# MPhys Physics with Astrophysics / Course details

Year of entry: 2024

## Course unit details:Physics of Fluids

Unit code PHYS30652 10 Level 3 Semester 2 Department of Physics & Astronomy No

### Overview

Physics of Fluids

### Pre/co-requisites

Unit title Unit code Requirement type Description
Mathematics of Waves and Fields PHYS20171 Pre-Requisite Recommended

### Aims

To enable the student to understand this area of classical physics with an emphasis on applications.

### Learning outcomes

On completion successful students will be able to:

1. describe the key concepts in fluid dynamics

2. solve the Navier-Stokes equations in specific scenarios

3. apply key concepts in the viscous limit to specific scenarios such as lubrication, Stokes settling and swimming

4. apply key concepts in the inviscid limit to specific scenarios such as boundary layers, irrotational flow, vorticity, lift and aerofoils

### Syllabus

1. Basic concepts and governing equations of fluids

Fluids as continua; streamlines and pathlines; conservation of mass and the equation of continuity; rate of change following the fluid; conservation of momentum and the stress tensor; the constitutive equations and the Navier-Stokes equations.

2. Unidirectional flows

Boundary conditions for viscous flow; unidirectional flows in two dimensions; Poiseuille and Couette flow; some exact solutions of the Navier-Stokes equations; Poiseuille flow in a tube; flow down an inclined plane; examples of unsteady flows.

a. Dynamical similarity and the Reynolds number

Dynamical similarity and the Reynolds number; scaling of the Navier-Stokes equations

b. Viscous flows

Stokes flow past a sphere; flow reversibility; swimming at low Reynolds number; lubrication

theory;viscous penetration depth.

c. Inviscid flows

Governing equations and boundary conditions; Bernoulli’s equation; vorticity and its physical

meaning; Kelvin’s theorem; potential flow; the stream function; irrotationnal flows in various

geometries; flow around aerofoils; lift force.

d. Boundary layer theory

Prandtl’s boundary layer theory; Blasius flow; boundary layer separation.

e. Hydrodynamic instabilities and turbulence

Examples of hydrodynamic instabilities; pathways to turbulence; the Kolmogorov spectrum.

### Assessment methods

Method Weight
Written exam 100%

### Feedback methods

Feedback will be available on students’ individual written solutions to examples sheets, which will be marked, and model answers will be issued.

### Recommended reading

Acheson, D.J. Elementary Fluid Dynamics, (OUP)

Tritton, D.J. Physical Fluid Dynamics, (OUP)

Guyon E, Hulin J-P, Petit L. and Mitescu C.D., Physical hydrodynamics, (OUP)

### Study hours

Scheduled activity hours
Assessment written exam 1.5
Lectures 23
Independent study hours
Independent study 75.5

### Teaching staff

Staff member Role
Philippa Browning Unit coordinator

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