Equations of change

Question 1

Equation of continuity

Answer 1

∂ρ/∂t = -(∇ * ρ * v) : Describes the rate of change of the fluid density at a fixed point in space

Question 2

Equation of continuity for fluid with constant density

Answer 2

(∇ * v)=0 : This is the instance for an incompressible fluid

Question 3

Equation of motion

Answer 3

∂(ρv)/∂t = -[∇ * ρvv] - ∇ p- [∇ * τ] + ρg : Describes the rate of change in combined in spacemomentum

Question 4

Difference between convective and molecular momentum

Answer 4

Convective: Heat / Mass transfer or transport of fluid across porours membrane
Molecular transport: Movement of material across membrane

Question 5

Navier-Stokes equation

Answer 5

ρd(v)/dt = -∇ p + μ ∇^2 v + ρg : Simplification of equation of motion when μ and ρ are constant

Question 6

Stokes flow equation / Creeping flow

Answer 6

0 = -∇ p + μ ∇^2 v + ρ*g : Simplification of equation of motion (with low Reynolds value Re -> 0)