MEK4200 – Viscous Flow and Elastic Media
Course description
Course content
Vectors and tensors. Index notation. Stress tensors for fluids and solids. Cauchy's relations. Principal stresses and principal directions. Velocities, displacement and acceleration. Deformation (strain). Relation between stress and strain. Newton's law of friction in fluids. Hooke's law for elastic matter. Simple viscous elastic models. The equation of motion for viscous fluids (the Navier Stokes equation). The equation of motion for isotropic linear elastic matter. Explicit solutions for equations for elastic matter: Stress distribution caused by gravity, axial strain, torsion of cylindrical rod, longitudinal and transversal (p- and s-waves), reflection of waves. Explicit solutions for equations for viscous fluids: Couette flow, laminar flow in pipes, flow on inclined planes, boundary layers. Equations of energy conservation, energy dissipation, equation of thermal transport, heat flow, Fourier's law. Scale analysis and principles and modeling.
Learning outcome
To give an introduction to the basic equations and solution methods for mathematical modeling of viscous fluids and elastic matter. The course provides a basis for further studies in mechanics, applied and industrial mathematics, physics, geology, geophysics, and astrophysics.
Admission
Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.
If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.
Prerequisites
Recommended previous knowledge
MAT1100 – Calculus, MAT1110 – Calculus and Linear Algebra, MAT1120 – Linear Algebra, FYS-MEK1110 – Mechanics and MEK1100 – Vector Calculus.
Overlapping courses
10 credits with MEK2200 – Continuum Mechanics.
10 credits with ME115.
*The information about overlaps is not complete. Contact the department for more information if necessary.
Teaching
Colloquia/exercises for the duration of one semester. The exercises are mainly based on independent work from the students. The students must hand in compulsory assignments.
Examination
Two compulsory assignments have to be handed in and approved. Final written examination. Letter grading (A-F).
Rules for compulsory assignments at the Department of Mathematics (norwegian only)
Examination support material
Rottmann's formula list + approved calculator.
Language of examination
Subjects taught in English will only offer the exam paper in English.
You may write your examination paper in Norwegian, Swedish, Danish or English.
Explanations and appeals
Resit an examination
Information about deferred and new examination (also called repeat examination) is found here (only in Norwegian) .
Evaluation
The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.