Flow Rate-Pressure Drop Relationships

Calculation of flow rate-pressure drop relationship for laminar flow using r-y data... 

Matrix flow relative to the reinforcing fibers is caused by thermal expansion of the fiber-matrix mass within the confines of the die and by the geometrical constriction of the die taper. Once the matrix flow distribution is known, the matrix pressure distribution may be determined using a flow rate-pressure drop relationship. One-dimensional flow models of thermoset pultrusion have been reasonably well verified qualitatively [15-17]. A onedimensional flow model of thermoplastic pultrusion [14,18] has similarly been compared with experimental data and the correlation found to be encouraging [19]. 

To obtain the pressure distribution in the tapered die from the flow distribution, a flow rate-pressure drop relationship is required. One approach to obtain such a relationship is through an extension of the empirically derived Darcy s law for steady-state flow of Newtonian fluids through macroscopically isotropic beds [24]. It has been suggested that an equivalent expression for a bed of aligned fibers may be obtained through application of the hydraulic-radius concept, thus yielding [25]... 

EN 12117 Fittings, valves and ancillaries - determination of gaseous flow rate/pressure drop relationships. 

The theory of Schubert and Neesse points to small cone angle and curved feed inlets for clarification duties where high mass recoveries are required. The authors compared the above correlation with many published experimental results and found the correspondence better for umbrella (or spray) discharge. No flow rate-pressure drop relationship was proposed. 

As with other separation equipment, the main characteristics of filters are the flow rate-pressure drop relationships and other performance characteristics such as the separation efficiency. In filtration however, these relationships are more complex as there are many variables and factors (cake thickness, mass of cake per unit area, specific cake resistance etc.) which greatly influence the process. 

If a centrifugal pump is used, its flow rate-pressure drop relationship may follow the curve shown in Figure 9.12. 

The relationship between flow rate, pressure drop, and pipe diameter for water flowing at 60°F in Schedule 40 horizontal pipe is tabulated in Appendix G over a range of pipe velocities that cover the most likely conditions. For this special case, no iteration or other calculation procedures are required for any of the unknown driving force, unknown flow rate, or unknown diameter problems (although interpolation in the table is usually necessary). Note that the friction loss is tabulated in this table as pressure drop (in psi) per 100 ft of pipe, which is equivalent to 100pef/144L in Bernoulli s equation, where p is in lbm/ft3, ef is in ft lbf/lbm, and L is in ft. 

Before closing this chapter, we feel that it is useful to list in tabular form some isothermal pressure-flow relationships commonly used in die flow simulations. Tables 12.1 and 12.2 deal with flow relationships for the parallel-plate and circular tube channels using Newtonian (N), Power Law (P), and Ellis (E) model fluids. Table 12.3 covers concentric annular channels using Newtonian and Power Law model fluids. Table 12.4 contains volumetric flow rate-pressure drop (die characteristic) relationships only, which are arrived at by numerical solutions, for Newtonian fluid flow in eccentric annular, elliptical, equilateral, isosceles triangular, semicircular, and circular sector and conical channels. In addition, Q versus AP relationships for rectangular and square channels for Newtonian model fluids are given. Finally, Fig. 12.51 presents shape factors for Newtonian fluids flowing in various common shape channels. The shape factor Mq is based on parallel-plate pressure flow, namely,... 

Theoretical analyses of the liquid holdup are given by Kolar and Broz28 and Hutton et al.24 Kolar and Broz presented a relation between the liquid holdup and the flow rates, and physical properties of the fluids. The relationship contains three parameters, the values of which must be determined by experiment. Hutton et al.24 derived relationships between the liquid flow rate, pressure drop, and liquid holdup. At low Reynolds numbers, only gravitjLand yisgous forces were considered to beTmporfant anct from a force balance on the trickle bed, they derived a relation... 

Typical velocities in plate heat exchangers for waterlike fluids in turbulent flow are 0.3-0.9 meters per second (m/s) but true velocities in certain regions will be higher by a factor of up to 4 due to the effect of the corrugations. All heat transfer and pressure drop relationships are, however, based on either a velocity calculated from the average plate gap or on the flow rate per passage. 

Tower diameter selection is usually made with the maximum expected gas and liquid flow rates and depends on the size and type of tower packing The portion of Fig. 3 with solid lines illustrates the pressure-drop relationship for 1.5-m. [3.81 -cm] Pull rings supplied by the manufacturer for typical superficial gas and liquid flow rates used in the chemical processing industry.1 This relationship is usually available in graphical form from any manufacturer of packed-tower packing elements. While these... 

The reject flow rate is controlled automatically at the predetermined optimum on die basis of the pressure-drop relationship de- railed previously. 

The final characteristic to be developed is the pressure-drop relationship as a function of both flow and reject rates. This is important because of the relationship between hydraulic capacity and the pressure driving force. Additionally, because wc use the pressure-drop characteristic for control purposes, this information is more significant. 

M 47] [M 48] [P 44] The current maximum flow rate of a small-scale interdigital concentric mixer (StarLam300) is 10001 h 1 at about 3 bar pressure drop [130], For the large-scale counterpart (StarLam3000) even 3000 1 h 1 at only 0.7 bar is determined. Extrapolating the flow rate-pressure relationship further to 10 bar yields a flow rate of nearly 2000 1 h 1 for the StarLam300 and nearly 10 000 1 h 1 for the... 

When a fluid is pumped through a certain length of tube, a pressure drop is observed due to the viscous drag effect of the fluid. This pressure drop is a function of the geometric size of the tube (inner diameter and length of tube) and the flow rate. Thus, this relationship is used to determine the viscosity of a fluid. Figure 14 shows a schematic diagram of a capillary tube. 

Experimental results with low concentration feeds or under conditions where M is close to 1.0 are in good agreement with the theoretical predictions. However, when the wall concentration becomes high, the solvent flux often cannot be controlled by adjusting the pressure difference. Thus, Eq. 117-401 no longer holds Some other phenomenon must be controlling the solvent flux. Careful examination of the membrane surface after these experiments shows a gel-like layer covering the membrane surface. This gel layer alters the flux-pressure drop relationship and controls the solvent flow rate. 

---