Fluid Mechanics - Vol 1 | 15. Conservation of Mass by Abraham | Learn Smarter
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15. Conservation of Mass

The chapter focuses on the conservation of mass in fluid mechanics, utilizing the Reynolds transport theorem to derive the conservation equations for mass, momentum, and energy. It categorizes different types of control volumes—fixed, moving, and deformable—while emphasizing the significance of mass conservation in solving fluid flow problems. Real-world applications, particularly the trajectory design for missions like the Mars Orbiter Mission, are illustrated to stress the importance of fluid mechanics in engineering.

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Sections

  • 15

    Fluid Mechanics

    This section introduces the concept of mass conservation in fluid mechanics, detailing the Reynolds transport theorem and types of control volumes.

    Learning Practice

  • 15.1.1

    Conservation Of Mass

    Learning

  • 15.2

    Control Volume And Reynolds Transport Theorem

    This section focuses on the concepts of control volumes and the Reynolds transport theorem, essential for understanding the conservation of mass in fluid mechanics.

    Learning Practice

  • 15.2.1

    Types Of Control Volumes

    This section explores the three types of control volumes in fluid mechanics: fixed, moving, and deformable control volumes.

    Learning Practice

  • 15.2.2

    Derivation Of Conservation Of Mass

    This section covers the derivation of the conservation of mass in fluid mechanics using the Reynolds transport theorem.

    Learning Practice

  • 15.2.3

    Applications Of Fluid Mechanics

    This section discusses the applications of fluid mechanics, illustrating its significance in various real-world scenarios including space missions.

    Learning Practice

  • 3

    Reynolds Transport Theorem

    The Reynolds Transport Theorem relates the conservation of mass within a fluid system to that of a control volume, forming the foundation for fluid flow analysis.

    Learning Practice

  • 15.3.1

    System Level Equations

    This section introduces the concept of system level equations in fluid mechanics, focusing on the conservation of mass and its derivation from the Reynolds transport theorem.

    Learning Practice

  • 15.3.2

    Control Volume Level Equations

    This section discusses control volume and mass conservation equations critical to fluid mechanics.

    Learning Practice

  • 15.3.3

    Assumptions For Fluid Flow Problems

    This section discusses key assumptions in fluid flow problems, particularly steady and incompressible flows.

    Learning Practice

  • 15.4

    Simplifications In Fluid Flow Problems

    This section discusses the conservation of mass in fluid mechanics, particularly how simplifying assumptions can help derive mass conservation equations in fluid flow problems.

    Learning Practice

  • 15.4.1

    Steady And Compressible Flow

    This section covers the principles of conservation of mass in fluid mechanics, focusing on steady and compressible flow dynamics.

    Learning Practice

  • 15.4.2

    Moving Control Volume

    This section covers the concept of moving control volumes in fluid mechanics, detailing their significance in deriving the equation of mass conservation and how they differ from fixed and deformable control volumes.

    Learning Practice

  • 15.4.3

    Uniformly Moving Control Volume

    This section explores the concept of uniformly moving control volumes in fluid mechanics, focusing on the conservation of mass and its derivations.

    Learning Practice

  • 15.4.4

    Deformable Control Volume

    This section introduces deformable control volumes in fluid mechanics and their significance in deriving the conservation of mass equation.

    Learning Practice

  • 15.5

    Conservation Principles In Fluid Mechanics

    This section provides an overview of mass conservation principles in fluid mechanics, particularly through the use of Reynolds transport theorem.

    Learning Practice

  • 15.5.1

    Conservation Of Mass

    This section discusses the concept of the conservation of mass in fluid mechanics, primarily utilizing the Reynolds transport theorem.

    Learning Practice

  • 15.5.2

    Conservation Of Linear Momentum

    This section introduces the principle of conservation of linear momentum, exploring its relationship with fluid mechanics and its application through the Reynolds transport theorem.

    Learning Practice

  • 15.5.3

    Conservation Of Energy

    The section discusses the principles and applications of mass conservation in fluid mechanics, emphasizing its significance through the Reynolds transport theorem.

    Learning Practice

  • 15.5.4

    Steady Flow Mass Conservation Equation

    This section discusses the derivation of the mass conservation equation in fluid mechanics, emphasizing the Reynolds transport theorem and its applications in various control volumes.

    Learning Practice

References

ch8 part a.pdf

Class Notes

Memorization

What we have learnt

  • The Reynolds transport theo...
  • There are three types of co...
  • The conservation of mass is...

Final Test

Revision Tests