Fluid Mechanics

01

Continuity

Conservation of mass requires the flow into and out of a control volume to balance appropriately.

∂ρ/∂t + ∇·(ρv) = 0

02

Bernoulli Principle

P + 1/2ρv² + ρgh = constant

The Bernoulli relation applies under restrictive assumptions, including steady, incompressible, inviscid flow along a streamline.

03

Navier-Stokes Equation

ρ(∂v/∂t + v·∇v) = -∇P + μ∇²v + ρg

The Navier-Stokes equations describe conservation of momentum for Newtonian fluids under the stated modeling assumptions.