basic concepts of fluid mechanics, (ii) brief mathematical concepts, (iii) detailed understanding of the Kinematics and Conservation laws in FM, (iv) various applications of the governing equations particularly the Bernoulli Principle, vortex dynamics, dynamic similarity and boundary layer approximation.

The fundamental fluid processes in simple and everyday applications will be clearly explained and discussed, for example the aerodynamics of aeroplanes and sports cars, the effect of different sports balls moving in air, river flows, and atmospheric and oceanographic flows.

Study-unit Aims:

Through this study-unit, the student will be introduced to the basics of Fluid Mechanics. Goals include its Kinematics and Conservation Laws: understanding Lagrangian and Eulerian descriptions and deriving the continuity equation (conservation of mass) and Navier-Stokes equation (conservation of momentum). Another objective of this course involves the applications of the fluid governing equations such as the derivation of Bernoulli equation and its application; the derivation of the momentum principle for a fixed volume and its applications; the derivation of the angular momentum principle for a fixed volume and its applications. The equations and applications in Vortex Dynamics, Dynamic Similarity and Similarity Solutions will be studied and discussed in detail. Finally, laminar and turbulent flows will be analysed, with the of aim of understanding the boundary layer approximation. Particular focus will be dedicated on aerodynamics of planes and sport cars.

Learning Outcomes:

1. Knowledge & Understanding
By the end of the study-unit the student will be able to:

- define shear stress, viscosity and surface tension;
- define and use the Gauss and Stokes theorems;
- define streamline, path line and streak line;
- distinguish between the Lagrangian and Eulerian descriptions;
- identify the physical meaning of the various terms of the Navier-Stokes equation;
- identify the physical meaning of the various terms of the mechanical energy equation;
- define the Boussinesq approximation;
- state and use Kelvin’s circulation theorem and the Helmholtz vortex theorem;
- identify the physical meaning of the various terms of the Vorticity Equation;
- classify events as high or low Reynold’s number events;
- explain the use of similarity solutions;
- state and justify the boundary layer approximation;
- explain how separation occurs.

2. Skills
By the end of the study-unit the student will be able to:

- determine the dot and cross products of vectors;
- use matrix algebra on a given matrix;
- determine the Gradient, the Divergence and the Curl of a quantity;
- use tensors algebra on a given tensor;
- use the comma notation as applied to tensors;
- derive the continuity equation from the principle of Conservation of Mass (both for Lagrangian and Eulerian form);
- derive the Cauchy’s equation from the principle of Conservation of Momentum;
- derive the Navier-Stokes equation;
- solve problems dealing with the Bernoulli equation and momentum principle (and angular momentum principle) for a fixed volume;
- explain how to apply the Boussinesq approximation;
- derive and describe the Kelvin’s circulation theorem;
- use Buckingham’s Pi theorem to identify non-dimensional parameter of a system;
- use model testing to solve problems;
- obtain the velocity and other properties of different steady flows between parallel plates;
- derive the velocity equation for problems with time scale and/or length scale.

Main Text/s and any supplementary readings:

Recommended textbooks:

- Fluid Mechanics. Kundu P.K., Cohen I.M., and Dowling D.R. (2011), 920 pp., ISBN-13: 978-0123821003.
- Essential Computational Fluid Dynamics. Zikanov O. (2010), ISBN 978-0-470-42329-5.
- Fundamental of Fluid Mechanics. Munson B.R., Young D.F., Okiishi T.H., and Huebsch W.W. (2009), ISBN 978-0470-26284-9.
- Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-scale Circulation. GK Vallis. (2006), 745 pp., ISBN-13: 978-0521849692.

The use of other books with similar content would be equivalently good.

ADDITIONAL NOTES Pre-Requisite: Good knowledge of Mathematics including calculus

STUDY-UNIT TYPE Lecture

METHOD OF ASSESSMENT
 Assessment Component/s Assessment Due Resit Availability Weighting Examination (2 Hours) SEM1 Yes 100%

LECTURER/S Anthony Galea

The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints.
Units not attracting a sufficient number of registrations may be withdrawn without notice.
It should be noted that all the information in the study-unit description above applies to the academic year 2019/0, if study-unit is available during this academic year, and may be subject to change in subsequent years.

https://www.um.edu.mt/course/studyunit