Flow resistance, dimensionless

The certified flow resistance factor, K[, is a dimensionless factor used to calculate the velocity head loss that results from the... 

In pHPLC, there are numerous types of columns used. The comparison and characterization of these columns are often discussed in terms of thermodynamic properties and kinetic characteristics. The retention factor, k, selectivity, a, and the peak asymmetry are believed to be representative parameters for the thermodynamic properties, while the kinetic characteristics are often expressed in dimensionless magnitudes of reduced plate height, h, separation impedance, E, and flow resistance factor, ( ). 3... 

Because of the flow resistance of the caps and risers in bubble-cap columns, there is a decrease in liquid depth as the liquid passes across the tray. Figure 16-4 shows an extreme example in which this liquid gradient is so great that only one out of the form bubble caps is operating normally. In general, the dimensionless ratio of total liquid gradient to pressure-drop head caused by the bubble-cap assembly should be less than 0.4 in order to ensure adequate vapor distribution, and, for single-pass crossflow trays, the rate of liquid flow across the tray should be less than 0.22 ft3/(sXft) diameter. 

Third dimensionless parameter, dimensionless flow resistance, , replaces permeability TiC ... 

The pressure drop can be calculated by use of the dimensionless flow resistance parameter, ... 

Dimensionless surface shear stress Flow resistance... 

Third dimensionless parameter, dimensionless flow resistance,, replaces permeability K. The pressure drop over one particle is compared with the flow along a particle ... 

ABSTRACT The characteristic of turbulent flow in jackets with triangular helical ducts was simulated and the velocity fields of fully developed turbulent fluid flow in the jackets were obtained. The features of the local coefficient of resistance C/Reiocai) on outer walls and inner wall were summed up and the effects of dimensionless curvature ratio and Reynolds number on the flow field and the flow resistance were analyzed. The results indicate that the structure of secondary flow is with two steady vortices at turbulent flow conditions. The distribution of/ eiocai on the outer walls differs from that of/ eiocai on the inner wall. The mean coefficient of resistance (/Rem) on the outer walls is about 1.41 1.5 7 times as much as that on the iimer wall. With the increase of dimensionless curvature ratio or Reynolds number,/Rem on the boundary walls increases. 

The problem of two-phase flow through noncircular ducts has received considerable attention in the last decades " and was studied specifically by Ransohoff and Radke. They addressed the problem of the low Reynolds number wetting liquid flow in a noncircular capillary occupied predominantly by a nonwetting gas phase by presenting a solution in terms of a dimensionless flow resistance, fi, depending on corner geometry and fluid parameters. 

Kaye [5] found that the model parameters A3-A5 depended mainly on three dimensionless groups Re, y and B. The Reynolds number is based on center-pipe diameter and reactor inlet velocity, y is the area ratio defined earlier and B is a measure of the flow resistance of the catalyst bed and baskets. The results of changing these three parameters are shown in Figures 1 3, and are similar to those found by Kaye [5], thus validating the solution obtained. Only CF-flow is shown , as there is little difference between CF- and CP-flows [2],... 

Q = volumetric flow, Sm /s Y = expansion factor, dimensionless K = flow resistance factor of pipes and fittings d = diameter, m Ap = differential pressure, kPa Pi = vessel pressure, kPaA T = temperature, K Sg = specific gravity (air = 1)... 

The flowrate of oil into the wellbore is also influenced by the reservoir properties of permeability (k) and reservoir thickness (h), by the oil properties viscosity (p) and formation volume factor (BJ and by any change in the resistance to flow near the wellbore which is represented by the dimensionless term called skin (S). For semisteady state f/owbehaviour (when the effect of the producing well is seen at all boundaries of the reservoir) the radial inflow for oil into a vertical wellbore is represented by the equation ... 

Friction factor, dimensionless Flow rate of one phase, GPM Aqueous phase flow rate, GPM Cy clone friction loss, expressed as number of cy clone inlet velocity heads, based on Drag or resistance to motion of body in fluid, poundals... 

The problem of axial conduction in the wall was considered by Petukhov (1967). The parameter used to characterize the effect of axial conduction is P = (l - dyd k2/k ). The numerical calculations performed for q = const, and neglecting the wall thermal resistance in radial direction, showed that axial thermal conduction in the wall does not affect the Nusselt number Nuco. Davis and Gill (1970) considered the problem of axial conduction in the wall with reference to laminar flow between parallel plates with finite conductivity. It was found that the Peclet number, the ratio of thickness of the plates to their length are important dimensionless groups that determine the process of heat transfer. 

The mass transfer coefficient describes the effect of mass transfer resistance of the reactants flowing from the gas phase to the surface of the individual particles in the bed. The mass transfer coefficient can be obtained from a correlation for the Sherwood number (or dimensionless mass transfer coefficient) given by Eq. (7) ... 

In liquid-liquid extraction using wetted-wall columns, analysis is possible only by dimensionless groups (75) for the core fluid, flowing up inside the tube, k varies as approximately D and for the fluid falling down the inner walls, varies as Systems studied include phenol-kerosene-water, acetic acid-methylisobutylketone-water, and uranyl nitrate between water and organic solvents (7S, 80-82) interfacial resistances of the order 100 sec.cm." are observed in the last system. These resistances are interpreted as being caused by a rather slow third-order interfacial exchange of of solvent molecules (S) coordinated about each UOa" ion ... 

Fig. 3.15 Variation of fractional approach to equilibrium with dimensionless time for spheres in creeping flow with negligible external resistance.

The same is true for fluid flow in piping. Experimental data must first be established to solve the piping fluid flow problems, specifically the / factor, also called the hL factor in the Fig. 6.1 analogy. Please note also that / is dimensionless. The / factor is used later in this chapter. The hL factor is in units of feet it is a force, requiring a workload, which is the force of friction resisting fluid flow. This friction of resistance is on the internal wall surface of the pipe. 

Figure E3.6c plots the dimensionless flow rate q/qd, where qd is the drag flow rate, namely, the flow rate with zero pressure gradient, versus the dimensionless pressure gradient G. The figure shows that, whereas for Newtonian fluids, as expected, there is a linear relationship, non-Newtonian fluids deviate from linearity. The more non-Newtonian the fluid is, the greater is the deviation. Of particular interest is the inflection point indicating, for example, that in screw extruders, even for the isothermal case, increasing die resistance brings about somewhat unexpected changes in flow rate.

Firstly, it has to be taken into account that criteria which characterize a state of flow have to be formulated in a dimensionless manner. Already W. Froude found in his experiments to determine the drag resistance of a ship s hull that the bow wave can only be reliably determined when the size of the ship model has the right proportions with respect to the travelling speed and channel width. 

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