Single-Course English 5 ECTS

## Overall Course Objectives

The aim of the course is to give the student a basic understanding of the physics of spatially extended media consisting of solid materials, liquids, and gasses. The course can be regarded as a natural extension of classical mechanics (including thermodynamics/statistical mechanics) or be the basis for more specialized studies in elasticity, hydrodynamics, microfluidics, biophysics, and complex systems.

Learning Objectives

• Explain the theory of hydrostatic equilibrium, including pressure, buoyancy, stability of a floating object, hydrostatic shapes and surface tension.
• Explain the concepts of strain and stress in elastic materials and explain the derivation of and apply the Cauchy equation and Hooke’s law.
• Explain the derivation of and apply the Euler, the Bernouilli, the Navier-Stokes, and the continuity equation for incompressible fluid flows.
• Describe flows at low Reynolds number.
• Derive the wave equation and the dispersion relation for linear surface waves and sound waves in fluid- and elastodynamic systems
• Apply linear stability theory and explain the Rayleigh-Plateau instability.
• Explain and apply Prandtl’s boundary layer equations.
• Apply dimensional analysis to make estimates in continuum physics.
• Solve analytic problems from selected models in continuum physics.
• Apply vector and tensor analysis with the index notation on models in continuum physics

Course Content

Introduction of velocity field and pressure field. Hydrostatic problems with special focus on surface tension. Strain and stress in elastic media. The equations for linear elasticity. Bending and buckling. Ideal, incompressible fluid motion (the Euler equation). Viscosity, Navier-Stokes equation, and boundary layers. Potential flow theory, surface waves and sound waves in fluid- and elastodynamic materials. Index notation in vector and tensor analysis.

Recommended prerequisites

01001/01002/02002/10033/10034, especially central material from classical physics and mathematics, i.e., knowledge of mechanics, thermodynamics, electromagnetism, vector analysis, and ordinary as well as partial differential equations.

Teaching Method

The weekly block of four hours will consist of a mixture of lectures, work with problems and computer exercises. Central in the course are two larger homework problems, which are graded and count as part of the final grade. The homework problems are new from year to year and each assignment focuses on a selected problem of current research interest.

Faculty

Remarks

Continuum Physics (10346) and Theoretical Microfluidics (10337) are independent. The courses only overlap in the introduction to the fundamental fluid dynamics equations.

See course in the course database.

## Registration

Language English 13 weeks Physics DTU Lyngby Campus 10346 Candidate Week 5 Week 19 Mon 13-17
Price 7.500,00 DKK