Momentum Equation / Navier Stokes

Question 1

What is the physical principal of the momentum equation?

Answer 1

Newton’s 2nd Law

Question 2

Why are there 3 equations?

Answer 2

Momentum and force are both vector quantities. Therefore we need 3 equations for 3 space directions

Question 3

Define body forces

Answer 3

These act on the volumetric mass. Gravitation, magnetic etc etc

Question 4

Define surface forces

Answer 4

These act directly on control volume surface.
Two categories: Pressure force (due to presence of surrounding fluid, always act inwards) and surface force (shear and normal)

Question 5

Shear and normal forces act through…

Answer 5

diffusion

Question 6

What is the first subscript on stress terms?

Answer 6

Face on which force is acting

Question 7

What is the second subscript on stress terms?

Answer 7

Direction in which stress is acting

Question 8

When is normal stress negative and positive?

Answer 8

Negative when in compression and positive in tension

Question 9

When is shear stress negative and positive?

Answer 9

Positive if in negative direction on negative faces

and if in positive direction.

Question 10

State convective terms in x and y direction

Answer 10

d/dx(rho.u.u) = x dir
d/dy(rho.u.v) = y dir

Question 11

State accumulation rate

Answer 11

d/dt(rho.u)

Question 12

State surface forces

Answer 12

-dp/dx + d/dx.sigma.xx + d/dy.tau.yx

Question 13

State body force

Answer 13

rho.f.x

Question 14

Define constitutive equations

Answer 14

Information associated with relationships between stresses and shear and the corresponding deformations of element fluid

Question 15

State the stress-rate of strain relationship for normal force in x direction

Answer 15

Lamba (del x u) +2.mu.du/dx

Question 16

State the stress-rate of strain relationship for normal force in y direction

Answer 16

Lamba (del x u) + 2.mu.dv/dy

Question 17

State the stress-rate of strain relationship for shear force

Answer 17

mu(du/dy + dv/dx)

Question 18

Define mu and lamba

Answer 18

Mu = dynamic viscosity
Lamba = second viscosity (=-2/3mu)

Question 19

Define del x u

Answer 19

The volumetric expansion or contraction

Question 20

State transient terms for Navier Stokes

Answer 20

du/dt

Question 21

State convective terms for Navier Stokes

Answer 21

u.du/dx +v.du/dy (convection of u in y direction) INCOMPRESSIBLE

Question 22

State source terms for Navier Stokes

Answer 22

-1/rho . dp/dx + fx

Question 23

State diffusive terms for Navier Stokes

Answer 23

mu/rho {d^2u/dx^2} (diffusion of u in x-direction due to normal stress)
mu/rho{d^2u/dy^2} (diffusion of u in y direction due to shear stress)

Question 24

What are the assumptions for the Navier Stokes equations

Answer 24

Constant viscosity