Fluid Dynamics II(D)
FLUID DYNAMICS II (D)
Methods and Fluid Dynamics are essential. It is recommended that students attend the associated Laboratory Demonstrations in Fluid Dynamics.
Governing equations for an incompressible Newtonian fluid
- Stress and rate-of-strain tensors and hypothesis of linear relation between them for an isotropic fluid; equation of motion; conditions at a material boundary; dissipation; flux of mass, momentum and energy; the Navier-Stokes equations. Dynamical similarity; steady and unsteady Reynolds numbers. [4]
Unidirectional flows
- Couette and Poiseuille flows; the Stokes layer; the Rayleigh problem. [2]
Stokes flows
- Flow at low Reynolds number; linearity and reversibility; uniqueness and minimum dissipation theorems. Flow in a corner; force and torque relations for a rigid particle in arbitrary motion; case of a rigid sphere and a spherical bubble. [4]
Flow in a thin layer
- Lubrication theory; simple examples; the Hele-Shaw cell; gravitational spreading on a horizontal surface. [3]
Generation and confinement of vorticity Vorticity equation; vortex stretching; flow along a plane wall with suction; flow toward a stagnation point on a wall; flow in a stretched line vortex. [3]
Boundary layers at high Reynolds number
- The Euler limit and the Prandtl limit; the boundary layer equation for two-dimensional flow. Similarity solutions for flow past a flat plate and a wedge. ∗Discussion of the effect of acceleration of the external stream, separation.∗ Boundary layer at a free surface; rise velocity of a spherical bubble. [6]
Stability of unidirectional inviscid flow
- Instability of a vortex sheet and of simple jets (e.g. vortex sheet jets). [2]
Appropriate books
- D.J. Acheson Elementary Fluid Dynamics. Oxford University Press 1990
- G.K. Batchelor An Introduction to Fluid Dynamics. Cambridge University Press 2000
- E. Guyon, J-P Hulin, L. Petit and C.D. Mitescu Physical Hydrodynamics. Oxford University Press 2000
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