PH30108: Fluid dynamics in physics & astrophysics
[Page last updated: 15 October 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: |
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| Assessment Summary: | EX 100% |
| Assessment Detail: |
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| Supplementary Assessment: |
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| 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 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; * interpret and apply the special relativistic equations of hydrodynamics for perfect fluids; * 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, 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 shock-jump conditions, relativistic and non-relativistic; * derive the basic equations of ideal magneto-hydrodynamics 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 non-steady 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; Navier-Stokes equations; boundary conditions; Reynolds Number Non-viscous 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
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