PH30108: Fluid dynamics in physics & astrophysics
[Page last updated: 12 August 2020]
Academic Year:  2020/1 
Owning Department/School:  Department of Physics 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Honours (FHEQ level 6) 
Period: 

Assessment Summary:  EX 100% 
Supplementary Assessment: 

Requisites: 
Before or while taking this module you must ( take PH20107 OR take MA20223 ) AND ( take PH10103 OR take PH20076 OR take PH20106 OR take PH20114 )
In taking this module you cannot take MA30253 OR take MA40255 
Description:  Aims: The aim of this unit is to introduce students to the fundamental concepts and equations of fluid dynamics in a physical and astrophysical setting. Learning Outcomes: After taking this unit the student should be able to: * analyse a twodimensional flow in terms of displacement, local rotation and local shearing; * derive the continuity and Euler equations; * perform a dimensional analysis of the NavierStokes equation and interpret the Reynolds number; * interpret and apply the special relativistic equations of hydrodynamics for perfect fluids; * explain and interpret mathematically the terms: steady and nonsteady flow, incompressible flow, irrotational flow, potential flow, laminar flow; * derive and use Bernoulli's equation; * solve simple potential flow and laminar viscous flow problems, as well as selected common applications in astrophysics; * derive and apply the wave equations for sound waves from the equations of hydrodynamics; * derive and apply the shockjump conditions, relativistic and nonrelativistic; * derive the basic equations of ideal magnetohydrodynamics by merging the equations of hydrodynamics with Maxwell's equations. Skills: Numeracy T/F A, Problem Solving T/F A. Content: Introduction to fluid dynamics: Definitions; steady and nonsteady flows; streamlines and pathlines; equation of state. 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; NavierStokes equations; boundary conditions; Reynolds Number Nonviscous flow: Bernoulli's equation; Circulation theorem; irrotational flow. 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. Advanced topics: Equations of ideal magnetohydrodynamics; fluid dynamics in special relativity; shock waves and sound waves. Astrophysics applications: Stars in hydrostatic equilibrium and the virial theorem; stellar winds; (relativistic) astrophysical explosions and shock waves; spherical accretion flow. 
Programme availability: 
PH30108 is Compulsory on the following programmes:Department of Physics
PH30108 is Optional on the following programmes:Department of Physics

Notes:
