Fluids and Continuum Physics

Physics in 13 chapters — from “The continuum hypothesis, pressure and the stress tensor” to “Acoustics: sound propagation, radiation and attenuation”.

Chapters

  1. The continuum hypothesis, pressure and the stress tensor
    • Molecules, parcels and the continuum hypothesis
    • Pressure and its isotropy at a point
    • Hydrostatic equilibrium and buoyancy
    • Definition of a fluid, viscosity and compressibility
    • The traction vector and the stress tensor
    • The stress tensor in three materials
    • Problems
  2. Mechanical properties of materials: the Young modulus, plasticity and fracture
    • Engineering stress and strain
    • The Young modulus and elastic strain energy
    • The stress-strain curve beyond yield
    • Ductile and brittle fracture and the Griffith crack
    • Problems
  3. Surface tension, capillarity and wetting
    • Surface energy and surface tension
    • The Young-Laplace pressure inside drops and bubbles
    • Contact angle and wetting
    • Capillary rise and the capillary length
    • Surfactants and Marangoni flow
    • Problems
  4. Kinematics of flow: fields, streamlines and the material derivative
    • The velocity field and the Eulerian description
    • The partial derivative of a field
    • Streamlines, pathlines, streaklines
    • The material derivative
    • The velocity gradient tensor and vorticity
    • Divergence and volume change
    • Problems
  5. Conservation of mass, momentum and energy
    • The control volume and flux
    • Conservation of mass in integral form
    • The momentum balance on a control volume
    • The mechanical energy budget and head loss
    • Problems
  6. Euler's equation and Bernoulli's theorem
    • The draining tank and the pressure gradient force
    • Euler's equation for an inviscid fluid
    • Euler's equation in rigid-body motion
    • Bernoulli's theorem along a streamline
    • The Bernoulli constant across streamlines
    • Static, dynamic and stagnation pressure
    • Problems
  7. Bernoulli at work: Venturi meters, Pitot tubes and lift
    • The Venturi meter
    • The Pitot-static tube and airspeed
    • Lift from pressure difference, and equal transit time
    • Lift coefficient and stall; the spinning ball
    • Problems
  8. Vorticity, circulation and vortex motion
    • The stirred cup and circulation round a loop
    • Line vortex and Rankine vortex
    • Kelvin's circulation theorem and the starting vortex
    • Vorticity equation and stretching
    • Helmholtz vortex theorems and vortex interactions
    • Problems
  9. Potential flow, complex potentials and lift
    • Velocity potential and Laplace equation
    • Stream function and elementary plane flows
    • The complex potential
    • Flow past a cylinder and d'Alembert's paradox
    • Cylinder with circulation and Kutta-Joukowski lift
    • Unsteady Bernoulli equation
    • Problems
  10. The Navier-Stokes equations and exact viscous solutions
    • The Newtonian constitutive law
    • The Navier-Stokes equation and the no-slip condition
    • Plane Couette and plane Poiseuille flow
    • Hagen-Poiseuille pipe flow
    • Viscous dissipation and head loss
    • Stokes drag and vorticity diffusion at walls
    • Problems
  11. Dimensional analysis, dynamical similarity and the dimensionless groups
    • Dimensional homogeneity and Buckingham Pi
    • The Reynolds number from the Navier-Stokes equation
    • Dynamical similarity and model testing
    • Drag coefficient and the drag curve
    • Pipe friction, transition and boundary-layer scaling
    • Problems
  12. Surface gravity and capillary waves
    • The linearised free-surface problem
    • The travelling-wave solution and the dispersion relation
    • Deep and shallow water limits
    • Phase and group velocity
    • Capillary waves and minimum phase speed
    • Particle orbits and wave energy
    • Problems
  13. Acoustics: sound propagation, radiation and attenuation
    • Newton's error and the linearised acoustic equations
    • The acoustic wave equation and its travelling solutions
    • The speed of sound
    • Acoustic impedance and intensity
    • Spherical waves and monopole radiation
    • Attenuation of sound by viscosity
    • The Mach number and incompressible limit
    • Problems