Hydraulic Engineering - Vol 3 | 21. Velocity Potential Derivation by Abraham | Learn Smarter
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Knowledge
21. Velocity Potential Derivation

The chapter delves into the derivation and understanding of the velocity potential for wave propagation in water bodies under specific conditions. Key equations such as the Laplace equation and Bernoulli’s equation are employed to analyze dynamic boundary conditions and obtain expressions for wave behavior. The dispersion relationship is established, detailing the relationship between wavelength, period, and water depth, emphasizing its significance in wave mechanics.

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Sections

  • 1

    Velocity Potential Derivation

    This section explains the derivation of the velocity potential for water waves, utilizing key equations and boundary conditions.

    Learning Practice

  • 1.1

    Dynamic Boundary Conditions

    This section discusses dynamic boundary conditions in wave mechanics, focusing on governing equations and their implications for velocity potential in water waves.

    Learning Practice

  • 1.2

    Kinematic Bottom Boundary Condition

    This section covers the derivation and application of kinematic and dynamic boundary conditions in determining velocity potentials for waves in a constant water depth.

    Learning Practice

  • 1.3

    Formation Of Velocity Potential

    This section discusses the formation of velocity potential in fluid dynamics, emphasizing the derivation and the significance of governing equations.

    Learning Practice

  • 1.4

    Amplitude Of The Wave And Wave Propagation

    This section covers the concepts of wave amplitude, wave propagation, and the governing equations involved in calculating wave characteristics such as velocity potential.

    Learning Practice

  • 1.5

    Final Velocity Potential Formula

    This section discusses the derivation and significance of the final velocity potential formula in fluid mechanics, particularly pertaining to wave propagation in constant water depth.

    Learning Practice

  • 1.6

    Celerity Calculation

    This section covers the derivation of wave celerity and its relationship with wave properties like wavelength and period in a constant water depth.

    Learning Practice

  • 2

    Dispersion Relationship

    This section covers the dispersion relationship, the governing equations for wave mechanics, and the velocity potential derived from small amplitude wave assumptions.

    Learning Practice

  • 2.1

    Small Amplitude Wave Assumption

    This section covers the principles of small amplitude wave assumptions, including the derivation of governing equations for wave motion and the resulting velocity potential expressions.

    Learning Practice

  • 2.2

    Differentiation Of Wave Parameters

    This section discusses the derivation of wave parameters, focusing on the velocity potential and dispersion relationships in wave mechanics.

    Learning Practice

  • 2.3

    Equating Velocity Potential Terms

    This section delves into calculating the velocity potential terms for water waves, their derivation, and the celerity of waves.

    Learning Practice

  • 2.4

    Famous Dispersion Relationship

    This section discusses the derivation of the famous dispersion relationship for waves, highlighting its significance in understanding wave mechanics related to wavelength, period, and water depth.

    Learning Practice

  • 2.5

    Trial And Error Method For Solving Dispersion Equation

    This section covers the trial and error method for solving the dispersion equation in wave mechanics, detailing the significance of velocity potential and wave celerity.

    Learning Practice

  • 3

    Summary And Next Steps

    This section summarizes the derivation of the velocity potential for propagating waves in a fluid environment and introduces key concepts such as wave celerity and dispersion relationships.

    Learning Practice

References

61b.pdf

Class Notes

Memorization

What we have learnt

  • The total velocity potentia...
  • The celerity of the wave re...
  • The dispersion relationship...

Final Test

Revision Tests