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Programme & Unit Catalogues

## PH30087: Fluid dynamics

Owning Department/School: Department of Physics
Credits: 3
Level: Honours (FHEQ level 6)
Period: Semester 2
Assessment: EX 100%
Supplementary Assessment: Mandatory extra work (where allowed by programme regulations)
Requisites: Before taking this unit you must take PH20019
Description: Aims:
The aim of this unit is to introduce students to the fundamental concepts and equations of fluid dynamics.

Learning Outcomes:
After taking this unit the student should be able to:
* analyse a two-dimensional flow in terms of displacement, local rotation and local shearing;
* derive the continuity and Euler equations;
* perform a dimensional analysis of the Navier-Stokes equation and interpret the Reynolds number;
* explain and interpret mathematically the terms: steady and non-steady flow, incompressible flow, irrotational flow, potential flow, laminar flow;
* derive and use Bernoulli's equation;
* solve simple potential flow and laminar viscous flow problems.

Skills:
Numeracy T/F A, Problem Solving T/F A.

Content:
Introduction to fluid dynamics: Definitions; steady and non-steady flows, streamlines and pathlines.
Equations of motion for a fluid: Continuity equation, incompressible flows. Local nature of fluid motion; displacement, rotation and shear. Forces on a fluid; pressure gradient, gravity, viscosity. Acceleration of a fluid packet, rate of change of the velocity pattern. Navier-Stokes equations. Boundary conditions. Dedimensionalisation of the Navier-Stokes equations; Reynolds Number.
Non-viscous flow: Bernoulli's equation. Circulation theorem. Irrotational flow. Properties of potential flows. Examples including vortex flow, flow past a cylinder, waves on deep water.
Viscous flow: Laminar flow; flows in pipes and channels. Boundary layer flow. Separation and the transition to turbulence. Drag on a moving object.
Programme availability:

#### PH30087 is Optional on the following programmes:

Department of Mathematical Sciences
• TSMA-AFM08 : MSc Modern Applications of Mathematics (Full-time) - Year 1
• TSMA-AFL02 : PG Dip Modern Applications of Mathematics (Full-time) - Year 1
Department of Physics
• USPH-AFB01 : BSc (hons) Physics (Full-time) - Year 3
• USPH-AFB05 : BSc (hons) Physics with Computing (Full-time) - Year 3
• USPH-AKB06 : BSc (hons) Physics with Computing (with Placement) (Full-time with Thick Sandwich Placement) - Year 4
• USPH-AAB06 : BSc (hons) Physics with Computing with Year Abroad (Full-time with Study Year Abroad) - Year 4
• USPH-AKB02 : BSc (hons) Physics (with Placement) (Full-time with Thick Sandwich Placement) - Year 4
• USPH-AAB02 : BSc (hons) Physics with Year Abroad (Full-time with Study Year Abroad) - Year 4
• USPH-AFB09 : BSc Physics (Full-time) - Year 3
• USPH-AKB09 : BSc Physics (with Placement) (Full-time with Thick Sandwich Placement) - Year 4
• USPH-AFM02 : MPhys Physics (Full-time) - Year 3
• USPH-AFM04 : MPhys Physics with Research Placement (Full-time) - Year 3

Notes:
* This unit catalogue is applicable for the 2012/13 academic year only. Students continuing their studies into 2013/14 and beyond should not assume that this unit will be available in future years in the format displayed here for 2012/13.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.