Fluid Mechanics/Differential Analysis of Fluid Flow

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

Vorticity

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

Inviscid Flow

Irrotational Flow

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