In which, [??] represents the velocity vector, p the pressure, [rho] the liquid density, [??] the shear stress tensor, [??] the gravitational acceleration, and [[??].sub.b] any body force
(per unit volume) acting on the fluid.
The styrenic material studied here was also modeled previously using a one-dimensional formulation with only the body force
(1) [delta]u is displacement vector increment, t is time, [[rho].sub.t] is the mass density, [V.sub.t] is the volume bounded by the surface [a.sub.t], with the surface vector [a.sub.t] pointing outwards, [delta]S is the second Piola-Kirchhoff stress tensor increment, [sigma] is the Cauchy stress tensor at the beginning of the increment, [delta]F = grad [delta]u is the deformation gradient tensor increment and [delta][f.sub.b] is the resulting body force
(weight) is taken in the downward (-y) direction, and the term [q.sub.x] is zero.
where [Mathematical Expression Omitted] is the stress tensor and [Mathematical Expression Omitted] is the body force
. For isotropic linear elastic materials, the components of [Mathematical Expression Omitted] in Cartesian coordinates (13) are
Sgt Gerrard said: "We managed to force him to the ground by sheer body force
, but we still couldn't cuff him because he was too strong.
where [Mathematical Expression Omitted], [Mathematical Expression Omitted] are the body force
vector per unit mass and the acceleration vector, respectively.
ISLAMABAD -- The civic body force
behind encroachment operations breathed his last in the line of duty on Monday.
The smoothing length is h = [10.sup.-4] m, the distance between the walls is L = [10.sup.-3] m, the body force
is g = [10.sup.-3] m/[s.sup.2], and the imposed velocity is V = 2 x [10.sup.-4] m/s.
There are wide-ranging opportunities to optimize the tangential velocity -which would impact the magnitude of the body force
that inhibits mixing - by revising the geometry, and fuel injection strategy to avoid the very rich zone in the center; however, this is beyond the scope of the current work.
There are three forces acting on suspended particle such as buoyancy force, drag force and body force
. Their balance makes the nanoparticle stable.
where [F.sub.D] is the drag force, [F.sub.P] is the pressure gradient force, [F.sub.g] is the gravity force, and [F.sub.u] is the user-defined body force