MEK9200 – 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
PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.
If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.
PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.
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 MEK4200 – Viscous Flow and Elastic Media (discontinued).
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.
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.
Grading scale
Grades are awarded on a pass/fail scale. Read more about the grading system.
Explanations and appeals
Resit an examination
Information about deferred and new examination (also called repeat examination) is found here (only in Norwegian) .
Other
Course evaluation
Feedback from our students is an essential to us in our efforts to ensure and further improve the high quality of our programmes and courses. As a student at the University of Oslo you will therefore be asked to participate in various types of evaluation of our courses, facilities and services. All study programmes and courses are subject to continuous evaluation. At regular intervals we also ask students enrolled in a particular programme or course to participate in a more comprehensive, in-depth evaluation of their programme or course. The next evaluation of this course will be carried out during the autumn term of 2005.