[
] : fluid density
[
] : dynamic viscosity
[
] : kinematic viscosity
[
] : velocity
: volume
Conservation of mass
- For a system:
- For a C.V. (Reynolds transport theorem):\]
Differential form (\delta x\delta y\delta z):
Conservation of momentum
- For a system:
- For a C.V.:
Differential form ( ,
)
Normal stress ():
Shearing stress ():
General Equations (momentum & mass)
Navier-Stokes Equation
Newtonian fluids: linear relationship between stresses & rates of deformation.
Incompressible fluid:
- Normal stresses:
- Shearing stresses (simmetry):
General equation
Vector notation
3 equations (momentum) + continuity
,
,
,
,