Momentum Equation / Navier Stokes Flashcards
What is the physical principal of the momentum equation?
Newton’s 2nd Law
Why are there 3 equations?
Momentum and force are both vector quantities. Therefore we need 3 equations for 3 space directions
Define body forces
These act on the volumetric mass. Gravitation, magnetic etc etc
Define surface forces
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)
Shear and normal forces act through…
diffusion
What is the first subscript on stress terms?
Face on which force is acting
What is the second subscript on stress terms?
Direction in which stress is acting
When is normal stress negative and positive?
Negative when in compression and positive in tension
When is shear stress negative and positive?
Positive if in negative direction on negative faces
and if in positive direction.
State convective terms in x and y direction
d/dx(rho.u.u) = x dir d/dy(rho.u.v) = y dir
State accumulation rate
d/dt(rho.u)
State surface forces
-dp/dx + d/dx.sigma.xx + d/dy.tau.yx
State body force
rho.f.x
Define constitutive equations
Information associated with relationships between stresses and shear and the corresponding deformations of element fluid
State the stress-rate of strain relationship for normal force in x direction
Lamba (del x u) +2.mu.du/dx
State the stress-rate of strain relationship for normal force in y direction
Lamba (del x u) + 2.mu.dv/dy
State the stress-rate of strain relationship for shear force
mu(du/dy + dv/dx)
Define mu and lamba
Mu = dynamic viscosity Lamba = second viscosity (=-2/3mu)
Define del x u
The volumetric expansion or contraction
State transient terms for Navier Stokes
du/dt
State convective terms for Navier Stokes
u.du/dx +v.du/dy (convection of u in y direction) INCOMPRESSIBLE
State source terms for Navier Stokes
-1/rho . dp/dx + fx
State diffusive terms for Navier Stokes
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)
What are the assumptions for the Navier Stokes equations
Constant viscosity
