Lecture

Linear Momentum Conservation and Stress in Continuum

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture covers the conservation of linear momentum and stress in a continuum, discussing topics such as mass conservation, momentum conservation, stress tensor evaluation, constitutive laws for Newtonian fluids and Hookean solids, and the geometry of body motion. The instructor explains the governing equations, constitutive laws, continuum mechanics, and the tools needed for problem-solving, emphasizing the importance of material derivatives, convective derivatives, and the use of tensor calculus.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Official source

Ontological neighbourhood

Physics

Mechanics: Fluid mechanics, Classical mechanics

Chemical engineering

Materials science: Deformation of materials

Related concepts (32)

Fluid mechanics

Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology. It can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion.

Newtonian fluid

A Newtonian fluid is a fluid in which the viscous stresses arising from its flow are at every point linearly correlated to the local strain rate — the rate of change of its deformation over time. Stresses are proportional to the rate of change of the fluid's velocity vector. A fluid is Newtonian only if the tensors that describe the viscous stress and the strain rate are related by a constant viscosity tensor that does not depend on the stress state and velocity of the flow.

Spacetime

In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects such as how different observers perceive where and when events occur. Until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe (its description in terms of locations, shapes, distances, and directions) was distinct from time (the measurement of when events occur within the universe).

Material derivative

In continuum mechanics, the material derivative describes the time rate of change of some physical quantity (like heat or momentum) of a material element that is subjected to a space-and-time-dependent macroscopic velocity field. The material derivative can serve as a link between Eulerian and Lagrangian descriptions of continuum deformation. For example, in fluid dynamics, the velocity field is the flow velocity, and the quantity of interest might be the temperature of the fluid.

Navier–Stokes equations

The Navier–Stokes equations (nævˈjeː_stəʊks ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842-1850 (Stokes). The Navier–Stokes equations mathematically express momentum balance and conservation of mass for Newtonian fluids.

Related lectures (64)

Fluid Mechanics: Control Volume Approach

Introduces powerful tools for analyzing fluid mechanics problems, emphasizing mass conservation, Newton's second law, and the continuity equation.

Continuum Mechanics: Newton's Laws and Stress Tensor Symmetry

Discusses Newton's third law, stress tensor symmetry, and the governing equations in continuum mechanics.

Lorentz Covariant Formulation: Maxwell Equations

Covers Lorentz transformations, Maxwell equations, and charge conservation in Lorentz invariant physics.

Introduction to Continuum Mechanics

Covers the basics of continuum mechanics, including vector and tensor analysis, kinematics, and fluid mechanics.

Flow Characteristics and Equations