Normal velocity component

Though the velocity component parallel to the shock wave remains unchanged, Vi = V2, the velocity component normal to the shock wave, Ui — M2, changes through the shock wave. The change in the normal velocity component through the oblique... 

The reflection of the electron should be expected in the case r Tu-when the maximum potential energy of the electron in the evanescent wave is higher than its kinetic energy associated with its normal motion toward the dielectric surface (i.e., Umax > E ). The maximum normal velocity component of the reflected electrons is given by... 

Knowing the flow field before the flame front, one can find the shape of its surface. For this, one should use the fact that the normal velocity component at the front must be equal to the normal flame velocity. In the simplest case, when the normal velocity of the flame is constant at all points of the surface, we obtain ... 

At the flame front the front-normal velocity component grows step-like due to variation of the gas density in accordance with the mass flow conservation law... 

H steady dimensionless function corresponding to the normal velocity component... 

Grootenhuis (Proc. Inst. Mech. Eng. [London], A168, 837—846 [1954]) presents data which indicate that for a series of screens, the total pressure drop equals the number of screens times the pressure drop for one screen, and is not affected by the spacing between screens or their orientation with respect to one another, and presents a correlation for frictional losses across plain square-mesh screens and sintered gauzes. Armour and Cannon (AIChE J., 14,415-420 [1968]) give a correlation based on a packed bed model for plain, twill, and dutch weaves. For losses through monofilament fabrics see Pedersen (Filtr. Sep., 11, 586-589 [1975]). For screens Inclined at an angle 0, use the normal velocity component V ... 

A gas flows between large parallel porous plates. The same gas is blown through one wall and exhausted through the other in such a way that the same normal velocity component, v exists at both walls. The plates are kept at uniform but different temperatures. Assuming folly developed, constant fluid-property flow, find equations for the velocity and temperature profiles. 

Specific type of free stream condition can be represented by finding the appropriate functions, B a, u ) and D a, cu) defining the tangential and normal velocity components. The additional subscript (oo) refers to the conditions being evaluated at the free stream y = Y). Now one can solve for the constants C to C4 by simultaneously solving (2.6.94) and (2.6.96) - (2.6.98). All these can also be written as the following linear algebraic equation,... 

The tangential and normal velocity components are, respectively, Vx and Vy. According to Marchiano and Arvia, the velocity components can be expressed as a function of dimensionless coordinate... 

Other types of flow lines also can be used. Oil-flow lines are pathlines that are constrained to a given boundary surface. When calculating the pathline, velocity components that are tangent to the given boundary surface are included and normal velocity components are ignored. This is useful for visualization... 

An inlet boundary is determined when the normal velocity component and the known scalar variables are specified. The turbulence quantities are generally estimated based on simple empirical relations. 

The rate of work, W, done by pressure forces occurs at the surface only, all work on internal portions of the material in the control volume is by equal and opposite forces and is self-canceling. The pressure work equals the pressure force on a small surface element, da, times the normal velocity component into the control volume ... 

At an axi-symmetric boundary Neuman conditions are used for all the fields, except for the normal velocity component which is zero because the flow direction turns at this point. The assumption of cylindrical axi-symmetry in the computations prevents lateral motion of the dispersed gas phase and leads to an unrealistic radial phase distribution [73, 66[. Krishna and van Baten [73] obtained better agreement with experiments when a 3D model was applied. However, experience showed that it is very difficult to obtain reasonable time averaged radial void profiles even in 3D simulations. 

The governing equations are elliptic so boundary conditions are required at all boundaries. The normal velocity components for both phases are set to zero at the vertical boundaries. The wall boundary conditions for the vertical velocity component, k and e are specified in accordance with the standard wall function approach. The particle phase is allowed to slip along the wall following the boundary condition given by (4.99). 

Boundary conditions t >0) The standard conditions for axi-symmetric flow in a 2D tube can be specified in the following manner. There is no flow through the reactor wall. The normal velocity component is set to zero at the symmetry boundary. Plug flow is assumed at the inlet. A prescribed pressure is specified at the reactor outlet. For the scalar variables Dirichlet boundary conditions are used at the inlet, whereas Neumann conditions are used at the other boundaries, as for the 2D dispersion model simulations. 

The constant C Jt = 3.68 according to (3.25). In the limiting case Pe — oo, particles follow the Ruid and deposit when a streamline passes within one radius of the surface. This effect is called direct interception. The efficiency is obtained by integrating (3.13b) for the normal velocity component over the front half of the cylinder surface ... 

The analysis of this section is typical of all lubrication problems. First, the equations of motion are solved to obtain a profile for the tangential velocity component, which is always locally similar in form to the profile for unidirectional flow between parallel plane boundaries, but with the streamwise pressure gradient unknown. The continuity equation is then integrated to obtain the normal velocity component, but this requires only one of the two boundary conditions for the normal velocity. The second condition then yields a DE (known as the Reynolds equation) that can be used to determine the pressure distribution. 

Although the solution (5 74) seems to be complete, the key fact is that the pressure gradient V.s//0) in the thin gap, and thus p(0 xs, 0, is unknown. In this sense, the solution (5-74) is fundamentally different from the unidirectional flows considered in Chap. 3, where p varied linearly with position along the flow direction and was thus known completely ifp was specified at the ends of the flow domain. The problem considered here is an example of the class of thin-film problems known as lubrication theory in which either h(xs) and us, or h(xs, 0) and uz are prescribed on the boundaries, and it is the pressure distribution in the thin-fluid layer that is the primary theoretical objective. The fact that the pressure remains unknown is, of course, not surprising as we have not yet made any use of the continuity equation (5-69) or of the boundary conditions at z = 0 and h for the normal velocity component ui° ... 

Finally, if we wished to continue to obtain higher-order approximations, the next step would be to seek the second term in the boundary-layer expansion, (5-206). We have now added a second approximation to the core solution. As in the case of the leading-order term fo (z), we obtained the solution (5-220) by requiring that the normal velocity components (i.e., /) match as we approach the base of the disk, but with no consideration of any boundary condition on the radial velocity component in the core region. Hence, by adding /, we will have introduced some additional slip that must be matched by a new, second term in the... 

The normal velocity component is obtained from (6-229), by integrating the continuity equation (6-215b). After applying the boundary condition for u>(0) at z = 0 from (6-217a), this gives... 

It then follows from (9-268) and the continuity equation that the normal velocity component must be linear in y, that is,... 

However, the normal velocity component is zero at the surface of the body, and (10-38) is reduced in the limit y - 0 to an equation for the pressure gradient that is required in (10-36),... 

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