Fluid Mechanics - Vol 1 | 19. Surface Forces and Stress Tensors by Abraham | Learn Smarter
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19. Surface Forces and Stress Tensors

The chapter focuses on the significance of stress tensors in the analysis of surface forces, particularly in fluid mechanics. It covers the definition and composition of stress tensors, differentiating between normal and shear stresses, and emphasizes the importance of understanding control volumes in analyzing fluid forces. Important concepts such as pressure components and momentum flux are introduced, along with applications to practical fluid mechanics problems.

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Sections

  • 19

    Surface Forces And Stress Tensors

    This section discusses the concepts of surface forces and stress tensors in fluid and solid mechanics as a method of describing forces acting on a control volume.

    Learning Practice

  • 19.1.1

    Definition Of Stress Tensor

    This section introduces the concept of the stress tensor, discussing its significance in representing surface forces in fluid mechanics and solid mechanics.

    Learning Practice

  • 19.1.2

    Components Of The Stress Tensor

    The section elaborates on the components of the stress tensor in fluid mechanics, emphasizing the importance of understanding stress distribution in both solid and fluid mechanics.

    Learning Practice

  • 19.1.3

    Surface Force Acting On A Differential Surface Element

    This section covers the concept of surface forces represented by stress tensors in fluid and solid mechanics, detailing components of stress and their significance in control volume analysis.

    Learning Practice

  • 19.1.4

    Total Surface Force Acting On Control Surface

    This section discusses the total surface forces acting on a control surface, defining them within the framework of stress tensors in fluid mechanics.

    Learning Practice

  • 19.1.5

    Total Force Acting On Control Volume

    This section discusses the calculation and significance of total forces acting on control volumes, including body forces and surface forces, with a focus on stress tensors and their components.

    Learning Practice

  • 19.2

    Simplification Of Force Components

    This section discusses the simplification of surface forces using stress tensors and the process of integrating these forces for fluid mechanics applications.

    Learning Practice

  • 19.2.1

    Linear Momentum Equations

    This section discusses the concept of linear momentum within the context of fluid mechanics, specifically through stress tensors and control volumes.

    Learning Practice

  • 19.3

    Applying Linear Momentum Equations

    This section explains the application of linear momentum equations through the use of stress tensors and control volumes in fluid mechanics.

    Learning Practice

  • 19.3.1

    Considering Gauge Pressure

    This section introduces the concept of gauge pressure, discussing its relation to absolute pressure and how atmospheric pressure is managed in fluid mechanics.

    Learning Practice

  • 19.3.2

    Choosing Control Volume

    This section discusses the concepts of control volumes, particularly in relation to fluid mechanics, and outlines the role of stress tensors, body forces, and the importance of choosing an appropriate control volume.

    Learning Practice

  • 19.4

    Reynolds Transport Theorem

    The Reynolds Transport Theorem (RTT) relates differential changes in fluid motion to the overall motion of a control volume, emphasizing the importance of surface and body forces.

    Learning Practice

  • 19.4.1

    Momentum Equations And Control Volumes

    This section discusses the momentum equations related to control volumes in fluid mechanics, focusing on stress tensors, surface forces, and the concepts of body forces.

    Learning Practice

  • 19.4.2

    Special Cases In Momentum Flux

    This section explores the intricacies of momentum flux, focusing on surface forces defined by stress tensors and the simplification of control volumes in fluid mechanics.

    Learning Practice

  • 19.5

    Momentum Flux Correction Factor

    This section discusses the concept of momentum flux correction factors within fluid mechanics, focusing on the significance of stress tensors in understanding surface forces.

    Learning Practice

  • 19.5.1

    Use Of Correction Factors In Real Fluid Flow

    This section discusses the application of correction factors in fluid mechanics to accurately compute momentum flux due to non-uniform velocity distributions.

    Learning Practice

  • 19.6

    Conclusion Of The Lecture

    The conclusion summarizes key concepts related to surface forces and stress tensors, emphasizing their critical role in fluid mechanics.

    Learning Practice

  • 19.6.1

    Summary Of Key Points

    This section explores the concept of stress tensors and their importance in defining surface forces in fluid and solid mechanics.

    Learning Practice

  • 19.6.2

    Preparation For Next Class

    This section explores the concept of stress tensors and their role in defining surface forces in fluid mechanics and solid mechanics.

    Learning Practice

References

ch9 part b.pdf

Class Notes

Memorization

What we have learnt

  • Stress tensors describe sur...
  • Normal and shear stresses a...
  • Control volumes are critica...

Final Test

Revision Tests