Fluid Mechanics

The section covers the Navier-Stokes equations, their derivations, significance in fluid dynamics, and the distinctions between Newtonian and non-Newtonian fluids.

Lec 28: The Navier-Stokes Equation

This section covers the foundational concepts of the Navier-Stokes equations, their derivation, and their significance in fluid mechanics.

Introduction To Navier-Stokes Equations

This section introduces the Navier-Stokes equations, foundational in fluid dynamics, detailing their derivation and significance.

Newtonian And Non-Newtonian Fluids

This section introduces the concepts of Newtonian and Non-Newtonian fluids, emphasizing their differences and respective behaviors under shear stress.

Derivations Of Navier-Stokes Equations

This section discusses the derivation of the Navier-Stokes equations, key equations in fluid mechanics, and their significance in solving complex fluid flow problems.

Deriving Cauchy Equations

This section introduces the derivation of Cauchy's equations, which are essential for understanding fluid dynamics, particularly in the context of the Navier-Stokes equations.

Linear Momentum Equations

The section introduces the foundations of linear momentum equations within fluid mechanics, particularly focusing on the Navier-Stokes equations.

Divergence Of Velocity

This section discusses the significance of divergence of velocity in fluid dynamics, specifically relating to the Navier-Stokes equations and their derivations.

Vector Notations And Dimensions

This section discusses vector notations and dimensional analysis in fluid mechanics, focusing on the Navier-Stokes equations and their derivations.

Control Volumes And Forces

This section discusses the fundamental principles of control volumes and their associated forces, leading into the derivation of the Navier-Stokes equations from the laws of fluid motion.

Application Of Newton's Laws

This section discusses the application of Newton's laws in fluid mechanics, specifically through the derivation and significance of the Navier-Stokes equations.

Deriving Momentum Equations

This section explores the derivation of momentum equations, focusing on the Navier-Stokes equations and their application in fluid dynamics.

Navier-Stokes Equations

This section explores the Navier-Stokes equations, fundamental to fluid mechanics, emphasizing their derivation and significance in computational fluid dynamics.

Properties Of Stress Tensor

This section discusses the properties of the stress tensor in fluid mechanics, elaborating on its components and how they relate to fluid dynamics.

Assumptions For Deriving Equations

This section discusses the foundational assumptions necessary for deriving the Navier-Stokes equations in fluid mechanics.

Respective Forces In Fluid Flow

This section explores the Navier-Stokes equations, foundational to understanding fluid dynamics, by discussing forces acting in fluid flow including body forces and surface forces.

Approximate Solutions To Navier-Stokes Equations

This section discusses the approximate solutions to the Navier-Stokes equations, highlighting their relevance in computational fluid dynamics and the challenges in finding exact solutions.

Incompressible Flow

This section discusses the fundamentals of incompressible flow, with a focus on the derivation and applications of the Navier-Stokes equations.

Isothermal Flow

Isothermal flow refers to fluid movement where the temperature remains constant throughout the fluid domain, particularly under incompressible conditions.

Cylindrical Coordinates

This section covers cylindrical coordinates, essential for applying the Navier-Stokes equations in fluid mechanics.

Navier-Stokes In Cylindrical Coordinates

This section introduces the Navier-Stokes equations in cylindrical coordinates, exploring their significance in fluid mechanics and the assumptions underlying their derivation.