Channel number ratio

Figure 1.1 Variation ofthe specific energy ratio as a function ofthe characteristic time ratio for values of the channel number ratio equal to l,2and 10, at fixed reactorvolume.Averagevalues ofthe exponents are a = 2.5, b = 1 and c = 3.5.

Equations (3.11) and (3.12) show that the friction factor of a rectangular micro-channel is determined by two dimensionless groups (1) the Reynolds number that is defined by channel depth, and (2) the channel aspect ratio. It is essential that the introduction of a hydraulic diameter as the characteristic length scale does not allow for the reduction of the number of dimensionless groups to one. We obtain... 

The numbers are generic for our example and may be different for a real system, depending on the number of channels used in the MCA and the frequency chosen for the drive system. The channel numbers are usually a certain power of two like 512 = 2. The value of p IOO ps applies to a spectrometer with 512 channels operated at 20 Hz, which means a period time of 50 ms. The exact dwell time is obtained from the ratio of period time to the number of channels, which is 50 ms/ 512 = 97.7 ps per channel. 

The channel 1/channel 2 ratio is a value that will be provided by the instructor. It is a correction factor that takes into account the fact that some 14C counts per minute were counted in channel 1. The instructor determined this ratio by scintillation counting of a sample containing a known number of 14C disintegrations per minute in channel 1 and channel 2 under conditions identical to your experiment. Refer to Section I, Experiment 3 for further discussion of the channel ratio method of quantifying radioactivity. 

Spectrometers have additional parameters for which response should be tracked. These include the count rate in spectral energy regions of interest, peak channel numbers at selected energies, difference in channel numbers between two specified energy peaks, peak energy resolution at specified energies, and the peak to Compton ratio (see Section 8.3.4). A QC chart can be established for each parameter by replicate measurements. This chart will display each data point as well as lines at the mean value and at 2a and 3a values. 

The ratio of channel numbers describes the multi-scale aspect. 

These values confirm what has been observed previously in a single tubular reactor using Ni = N2 and Vi = V2 demonstrates that heat-transfer acceleration (ti > 2) implies an increase in the required specific energy (E2>Ei). This effect is still observed with multi-scale reactors, since the exponent c is always positive. Nevertheless, this increase can be counter-balanced by adapting the multi-scale design with an appropriate value of the ratio of channel numbers. 

The present problem is governed by a total of 8 dimensionless numbers droplet length to channel width ratio iJi/W), density ratio p /pi), viscosity ratio (jiilpii), thermal diffusivity ratio ai/ai), Prandtl number (Pr), Reynolds number (Re), Capillary number (Ca) and Marangoni number (Ma). Pr, Re, Ca and Ma are defined respectively as... 

Where H is the charmel height (the smaller dimension in a rectangular channel), tw,av the average wall shear stress, V the kinematic viscosity, and p the density of the fluid. In internal flows, the laminar to turbulent transition in abrupt entrance rectangular ducts was found to occur at a transition Reynolds number Ret = 2200 for an aspect ratio ac = I (square ducts), to Ret = 2500 for flow between parallel planes with = 0 [4]. For intermediate channel aspect ratios, a linear interpolation is recommended. For circular tubes. Ret = 2300 is suggested. These transition Reynolds number values are obtained from experimental observations in smooth channels in macroscale applications of 3 mm or larger hydraulic diameters. Their applicability to microchannel flows is still an open question. 

Table 3 is the calculated area of the neural-recording system with various channel numbers and ADCs. As shown, the total chip area increases as the number of ADCs does, which is a straightforward conclusion. Therefore, there must be an optimal multiplexing ratio that makes the system s power-area product minimum. Table 4 is the power-area product based on Tables 2 and 3. From Table 4, we can deter-... 

The dimensional analysis reported in the previous section does not include the influence of channel aspect ratio or size. We try to bring the effect of channel cross-section size in this section. In comparison to the example discussed in the last section, most systems are characterized by more than one length scale, which leads to a more involved Reynolds number analysis. As an example, consider a section of length L and width w of the infinite, parallel-plate channel with height h shown in Figure 2.5. The system is translation invariant... 

A numerical study of the effect of area ratio on the flow distribution in parallel flow manifolds used in a Hquid cooling module for electronic packaging demonstrate the useflilness of such a computational fluid dynamic code. The manifolds have rectangular headers and channels divided with thin baffles, as shown in Figure 12. Because the flow is laminar in small heat exchangers designed for electronic packaging or biochemical process, the inlet Reynolds numbers of 5, 50, and 250 were used for three different area ratio cases, ie, AR = 4, 8, and 16. 

Figure 15 shows the effect of the width ratio DJthe ratio of the combining header width to the dividing header width, on the flow distribution in manifolds for Reynolds number of 50. By increasing DJthe flow distribution in the manifold was significantly improved. The ratio of the maximum channel flow rate to the minimum channel flow rate is 1.2 for the case of D /= 4.0, whereas the ratio is 49.4 for the case oiDjD,=0.5. 

Figure 20 shows values of the channel enthalpy extraction ratio for a number of channels. Enthalpy extraction (111) equal to that required by a proposed demonstration plant (112) has been achieved. Channels have performed generally in accordance with predictions. 

The Knudsen number Kn is the ratio of the mean free path to the channel dimension. For pipe flow, Kn = X/D. Molecular flow is characterized by Kn > 1.0 continuum viscous (laminar or turbulent) flow is characterized by Kn < 0.01. Transition or slip flow applies over the range 0.01 < Kn < 1.0. 

Reynold s number It is a dimensionless number that is significant in the design of any system in which the effect of viscosity is important in controlling the velocities or the flow pattern of a fluid. It is equal to the density of a fluid, times its velocity, times a characteristic length, divided by the fluid viscosity. This value or ratio is used to determine whether the flow of a fluid through a channel or passage, such as in a mold, is laminar (streamlined) or turbulent. 

Pfund et al. (2000) studied the friction factor and Poiseuille number for 128-521 pm rectangular channels with smooth bottom plate. Water moved in the channels at Re = 60—3,450. In all cases corresponding to Re < 2,000 the friction factor was inversely proportional to the Reynolds number. A deviation of Poiseuille number from the value corresponding to theoretical prediction was observed. The deviation increased with a decrease in the channel depth. The ratio of experimental to theoretical Poiseuille number was 1.08 0.06 and 1.12 zb 0.12 for micro-channels with depths 531 and 263 pm, respectively. 

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