Divergent flow 0, defined

As a complication some sources define a flow index as the reciprocal of that defined above so that some care has to be taken in interpretation. In such cases the values are greater than unity for polymer melts and the greater the value the greater the divergence from Newtonian behaviour.)... 

F = (H+ cosor) (wVe/g) + (Pe-P0)Ae where oc = half of the divergence angle of the nozzle, w - weight rate of proplnt flow, g = acceleration of gravity, Ve = exit flow velocity, Pe = nozzle exit pressure, PQ = external atm pressure, and Ae = cross section at nozzle exit plane. An effective exhaust velocity is defined by... 

The situation is different for incompressible flow. In that case, no equation of motion for the pressure field exists and via the mass conservation equation Eq. (17) a dynamic constraint on the velocity field is defined. The pressure field entering the incompressible Navier-Stokes equation can be regarded as a parameter field to be adjusted such that the divergence of the velocity field vanishes. 

For an incompressible liquid (i.e. a liquid with an invariant density which implies that the mass balance at any point leads to div v = 0) the time dependency of the concentration is given by the divergence of the flux, as defined by equation (13). Mathematically, the divergence of the gradient is the Laplacian operator V2, also frequently denoted as A. Thus, for a case of diffusion and flow, equation (10) becomes ... 

In other words, in a solenoidal Beltrami field the vector lines are situated in the surfaces c = constant. This theorem was originally derived by Ballabh [4] for a Beltrami flow proper of an incompressible medium. For the sake of completeness, we mention that the combination of the three conditions (1), (2), and (3) only leads to a Laplacian field, that is better defined by a vector field that is both solenoidal (divergence-less) and lamellar (curlless). 

When the wind blows past an obstacle, the streamlines of air flow diverge to pass round it. Particles carried in the wind tend to carry straight on and may impact on the obstacle. The efficiency of impaction C, is defined as the ratio of the number of impacts to the number of particles which would have passed through the space occupied by the obstacle if it had not been there. If vg is the velocity of deposition relative to the profile area of the obstacle, then C = vglux where ux is the free stream air velocity. C, is thus analogous to Cd, the drag coefficient of the obstacle. 

In order to obtain Green s identities for the flow field (u,p), a vector z is defined as the dot product of the stress tensor a(u, p) and a second solenoidal vector field v (divergence-free). The divergence or Gauss Theorem (10.1.1) is applied to the vector z... 

Two traditional approaches to the closure of the Reynolds equation are outlined below. These approaches are based on Boussinesq s model of turbulent viscosity completed by Prandtl s or von Karman s hypotheses [276, 427]. For simplicity, we confine our consideration to the case of simple shear flow, where the transverse coordinate Y = Xi is measured from the wall (the results are also applicable to turbulent boundary layers). According to Boussinesq s model, the only nonzero component of the Reynolds turbulent shear stress tensor and the divergence of this tensor are defined as... 

Now taking the exit area at the section B-B rather than C-C seems physically more intuitive for all the nozzles, since B-B represents the limit of physical constraint on the flow. Therefore we shall define a new term, the physical divergence ratio , as ... 

The new phase transition (a critical point) is to be characterized by its own set of exponents. An important quantity is the length scale behaviour. The flow equation around the fixed point for d > 2 shows that one may define a diverging length-scale associated with the critical point as... 

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