Fluid Mechanics - Vol 3 | 4. Continuity Equations by Abraham | Learn Smarter
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4. Continuity Equations

4. Continuity Equations

This chapter focuses on the mass conservation equation, exploring its derivation through the analysis of infinitely small control volumes. It emphasizes the application of Taylor series expansions in understanding velocity and density fields and discusses the continuity equations in both Cartesian and cylindrical coordinates. Additionally, it differentiates between compressible and incompressible flows, providing insights into practical applications such as internal combustion engines.

16 sections

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Sections

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  1. 4
    Fluid Mechanics

    This section discusses the Mass Conservation Equation in fluid mechanics,...

  2. 4.1.1
    Continuity Equations

    This section explores the concept of continuity equations, specifically the...

  3. 4.1.2
    Mass Conservation Equation - Ii

    This section delves into the mass conservation equations, focusing on...

  4. 4.1.3
    Understanding Control Volumes

    This section discusses the concept of control volumes in fluid mechanics,...

  5. 4.1.4
    Taylor Series Applications

    This section discusses the application of Taylor series in deriving the mass...

  6. 4.1.5
    Mass Flux Components

    This section discusses the mass conservation equation for fluid mechanics,...

  7. 4.1.6
    Steady Compressible Flow

    This section focuses on the principles of mass conservation in steady...

  8. 4.1.7
    Cylindrical Coordinate Systems

    This section discusses the mass conservation equations in cylindrical...

  9. 4.1.8
    Case Studies And Problems

    This section focuses on mass conservation in fluid mechanics, exploring the...

  10. 4.2
    Mass Conservation In Control Volumes

    This section explains the mass conservation equations within control...

  11. 4.2.1
    Rate Of Change Of Mass

    This section discusses the mass conservation equations related to fluid...

  12. 4.2.2
    Outflow And Inflow Of Mass

    This section explores the principles of mass conservation in fluid dynamics,...

  13. 4.2.3
    Divergence Of Velocity

    This section discusses the concept of mass conservation in fluid mechanics,...

  14. 4.3
    Incompressible Vs. Compressible Flow

    This section examines the differences between incompressible and...

  15. 4.3.1
    Velocity Divergence In Incompressible Flow

    This section explores the concept of velocity divergence in the context of...

  16. 4.3.2
    Implications Of Mass Conservation

    This section discusses the implications of mass conservation in fluid...

What we have learnt

  • Mass conservation is articulated through the continuity equation, highlighting the balancing of mass influx and outflux.
  • The importance of applying Taylor series for approximating functions related to velocity and mass flux in small control volumes.
  • The difference in behavior between steady compressible and incompressible flows regarding mass storage and flow disturbances.

Key Concepts

-- Continuity Equation
A fundamental equation in fluid mechanics that expresses the principle of mass conservation in fluid flow.
-- Taylor Series Expansion
A mathematical series that approximates functions by polynomials, allowing for the analysis of fluid properties at small scales.
-- Compressible Flow
A type of fluid flow where density changes are significant in response to pressure variations.
-- Incompressible Flow
Flow where density remains constant, leading to simplifications in analysis and calculations.
-- Divergence
A vector operation that represents the magnitude of a source or sink at a given point in a flowing fluid field.

Additional Learning Materials

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