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

$\overrightarrow{\zeta }=2\overrightarrow{\omega }=\overrightarrow{\mathrm{\nabla }}\times \overrightarrow{V}$

Inviscid Flow

Irrotational Flow

$\underset{{\omega }_x}{\underbrace{\frac{1}{2}(\frac{\partial w}{\partial y}-\frac{\partial v}{\partial z})}}+\underset{{\omega }_y}{\underbrace{\frac{1}{2}(\frac{\partial u}{\partial z}-\frac{\partial w}{\partial x})}}+\underset{{\omega }_z}{\underbrace{\frac{1}{2}(\frac{\partial v}{\partial x}-\frac{\partial u}{\partial y})}}$