## PH30108: Fluid dynamics in physics & astrophysics

[Page last updated: 05 August 2021]

Academic Year: 2021/2
Owning Department/School: Department of Physics
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Honours (FHEQ level 6)
Period:
Semester 1
Assessment Summary: EX 100%
Assessment Detail:
• Examination (EX 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
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
• USPH-AFM10 : MPhys(Hons) Physics with Astrophysics (Year 3)
• USPH-AFM11 : MPhys(Hons) Physics with Astrophysics with Research placement (Year 3)
• USPH-AAM14 : MPhys(Hons) Physics with Astrophysics with Study year abroad (Year 4)
• 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)
• USPH-AAM15 : MPhys(Hons) Physics with Astrophysics with Study year abroad and Research Placement (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-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-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)
• USPH-AAM13 : MPhys(Hons) Physics with Study year abroad and Research Placement (Year 4)

 Notes: This unit catalogue is applicable for the 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22. Programmes and units are subject to change 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. Find out more about these and other important University terms and conditions here.