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MPhys Physics

Year of entry: 2021

Course unit details:
Physics of Fluids

Unit code PHYS30652
Credit rating 10
Unit level Level 3
Teaching period(s) Semester 2
Offered by Department of Physics & Astronomy
Available as a free choice unit? 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

This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.  Please see Blackboard / course unit related emails for any further updates

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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