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MMath&Phys Mathematics and Physics / Course details
Year of entry: 2024
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Course unit details:
Physics of Fluids
|Department of Physics & Astronomy
|Available as a free choice unit?
Physics of Fluids
|Mathematics of Waves and Fields
To enable the student to understand this area of classical physics with an emphasis on applications.
On completion successful students will be able to:
1. describe the key concepts in fluid dynamics
2. solve the Navier-Stokes equations in specific scenarios
3. apply key concepts in the viscous limit to specific scenarios such as lubrication, Stokes settling and swimming
4. apply key concepts in the inviscid limit to specific scenarios such as boundary layers, irrotational flow, vorticity, lift and aerofoils
1. Basic concepts and governing equations of fluids
Fluids as continua; streamlines and pathlines; conservation of mass and the equation of continuity; rate of change following the fluid; conservation of momentum and the stress tensor; the constitutive equations and the Navier-Stokes equations.
2. Unidirectional flows
Boundary conditions for viscous flow; unidirectional flows in two dimensions; Poiseuille and Couette flow; some exact solutions of the Navier-Stokes equations; Poiseuille flow in a tube; flow down an inclined plane; examples of unsteady flows.
a. Dynamical similarity and the Reynolds number
Dynamical similarity and the Reynolds number; scaling of the Navier-Stokes equations
b. Viscous flows
Stokes flow past a sphere; flow reversibility; swimming at low Reynolds number; lubrication
theory;viscous penetration depth.
c. Inviscid flows
Governing equations and boundary conditions; Bernoulli’s equation; vorticity and its physical
meaning; Kelvin’s theorem; potential flow; the stream function; irrotationnal flows in various
geometries; flow around aerofoils; lift force.
d. Boundary layer theory
Prandtl’s boundary layer theory; Blasius flow; boundary layer separation.
e. Hydrodynamic instabilities and turbulence
Examples of hydrodynamic instabilities; pathways to turbulence; the Kolmogorov spectrum.
Feedback will be available on students’ individual written solutions to examples sheets, which will be marked, and model answers will be issued.
Acheson, D.J. Elementary Fluid Dynamics, (OUP)
Tritton, D.J. Physical Fluid Dynamics, (OUP)
Guyon E, Hulin J-P, Petit L. and Mitescu C.D., Physical hydrodynamics, (OUP)
|Scheduled activity hours
|Assessment written exam
|Independent study hours