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PH4031   Fluids

Academic year(s): 2019-2020

Key information

SCOTCAT credits : 15

ECTS credits : 7

Level : SCQF level 10

Semester: 2

Availability restrictions: Not automatically available to General Degree students

Planned timetable: 11.00 am even Mon, 2.00 pm odd Tue, 11.00 am Tue & Thu

This module provides an introduction to fluid dynamics, and addresses the underlying physics behind many everyday flows that we see around us. It starts from a derivation of the equations of hydrodynamics and introduces the concept of vorticity and the essentials of vorticity dynamics. The influence of viscosity and the formation of boundary layers is described with some straightforward examples. The effect of the compressibility of a fluid is introduced and applied to shock formation and to the conservation relations that describe flows through shocks. A simple treatment of waves and instabilities then allows a comparison between theory and readily-observed structures in clouds, rivers and shorelines.

Relationship to other modules

Pre-requisite(s): Before taking this module you must pass PH3081 or pass PH3082 or ( pass MT2506 and pass MT2507 )

Learning and teaching methods and delivery

Weekly contact: 3 lectures and some tutorials.

Scheduled learning hours: 32

Guided independent study hours: 118

Assessment pattern

As used by St Andrews: 2-hour Written Examination = 100%

As defined by QAA
Written examinations : 100%
Practical examinations : 0%
Coursework: 0%

Re-assessment: Oral Re-assessment, capped at grade 7


Module coordinator: Dr C Helling
Module teaching staff: Dr C Helling

Additional information from school

Aims & Objectives
  • To present an introduction to fluid dynamics, focussing particularly on the underlying physics including the use of conservation relations (mass, momentum, energy) to describe flows
  • a physical understanding of vorticity and its evolution in a flow
  • the role of viscosity and its effect on flows at boundaries
  • the use of conservation relations to describe the behaviour of fluids at a shock
  • the onset of simple instabilities


Learning Outcomes

By the end of the module students will have an understanding of the physics of fluid flow as presented in the lectures and will be able to:


  • apply conservation relations to determine the properties of given flow patterns
  • determine the vorticity of a flow and describe its behaviour
  • use Bernoulli's equation to analyse simple flows - describe the role of viscosity and solve for simple ideal fluid flows
  • use the shock relations to relate fluid properties on each side of a shock
  • describe and calculate the onset of simple instabilities



Introduction of Lagrangian and Eulerian derivatives. Derivation of the vector form of the equations of conservation of mass, momentum and energy. Brief review of simple equations of state. Introduction of the concept of vorticity and the essentials of vorticity dynamics. Bernoulli's equation with simple examples. De Laval nozzle flow and transition to supersonic flow. Basic introduction to viscosity and its importance in boundary layers. Reynolds number. Sound waves and formation of shocks. Conservation relations. Simple treatment of instabilities (convection, Rayleigh-Taylor, Kelvin-Helmholtz).


Accreditation Matters

This module may not contain material that is part of the IOP “Core of Physics”, but does contribute to the wider and deeper learning expected in an accredited degree programme.  The skills developed in this module, and others, contribute towards the requirements of the IOP “Graduate Skill Base”.


Recommended Books

Please view University online record:


General Information

Please also read the general information in the School's honours handbook that is available via