Velocity equal

A steady-state rocket-type combustion spray unit has been developed, called high velocity oxy fuel (HVOF), that creates a steady state, continuous, supersonic spray stream (1.2—3 mm dia) resembling a rocket motor exhaust. The portable device injects and accelerates the particles inside a barrel (rocket nozzle). It produces coating quaHty and particle velocities equal to the D-gun at 5—10 times the spray rate with significantly reduced coating costs. 

Because the Navier-Stokes equations are first-order in pressure and second-order in velocity, their solution requires one pressure bound-aiy condition and two velocity boundaiy conditions (for each velocity component) to completely specify the solution. The no sBp condition, whicn requires that the fluid velocity equal the velocity or any bounding solid surface, occurs in most problems. Specification of velocity is a type of boundary condition sometimes called a Dirichlet condition. Often boundary conditions involve stresses, and thus velocity gradients, rather than the velocities themselves. Specification of velocity derivatives is a Neumann boundary condition. For example, at the boundary between a viscous liquid and a gas, it is often assumed that the liquid shear stresses are zero. In numerical solution of the Navier-... 

Most often, the Mach number is calculated using the speed of sound evaluated at the local pressure and temperature. When M = 1, the flow is critical or sonic and the velocity equals the local speed of sound. For subsonic flowM < 1 while supersonic flows have M > 1. Compressibility effects are important when the Mach number exceeds 0.1 to 0.2. A common error is to assume that compressibihty effects are always negligible when the Mach number is small. The proper assessment of whether compressibihty is important should be based on relative density changes, not on Mach number. 

Boundary layer flows are a special class of flows in which the flow far from the surface of an object is inviscid, and the effects of viscosity are manifest only in a thin region near the surface where steep velocity gradients occur to satisfy the no-slip condition at the solid surface. The thin layer where the velocity decreases from the inviscid, potential flow velocity to zero (relative velocity) at the sohd surface is called the boundary layer The thickness of the boundary layer is indefinite because the velocity asymptotically approaches the free-stream velocity at the outer edge. The boundaiy layer thickness is conventionally t en to be the distance for which the velocity equals 0.99 times the free-stream velocity. The boundary layer may be either laminar or turbulent. Particularly in the former case, the equations of motion may be simphfied by scaling arguments. Schhchting Boundary Layer Theory, 8th ed., McGraw-HiU, New York, 1987) is the most comprehensive source for information on boundary layer flows. 

Arbitrary-Lagrangian-Eulerian (ALE) codes dynamically position the mesh to optimize some feature of the solution. An ALE code has tremendous flexibility. It can treat part of the mesh in a Lagrangian fashion (mesh velocity equation to particle velocity), part of the mesh in an Eulerian fashion (mesh velocity equal to zero), and part in an intermediate fashion (arbitrary mesh velocity). All these techniques can be applied to different parts of the mesh at the same time as shown in Fig. 9.18. In particular, an element can be Lagrangian until the element distortion exceeds some criteria when the nodes are repositioned to minimize the distortion. 

Diffuser jet throw, L, is a parameter commonly used in air diffuser sizing defined as the distance from the diffuser face to the jet cross-section where the centerline velocity equals a terminal velocity (v is often assumed to be 0.25 rn/s). Therefore, the throw (L) can be determined by velocity decay equations with v. equal to the terminal velocity ... 

Shepelev and Gelman - and Regenscheit computed air temperature along the first three zones of jets supplied from outlets with finite size using the method of superposition of the multiple-jet system. These jets originate from the points with supply air velocity equal to the average air velocity at the outlet. 

A similar effect was observed for changes in hood flow rate. With a fixed cross-draft velocity, capture efficiency decreased with decreasing hood flow rate. This effect was much more important when freeboard height was small. Their results showed that when hood flow rate was 1.5 m s m, efficiency remained close to 1.0 as long as the cross-draft velocin. was less than 0.45 in s. The most severe conditions tested were a hood flow rate equal to 0.33 m s" nr- and crossdraft velocity equal to 1.15 m s. Under these conditions, capture efficiency was equal to 0.83 for freeboard hei t equal to 0.3 m, but decreasing to 0.4 when freeboard height was decreased to 0.1 m. 

FIGURE 10.52 Critical contamination region in a uniform parallel flow field. Qualitative solution of the difliision equation in a velocity field with the velocity equal to 0.45 m s, difliision coefficient equal to 2.4 cm s , and the distance between the working surface and the contamination source of 30 cm. 

The velocity potential for the flow field in front of an expanding piston surface can now be derived from the boundary condition so that at its surface the medium velocity equals the piston velocity. In this way, Taylor (1946) found... 

If the velocity of the gas/fluid equals or exceeds the speed of sound, shock waves are set up, and vibrations and other mechanically related problems may result, compared to the conditions when velocities are below the speed of sound. For a Mach of 1.0, the gas velocity equals the velocity of sound in the fluid. 

The concept of a stationary component may be envisaged by considering the effect of moving the box, discussed in Section 10.1, in the opposite direction to that in which B is diffusing, at a velocity equal to its diffusion velocity, so that to the external observer B appears to be stationary. The total velocity at which A is transferred will then be increased to its diffusion velocity plus the velocity of the box. 

A power law fluid is flowing under laminar conditions through a pipe of circular cross-section. At what radial position is the fluid velocity equal to the mean velocity in the pipe Where does this occur for a fluid with an n-value of 0.2 ... 

In a drop extractor, liquid droplets of approximate uniform size and spherical shape are formed at a series of nozzles and rise eountercurrently through the continuous phase which is flowing downwards at a velocity equal to one half of the terminal rising velocity of the droplets. The flowrates of both phases are then increased by 25 per cent. Because of the greater shear rate at the nozzles, the mean diameter of the droplets is however only 90 per cent of the original value. By what factor will the overall mass transfer rate change ... 

Moreover, a neighbouring cell will have a velocity equal but opposite in direction, giving a total surface velocity difference across the gap, b, between the two cells of AUj = Yavgd- The average interstitial fluid velocity gradient is proportional to ... 

In the case when the pendulum path is an ellipse the effect of the earth s rotation is to cause the ellipse to rotate with an angular velocity equal to (—co sin X). As we know, at the poles it is approximately 7.3 x 10 s. In accordance with Equation (3.94), for an observer located at the z-axis above the earth the rotation is clockwise in the northern hemisphere, (A>0), and counterclockwise in the southern hemisphere, (A<0). For example, at the North Pole the direction of the pendulum rotation and the earth are opposite to each other. During swinging the pendulum moves from the point a to the opposite point of the path b, which is shifted at some small distance because of the earth s rotation. Fig. 3.5c. Suppose that the radius of the circle is sq, then the displacement bd during a half period of swinging, Tjl, is... 

Thus from Equation (2.13) we see that a working definition of KM is the substrate concentration that yields a velocity equal to half of the maximum velocity. Stated another way, the Ku is that concentration of substrate leading to half saturation of the enzyme active sites under steady state conditions. 

The discussion above was concerned with the effects of solution conditions on enzyme activity, hence reaction velocity. Equally important for the purpose of assay design is the influence of specific solution conditions on the detection method being used. This latter topic is beyond the scope of the present text. Nevertheless, this is an important issue for screening scientists whose job is often to balance the needs of biochemical rigor and assay practicality in development of an HTS assay. An... 

If the time of settling was such that particles with a velocity equal to 1.03 x 10 6 m/s settled, then the bottom product would contain quartz. This is not so and hence the maximum size of galena particles still in suspension is given by ... 

Glass spheres are fluidised by water at a velocity equal to one half of their terminal falling velocities. Calculate ... 

The upper part of the bubble moves with a velocity equal to the rate of change of its diameter, whereas its base remains stationary. Thus, the average velocity of the bubble can be assumed to be that with which the center of the bubble is ascending, which is equal to the rate of change of the bubble radius ... 

The first step is to determine the size of a particle which has a settling velocity equal to that of the upward flow of fluid, that is 5 mm/s. 

If the flow of fluidising liquid to a completely segregated bed is suddenly stopped, the particles will all then start to settle at a velocity equal to that at which they have been fluidised, because equation 6.31 is equally applicable to sedimentation and fluidisation. 

In the introduction to this chapter a combustion wave was considered to be propagating in a tube. When the cold premixed gases flow in a direction opposite to the wave propagation and travel at a velocity equal to the propagation velocity (i.e., the laminar flame speed), the wave (flame) becomes stationary with respect to the containing tube. Such a flame would possess only neutral stability, and its actual position would drift [1], If the velocity of the unbumed mixture is increased, the flame will leave the tube and, in most cases, fix itself... 

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