Unit of flow

For convenience, the loading on a flow reactor is expressed as a size of reactor per unit of flow rate, say V /V, and is labeled the. space velocity. Some of the units in practical use are stated in the Introduction. How the actual residence time is calculated when the density of flowvaries is illustrated in Table 7-8. 

For catalytic reactions in an open system, V reactor volume contains the catalyst and concentrations arc referred per unit of flowing volume, m /s. 

Obviously, the total flow in the paths from source to sink cannot exceed the flow through the capacity of the cut-set. Hence, max (flow) min (cut-set capacity). To prove the equality we note that if no cutset exists all of whose arcs are filled to capacity, then we can produce by a constructive procedure, an unsaturated path in which one or more units of flow can be introduced, ultimately obtaining saturation of a set of arcs that contains a cut-set. This cut-set has minimum total capacity. 

When a stress is applied to the bulk polymer melt, the mass flows in the direction that relieves the stress. At the molecular level, the probability of a molecular jump becomes higher in the direction of the stress than in any other direction and hence these stress-relieving motions predominate, leading to the observed pattern of flow. There is evidence that the molecular unit of flow is not the complete macromolecule but rather a segment of the molecule containing up to 50 carbon atoms. Viscous flow takes place by successive jumps of such segments until the entire macromolecule has shifted. 

Let s examine a fluid flowing through a straight horizontal piece of pipe as shown in Figure 5.6. The flow of the fluid is represented by the arrow, and the volume of fluid is represented by the blue section. Flow rate is the volume of fluid passing a particular point (e.g., the black line) per unit time. Thus flow rate will have units of volume divided by time such as gallons per minute or liters per hour. However, the official SI units of flow rate are cubic meters per second (m3/s). So, if the volume of the blue section is 1 m3, and it takes 1 s to flow past the black line, the flow rate is 1 m3/s. 

Rate of elimination = CL C with units of flow (e.g., mL/min) such that... 

The load distribution can be computer-optimized by calculating compressor efficiencies (in units of flow per unit power) and loading the compressors in their order of efficiencies. The pressure controller (PC-22) directly sets the set points of SC-21 and SC-23, whereas the balancing controllers (FFC-22 and FFC-24) slowly bias those settings as they follow the total H2 generation of the electrolyzers (FT-4). The flow ratio controllers (FFCs) are also protected from reset windup, as was explained in Section 2.5.4. 

In polymers, however, E levels off at a value independent of molecular mass. This means that in long chains the unit of flow is considerably smaller than the complete molecule. It seems that viscous flow in polymers takes place by successive jumps of segments until the whole chain has shifted. 

Eyring assumed that (A2A3A2/A1) is of the order of the volume of the unit of flow, and if the volume per mol of this unit is V, 22222 /2ic VIN, where iV= Avogadro s number, and ... 

In the case of molten polymers, oligomers or solvents characterized by highly extended linear backbones, the proposed expression is the same but Ey corresponds to the so-called unit of flow energy, i.e. the energy needed to move the proper segment of the chain in the viscous flow (Van Krevelen, 1976). The same concept is applied also to Fs, which becomes the molar volume of the segment . 

AHev molar heat of vaporization of liquid or polymer unit of flow... 

The ratio of convection heat transfer (per unit duct surface area) to amount virtually transferable (per unit of flow cross-sectional area) no dependence upon any geometric characteristic dimension... 

This is illustrated in Fig.lO [26] where the flow resistance per unit of bed depth and per unit of flow velocity is plotted against fee mean diameter of the particles. Unfortunately, the kinetics of adsorption are inversely proportional to the mean diameter of the activated carbon particles. As a result, smaller particles exhibit better adsorption characteristics but cause a higher breathing resistance. This can be overcome by using assisted filtration in which... 

Now, we need to turn to converting the concentrations into appropriate units. Since the total flowrates are given in terms of mass, a unit that expresses the concentration in terms of mass of the components would be most useful. The vapor stream compositions are given as mass percents, which works well with the units of flow. However, the liquid phase concentration given in terms of a molarity is not useful for finding a mass flow rate of ethanol (or of water). Hence we must convert the concentration to something more useful. 

Flow rate is defined as the volumes or masses of fluids flowing through a special area in unit time. The standard unit of flow rate... 

The output from LDF is measured not in easily interpretable units of flow but rather in hertz. It would be ideal to define a single calibration factor that could be used in all tissues to convert laser output to flow in absolute units. Unfortunately, the calibration to determine an absolute flow is limited by the lack of a comparable standard and the lack of preset controlled conditions. This may be due to varying tissue optical properties affected by tissue density (Obeid et al., 1990). Further, LDF signals can be affect by movement of the probe relative to the tissue. 

Here x and y are dimensions of the jump unit of flow and V is the displacement volume of the unit of flow. The values of x, y, and V for real systems are unknown. However, the dimensionality of xy/ V is a unit of reciprocal length which looks very similar to the shift factor used by Schonhorn et aV Although experiments to test the validity of the Cherry and Holmes expression will be difficult, the apparent agreement of their derivation with the results of Schonhorn et al is very satisfying in the conceptual sense. Cherry and El Muddarris have attempted to determine the effect of wetting kinetics on the strength of adhesive bonds, but the results were not conclusive. " ... 

We may choose not to have the flow of the manipulated fuel to be conditioned to energy units if, for example, its properties change little. We then need to include the NHV in the calculation of K, ensuring we use engineering units consistent with the units of flow. 

As given here the controller gain has units of flow/height or m min". In commercial controllers the manipulated and controlled variables are often made dimensionless with the range and standard signal of the transmitter and actuator so that the units of the gain would be, for example, %/% or mA/mA. Also, in older controllers the term proportional band (PB) is used instead of controller gain and is defined by Eq. (84). 

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