Fluid Mechanics - Vol 3 | 7. The Navier-Stokes Equation by Abraham | Learn Smarter
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7. The Navier-Stokes Equation

7. The Navier-Stokes Equation

The chapter discusses the Navier-Stokes equations, which are fundamental in computational fluid dynamics, addressing complex fluid flow problems. It covers the derivation of these equations, emphasizing their application in incompressible isothermal flows using Cartesian and cylindrical coordinate systems. The discussion also extends to the assumptions behind Newtonian and non-Newtonian fluids, as well as their implications in fluid mechanics.

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Sections

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  1. 7
    Fluid Mechanics

    The section covers the Navier-Stokes equations, their derivations,...

  2. 7.1.1
    Lec 28: The Navier-Stokes Equation

    This section covers the foundational concepts of the Navier-Stokes...

  3. 7.1.2
    Introduction To Navier-Stokes Equations

    This section introduces the Navier-Stokes equations, foundational in fluid...

  4. 7.1.3
    Newtonian And Non-Newtonian Fluids

    This section introduces the concepts of Newtonian and Non-Newtonian fluids,...

  5. 7.1.4
    Derivations Of Navier-Stokes Equations

    This section discusses the derivation of the Navier-Stokes equations, key...

  6. 7.2
    Deriving Cauchy Equations

    This section introduces the derivation of Cauchy's equations, which are...

  7. 7.2.1
    Linear Momentum Equations

    The section introduces the foundations of linear momentum equations within...

  8. 7.2.2
    Divergence Of Velocity

    This section discusses the significance of divergence of velocity in fluid...

  9. 7.2.3
    Vector Notations And Dimensions

    This section discusses vector notations and dimensional analysis in fluid...

  10. 7.3
    Control Volumes And Forces

    This section discusses the fundamental principles of control volumes and...

  11. 7.3.1
    Application Of Newton's Laws

    This section discusses the application of Newton's laws in fluid mechanics,...

  12. 7.3.2
    Deriving Momentum Equations

    This section explores the derivation of momentum equations, focusing on the...

  13. 7.4
    Navier-Stokes Equations

    This section explores the Navier-Stokes equations, fundamental to fluid...

  14. 7.4.1
    Properties Of Stress Tensor

    This section discusses the properties of the stress tensor in fluid...

  15. 7.4.2
    Assumptions For Deriving Equations

    This section discusses the foundational assumptions necessary for deriving...

  16. 7.4.3
    Respective Forces In Fluid Flow

    This section explores the Navier-Stokes equations, foundational to...

  17. 7.5
    Approximate Solutions To Navier-Stokes Equations

    This section discusses the approximate solutions to the Navier-Stokes...

  18. 7.5.1
    Incompressible Flow

    This section discusses the fundamentals of incompressible flow, with a focus...

  19. 7.5.2
    Isothermal Flow

    Isothermal flow refers to fluid movement where the temperature remains...

  20. 7.6
    Cylindrical Coordinates

    This section covers cylindrical coordinates, essential for applying the...

  21. 7.6.1
    Navier-Stokes In Cylindrical Coordinates

    This section introduces the Navier-Stokes equations in cylindrical...

What we have learnt

  • The Navier-Stokes equations are derived from the principles of momentum conservation and density continuity.
  • The equations describe how the velocity, pressure, and density of fluid flow interact under various conditions.
  • Understanding Newtonian and non-Newtonian fluids is essential in applying the Navier-Stokes equations effectively in real-world scenarios.

Key Concepts

-- NavierStokes Equations
A set of non-linear partial differential equations that describe the motion of fluid substances.
-- Newtonian Fluid
A fluid that exhibits a linear relationship between shear stress and shear strain rate.
-- Incompressible Flow
A flow in which the fluid density remains constant throughout the fluid domain.
-- Isothermal Flow
A flow in which the temperature of the fluid remains constant within its domain.
-- Boundary Conditions
The conditions specified at the boundaries of the fluid flow region that allow for the determination of the flow field.

Additional Learning Materials

Supplementary resources to enhance your learning experience.