Velocity approach

The specific cake resistance is the most troublesome parameter ideally constant, its value is needed to calculate the resistance to flow when the amount of cake deposited on the filter is known. In practice, it depends on the approach velocity of the suspension, the degree of flow consoHdation that the cake undergoes with time, the feed soHds concentration, and, most importantly, the appHed pressure drop Ap. This changes due to the compressibiHty of most cakes in practice. often decreases with the velocity and the feed concentration. It may sometimes go through a maximum when it is plotted against soHds concentration. The strongest effect on is due to pressure, conventionally expressed as ... 

This effect of concentration is particularly pronounced with irregularly shaped particles. A possible explanation of the variation in the specific resistance is in terms of the time available for the particles to orient themselves in the growing cake. At higher concentrations, but with the same approach velocities, less time, referred to as particle relaxation time, is available for a stable cake to form and a low resistance results. 

For cross-flow plates, net area is the column cross section less that area blocked by the downcomer or downcomers (Fig. 14-22). The vapor velocity in the net area represents an approach velocity and thus controls the level of liquid entrainment. For counterflow plates, net area is the same as the column cross section, since no downcomers are involved. 

Approach velocity The velocity of airflow into a filter bank or heat exchanger. 

Whether a flame is transmitted through a flame arrester depends on the length and aperture size of the arrester, the approach velocity of the flame, the pressure rise, and the temperature of the arrester (Wilson and Flessner 1978). Wilson and Flessner state that the evidence indicates that low-speed flames can be quenched by an array of small passageways placed in a duct, provided that the effective passageway diameter (critical diameter) meets the following criterion ... 

The close-up images will allow the landing site to be chosen and the lander will be sent down to the surface in November 2014. The relative approach velocity for the landing will be less than 1 ms-1, which is something like a slow walk. Once there, the scientific objectives will be met by the following series of measurements ... 

Equation 8.19 is based on the following assumptions the approach velocity v is uniform and parallel, the streamlines are horizontal above the weir, there is atmospheric pressure under the nappe, and the flow is frictionless. 

Figure 17.8 shows the probe, which consists of a 1-millimeter diameter t3rpe K thermocouple centered between two 1-millimeter diameter pressure taps. Each of the pressure tubes was bent 90° and sheared at the bend. To obtain a measurement, the tube is rotated until the pressure difference between the two taps is maximized. This is the position at which one tube is directed into the oncoming flow and the other is parallel to it. The approach flow thus observes an approximately 1-millimeter thick planar obstruction. The pressure difference and temperature are then recorded. The pressure difference is related to the approach velocity, and the angle determines the tangential and axial velocity components in this case. The local mass flux is then determined from the axial velocity component and the temperature (necessary to compute the flow density), and... 

At the other extreme of Re, Achenbach (Al) investigated flow around a sphere fixed on the axis of a cylindrical wind tunnel in the critical range. Wall effects can increase the supercritical drag coefficient well above the value of 0.3 arbitrarily used to define Re in an unbounded fluid (see Chapter 5). If Re is based on the mean approach velocity and corresponds to midway between the sub- and super-critical values, the critical Reynolds number decreases from 3.65 x 10 in an unbounded fluid to 1.05 x 10 for k = 0.916. 

Figure 9.4 shows curves for the drag coefficient (based on the velocity for a freely settling sphere and the mean approach velocity for a fixed or suspended sphere) and for the fractional increase in drag caused by wall effects, Kp — 1). Up to Re of order 50, the results are approximated closely by an equation proposed by Fay on and Happel (F2) ... 

For a sphere rotating about an axis parallel to the direction of relative motion, flow may be characterized by Re and by the ratio vJU of equatorial surface speed to the approach velocity. As for top spin, screw rotation in... 

Because the approach velocity v, that is, the gas velocity prior to entering the powder bed is experimentally simple to measure, it is desirable to state equation (7.21) in terms of v rather than Dp. In order to make this conversion consider Fig. 7.2. The unshaded area represents gas contained between a piston and the surface of the powder bed. If the porosity p of the bed is 0.5, then in order to contain an equal volume of gas, the powder bed must be twice as long as the distance the piston can move. Clearly then, if the piston is displaced downward at a uniform rate the linear velocity through the bed must be twice the approach velocity, or... 

As shown in Fig. 10.8, many of the values of K are greater than unity, which is a result of including the correction for approach velocity with... 

Now the velocity v through the packing conduits is clearly v / where vf is the approach velocity. If Sv is the surface represented by a unit-volume of the particles, then Eq (13-35) becomes... 

Consider a sphere of radius a held fixed in a creeping flow field with approach velocity U. The fluid contains Brownian particles having a diffusion coefficient D. Should the Peclet number 2aUiDUj have a value much greater than unity, the diffusion boundary layer will be sufficiently thin so that curvature effects and tangential diffusion are negligible. Under these conditions the convective-diffusion equation assumes the following form ... 

Two things must be addressed with respect to Equation (3.7). First, remember that hi and the approach velocity were neglected and y2 was made equal to y + P-Second, the L must be corrected depending upon whether the above equation is to be used for a fully contracted rectangular weir or the suppressed weir. 

Bar size Width, mm Thickness, mm Bars clear spacing, mm Slope from vertical, degrees Approach velocity, m/s... 

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