Скачать или смотреть Define Navier Stokes Equation

The Navier-Stokes equation is a set of partial differential equations that describe the motion of viscous fluid substances like liquids and gases. It represents the principles of conservation of momentum, mass, and energy in fluid dynamics.

General Form:
For an incompressible and Newtonian fluid:

ρ( ∂v / ∂t +v⋅∇v )=−∇P+μ∇² v+f

Where:

ρ: Fluid density
v: Velocity vector
t: Time
P: Pressure
μ: Dynamic viscosity (measure of internal friction)
∇P: Pressure gradient
∇² v: Viscous term (Laplacian of velocity)
f: External body force (e.g., gravity)

⏩ Physical Meaning:

Momentum Conservation: Relates fluid acceleration to forces like pressure, viscosity, and external influences.
Viscous Effects: Includes the effects of internal friction within the fluid.

⏩ Applications:

Predicting weather patterns
Designing aircraft and vehicles
Modeling ocean currents
Engineering fluid flow systems