Velocity vector, component

The analysis of flow pattern models occurring inside the radial distribution of the velocity vector components and the pressure at swirl generator exit are nonuniform the same burner equipped with an annular vane swirl generator in the same furnace can produce different velocity vector components, when the quarl geometry is changed (dQ/di, = 2-3.5) the shape and size of CRZ are primarily a function of quarl geometry and not of vane swirler diameter. 

Figure 7.5 shows the geometry and boundary conditions for the laminar flow in porous media. The domain is a square box of dimensions 1x1, and the computational mesh contains 51 x 51 points. No slip condition is adopted for velocity vector components. The other conditions, not shown in Figure 7.5, are of the Neumann type. 

The distribution and mean values of speed, the magnitude of the velocity vector, are a useful characterization of gas behavior. Since speed, s, has no associated direction, a change of variables that separates the orientation (direction) of velocity from its magnitude is helpful. Hence, three coordinates, s, 0, and q>, are now defined in relation to velocity vector components, as shown in Figure 2.4. 

Velocity The term kinematics refers to the quantitative description of fluid motion or deformation. The rate of deformation depends on the distribution of velocity within the fluid. Fluid velocity v is a vector quantity, with three cartesian components i , and v.. The velocity vector is a function of spatial position and time. A steady flow is one in which the velocity is independent of time, while in unsteady flow v varies with time. 

The directing jet is supplied at a right angle to the mam stream axis with an initial velocity of I os from the nozzle with an inner diameter (d, -) located at the distance (Iq) from the plane of main stream supply and at the distance Yq from its geometrical axis. The momentum vector component along the Y axis remains constant and equal to the initial momentum (Fig. 7.57) ... 

If the magnitude and direction of a vector are known, its components are the products of the magnitude and the respective direction cosines. In the case of the velocity vector, for example, the components are... 

The velocity is always tangent to the path of motion, and thus the velocity vector has only one component (Equation 2-20). 

The acceleration vector has a component tangent to the path a = d v /d, which is the rate at which the magnitude of the velocity vector is changing, and a component perpendicular to the path a = v Vp, which represents the rate at which the direction of motion is changing (Equation 2-21). 

Velocity (vector v has components are directed along axis... 

For axial capillary flow in the z direction the Reynolds number, Re = vzmaxI/v = inertial force/viscous force , characterizes the flow in terms of the kinematic viscosity v the average axial velocity, vzmax, and capillary cross sectional length scale l by indicating the magnitude of the inertial terms on the left-hand side of Eq. (5.1.5). In capillary systems for Re < 2000, flow is laminar, only the axial component of the velocity vector is present and the velocity is rectilinear, i.e., depends only on the cross sectional coordinates not the axial position, v= [0,0, vz(x,y). In turbulent flow with Re > 2000 or flows which exhibit hydrodynamic instabilities, the non-linear inertial term generates complexity in the flow such that in a steady state v= [vx(x,y,z), vy(x,y,z), vz(x,y,z). ... 

Here, u, v, and w are the components of the velocity vector in the x, y, and z directions, respectively. Note that velocity is treated as a vector quantity, so that the vector sum ui + vj + wk (where i, j, and k are the unit vectors in the x, y, and z directions) represents both the direction and magnitude of the fluid velocity at a particular position and time. The symbol P represents fluid pressure, p is the fluid viscosity, p is the fluid density, and the F parameters are the components of a body force acting on the fluid in the x, y, and z directions. (A body force is a force that acts on the fluid as a result of its mass rather than its surface area gravity is the most common body force.)... 

Here vx and vy are the components of the velocity vector in the coordinate directions. Velocity v in an arbitrary direction is... 

Here, Rj is reaction rate (mol cm-3 s-1), the net rate at which chemical reactions add component i to solution, expressed per unit volume of water. As before, Q is the component s dissolved concentration (Eqns. 20.14—20.17), Dxx and so on are the entries in the dispersion tensor, and (vx, vy) is the groundwater velocity vector. For transport in a single direction, v, the equation simplifies to,... 

The first term on the right-hand side of (2.61) is the spectral transfer function, and involves two-point correlations between three components of the velocity vector (see McComb (1990) for the exact form). The spectral transfer function is thus unclosed, and models must be formulated in order to proceed in finding solutions to (2.61). However, some useful properties of T (k, t) can be deduced from the spectral transport equation. For example, integrating (2.61) over all wavenumbers yields the transport equation for the turbulent kinetic energy ... 

At an inflow boundary, the mean velocity vector will point into the flow domain. If we denote the component of the mean velocity normal to the inflow surface (Sin) by U n, then the total mass entering the system in time step At is34... 

Now with regard to stretch, consider first a plane oblique flame. Because of the increase in velocity demanded by continuity, a streamline through such an oblique flame is deflected toward the direction of the normal to the flame surface. The velocity vector may be broken up into a component normal to the flame wave and a component tangential to the wave (Fig. 4.44). Because of the energy release, the continuity of mass requires that the normal component... 

An example of this work is that of Farrell and co-workers [34], They present a rather complex model to attempt to account for the effects of fluid motion and turbulence in three different levels of scale, relative to the plume. They begin with classical equations of motion, but by breaking their particle velocity vector into three components related to the three scales of interest, they are able to introduce appropriate statistical descriptions for the components. The result is a model that retains both the diffusive and the filamentary nature of the plume. 

The electrophoretic separation principle is based on the velocity differences of charged solute species moving in an applied electric field. The direction and velocity of that movement are determined by the sum of two vector components, the migration and the electroosmotic flow (EOF). The solute velocity v is represented as the product of the electric field strength E and the sum of ionic mobility uUm and EOF coefficient /a OF ... 

From the definition of a particle used in this book, it follows that the motion of the surrounding continuous phase is inherently three-dimensional. An important class of particle flows possesses axial symmetry. For axisymmetric flows of incompressible fluids, we define a stream function, ij/, called Stokes s stream function. The value of Imj/ at any point is the volumetric flow rate of fluid crossing any continuous surface whose outer boundary is a circle centered on the axis of symmetry and passing through the point in question. Clearly ij/ = 0 on the axis of symmetry. Stream surfaces are surfaces of constant ij/ and are parallel to the velocity vector, u, at every point. The intersection of a stream surface with a plane containing the axis of symmetry may be referred to as a streamline. The velocity components, and Uq, are related to ij/ in spherical-polar coordinates by... 

---