Fluid Mechanics/Differential Analysis of Fluid Flow

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Sections Such as: This Chapter covers:

  • kinematic elements of flow
  • application of the concepts of stream function
  • charachterize simple flow fields
  • Analysis of Navier-Stokes equation.


Fluid Element Kinematics[edit]

Vorticity

\vec{\zeta} = 2 \vec{\omega} {{=}} {\vec{\nabla} \times \vec{V} }

Conservation of Mass[edit]

Inviscid Flow[edit]

Irrotational Flow[edit]

\underbrace{\frac{1}{2} ({\partial w \over \partial y }- {\partial v \over \partial z})}_{\omega_x}+
\underbrace{\frac{1}{2} ({\partial u \over \partial z }- {\partial w \over \partial x})}_{\omega_y}+
\underbrace{\frac{1}{2} ({\partial v \over \partial x }- {\partial u \over \partial y})}_{\omega_z}

Navier-Stokes Equations[edit]