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PH30108: Fluid dynamics in physics & astrophysics

[Page last updated: 12 August 2020]

Follow this link for further information on academic years Academic Year: 2020/1
Further information on owning departmentsOwning Department/School: Department of Physics
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Honours (FHEQ level 6)
Further information on teaching periods Period:
Semester 1
Further information on unit assessment Assessment Summary: EX 100%
Further information on supplementary assessment Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Further information on requisites 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.
Further information on programme availabilityProgramme availability:

PH30108 is Compulsory on the following programmes:

Department of Physics
  • USPH-AFB10 : BSc(Hons) Physics with Astrophysics (Year 3)
  • USPH-AAB10 : BSc(Hons) Physics with Astrophysics with Study year abroad (Year 4)
  • USPH-AKB10 : BSc(Hons) Physics with Astrophysics with Year long work placement (Year 4)
  • USPH-AFM10 : MPhys(Hons) Physics with Astrophysics (Year 3)
  • USPH-AFM11 : MPhys(Hons) Physics with Astrophysics with Research placement (Year 3)
  • USPH-AKM10 : MPhys(Hons) Physics with Astrophysics with Professional Placement (Year 4)
  • USPH-AKM11 : MPhys(Hons) Physics with Astrophysics with Professional and Research Placements (Year 4)

PH30108 is Optional on the following programmes:

Department of Physics
  • USXX-AFB03 : BSc(Hons) Mathematics and Physics (Year 3)
  • USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 4)
  • USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 4)
  • USPH-AFB01 : BSc(Hons) Physics (Year 3)
  • USPH-AAB02 : BSc(Hons) Physics with Study year abroad (Year 4)
  • USPH-AKB02 : BSc(Hons) Physics with Year long work placement (Year 4)
  • USPH-AFM02 : MPhys(Hons) Physics (Year 3)
  • USPH-AFM04 : MPhys(Hons) Physics with Research placement (Year 3)
  • USPH-AAM12 : MPhys(Hons) Physics with Study year abroad (Year 4)
  • USPH-AKM03 : MPhys(Hons) Physics with Professional Placement (Year 4)
  • USPH-AKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 4)

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