Velocity effective

Normally vessels are designed with the gas outlet location well above TDH. If circumstances force operation with a bed height so that the outlet is below TDH, an equivalent velocity, an effective velocity higher than the actual superficial gas velocity, is used ia the above calculation. The effective gas velocity can be determined from Figure 19 (27). 

Approaches used to model ozone formation include box, gradient transfer, and trajectoty methods. Another method, the particle-in-cell method, advects centers of mass (that have a specific mass assigned) with an effective velocity that includes both transport and dispersion over each time step. Chemistry is calculated using the total mass within each grid cell at the end of each time step. This method has the advantage of avoiding both the numerical diffusion of some gradient transfer methods and the distortion due to wind shear of some trajectory methods. 

Visi-osity High viscosity crudes may flow in the laminar flow regime which causes high pressure drops. This is especially true of emulsions of water in high-viscosity crudes where the effective velocity of the mi slur e could be as much as ten times that of the base crude (see Volume 11... 

Reynolds number for gas S = length of corrugation side Uge = effective velocity of gas Ug = superficial velocity of gas Ui = superficial velocity of liquid Ap = pressure drop per unit packed height e = packing void fraction 0 = angle of flow channel (from horizontal) fi = viscosity p = density... 

Current density requirements depend on the environment, galvanic effects, velocities and other factors influencing polarisation. In the absence of galvanic influences or other secondary effects 30mA/m may be sufficient in sea-water to maintain adequate polarisation for protection once it has been achieved it is however normally necessary to apply 100-150 mA/m to achieve initial polarisation within a reasonable period and if rapid protection is required, current densities as high as 500 mA/m may be applied. 

The form of the effective mobility tensor remains unchanged as in Eq. (125), which imphes that the fluid flow does not affect the mobility terms. This is reasonable for an uncharged medium, where there is no interaction between the electric field and the convective flow field. However, the hydrodynamic term, Eq. (128), is affected by the electric field, since electroconvective flux at the boundary between the two phases causes solute to transport from one phase to the other, which can change the mean effective velocity through the system. One can also note that even if no electric field is applied, the mean velocity is affected by the diffusive transport into the stationary phase. Paine et al. [285] developed expressions to show that reversible adsorption and heterogeneous reaction affected the effective dispersion terms for flow in a capillary tube the present problem shows how partitioning, driven both by electrophoresis and diffusion, into the second phase will affect the overall dispersion and mean velocity terms. 

When melt moves relative to solid and chemically exchanges with the solid, elements will move at different effective velocities. Consider a situation where a fluid moves interstitially through a solid and elements exchange between the melt and solid (for simplicity we will ignore the issue of melting in this example). The effective velocity (weff) of an element in one dimension can be approximately expressed as... 

Where /yand ps are the melt and solid densities, respectively, melt velocity. W is the solid upwelling velocity and A is the bulk partition coefficient. Note that if the partition coefficient A is 1, the effective velocity approaches the melt velocity, and also that the difference in effective velocity between elements with different Di decreases at larger porosities. In the following text, the subscripts 0, 1, and 2 are taken to refer to °Th, and Ra, respectively. 

The rate of separation of the fragments depends on the functions A r), C(r), Fc> and the fragmentation number, while the rate of rotation depends only on the function B(r). Further, it is apparent that the separation between the fragments increases only when the hydrodynamic force exceeds the binding physicochemical force. The pair of fragments rotates as a material element in an apparent flow with an effective velocity gradient tensor... 

The quantity G of the effective mixing mass flux is determined by the turbulent velocity fluctuations at the bubble-layer edge. The distance of the edge of the bubble layer from the wall is taken as the distance at which the size of the turbulent eddies is k times the average bubble diameter. Weisman and Pei have determined empirically that k equals 2.28. Only a fraction of the turbulent velocity fluctuations produced are assumed to be effective in reaching the wall. The effective velocity fluctuations are those in which the velocity exceeds the average velocity away from the wall produced by evaporation heat flux q"b. At the bubble layer-core interface, the effective mass flux to the wall is computed as... 

The terms represent, respectively, the effect of pressure gradient, acceleration, line friction, and potential energy (static head). The effect of fittings, bends, entrance effects, etc., is included in the term Ke correlated as a number of effective velocity heads. The inclination angle 0 is the angle to the horizontal from the elevation of the pipe connection to the vessel to the discharge point. The term bi is the two-phase multiplier that corrects the liquid-phase friction pressure loss to a two-phase pressure loss. Equation (23-39) is written in units of pressure/density. 

If transport is by diffusion and advection (effective velocity), the transport equation is... 

Note that q has the units of a velocity and is always smaller than the effective velocity in the pores, u, since < > < 1. It is assumed that the x-axis of the (local) coordinate system is always pointing in the direction of the mean flow. Since the mean flow usually does not follow a straight line, the x-axis does not necessarily point in a fixed direction either. 

This expression describes the fastest and most important mode of transport in groundwater. In fact, an important task of the hydrologist is to develop models to predict the effective velocity u (or the specific flow rate q). Like the Darcy-Weis-bach equation for rivers (Eq. 24-4), for this purpose there is an important equation for groundwater flow, Darcy s Law. In its original version, formulated by Darcy in 1856, the equation describes the one-dimensional flow through a vertical filter column. The characteristic properties of the column (i.e., of the aquifer) are described by the so-called hydraulic conductivity, Kq (units m s"1). Based on Darcy s Law, Dupuit derived an approximate equation for quasi-horizontal flow ... 

The root mean square velocity (rms) or effective velocity (ceff)... 

Since the thrust reaches a maximum value when pe = pa, a well designed rocket exhaust nozzle should exhaust gases at an exit pressure nearly or exactly equal to the ambient pressure. Near the point of maximum thrust the second term in the thrust equation (Eq. n. A. 9.) is like a small correction term. Thus it is appropriate to define another parameter, the effective velocity c, whose significance will be examined in more detail ... 

Comparing this with the slow reaction case, we note that the effective velocity has increased (by a factor 1.83), the dispersion coefficient is reduced by a factor 3 while the apparent reactor scale Damkohler number changed from Das to 8jp. 

Pore flow effect velocity parameter dependency... 

The specific impulse (7sp) is the change in the impulse (impulse = mass x velocity or force x time) per mass unit of the propellant. It is an important performance parameter of rocket motors and shows the effective velocity of the combustion gases when leaving the nozzle, and is therefore a measure for the effectiveness of a propellant composition. 

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