Flow resistivity

In packed beds of particles possessing small pores, dilute aqueous solutions of hydroly2ed polyacrylamide will sometimes exhibit dilatant behavior iastead of the usual shear thinning behavior seen ia simple shear or Couette flow. In elongational flow, such as flow through porous sandstone, flow resistance can iacrease with flow rate due to iacreases ia elongational viscosity and normal stress differences. The iacrease ia normal stress differences with shear rate is typical of isotropic polymer solutions. Normal stress differences of anisotropic polymers, such as xanthan ia water, are shear rate iadependent (25,26). 

System flow resistance as a function of flow rate is needed to select the proper fan size. For calculation of system pressure drop see References 5—8. The resistance pressure curve for a typical system (Fig. 4a) shows that the pressure required to force air through the system increases with the flow rate. 

Melt Index or Melt Viscosity. Melt index describes the flow behavior of a polymer at a specific temperature under specific pressure. If the melt index is low, its melt viscosity or melt flow resistance is high the latter is a term that denotes the resistance of molten polymer to flow when making film, pipe, or containers. ASTM D1238 is the designated method for this test. 

The flow resistance of pipe fittings (elbows, tees, etc) and valves is expressed in terms of either an equivalent length of straight pipe or velocity head loss (head loss = Kv /2g ). Most handbooks and manufacturers pubHcations dealing with fluid flow incorporate either tables of equivalent lengths for fittings and valves or K values for velocity head loss. Inasmuch as the velocity in the equipment is generally much lower than in the pipe, a pressure loss equal to at least one velocity head occurs when the fluid is accelerated to the pipe velocity. 

The hydrauhc diameter method does not work well for laminar flow because the shape affects the flow resistance in a way that cannot be expressed as a function only of the ratio of cross-sectional area to wetted perimeter. For some shapes, the Navier-Stokes equations have been integrated to yield relations between flow rate and pressure drop. These relations may be expressed in terms of equivalent diameters Dg defined to make the relations reduce to the second form of the Hagen-Poiseulle equation, Eq. (6-36) that is, Dg (l2SQ[LL/ KAPy. Equivalent diameters are not the same as hydraulie diameters. Equivalent diameters yield the correct relation between flow rate and pressure drop when substituted into Eq. (6-36), but not Eq. (6-35) because V Q/(tiDe/4). Equivalent diameter Dg is not to be used in the friction factor and Reynolds number ... 

Filter aids should have low bulk density to minimize settling and aid good distribution on a filter-medium surface that may not be horizontal. They should also be porous and capable of forming a porous cake to minimize flow resistance, and they must be chemically inert to the filtrate. These characteristics are all found in the two most popular commercial filter aids diatomaceous silica (also called diatomite, or diatomaceous earth), which is an almost pure silica prepared from deposits of diatom skeletons and expanded perhte, particles of puffed lava that are principally aluminum alkali siheate. Cellulosic fibers (ground wood pulp) are sometimes used when siliceous materials cannot be used but are much more compressible. The use of other less effective aids (e.g., carbon and gypsum) may be justified in special cases. Sometimes a combination or carbon and diatomaceous silica permits adsorption in addition to filter-aid performance. Various other materials, such as salt, fine sand, starch, and precipitated calcium carbonate, are employed in specific industries where they represent either waste material or inexpensive alternatives to conventional filter aids. 

Cake Filters Filters that accumulate appreciable visible quantities of solids on the surface of a filter medium are called cake filters. The slurry feed may have a solids concentration from about 1 percent to greater than 40 percent. The filter medium on which the cake forms is relatively open to minimize flow resistance, since once the cake forms, it becomes the effective filter medium. The initial filtrate therefore may contain unacceptable sohds concentration until the cake is formed. This situation may be made tolerable by recycling the filtrate until acceptable clarity is obtained or by using a downstream polishing filter (clarifying type). 

External-Cake Tubular Filters Several filter designs are available with vertical tubes supported by a filtrate-chamber tube sheet in a vertical cylindrical vessel (Fig. 18-115). The tubes may be made of wire cloth porous ceramic, carbon, plastic, or metal or closely wound wire. The tubes may have a filter cloth on the outside. Frequently a filter-aid precoat will be applied to the tubes. The prefilt slurry is fed near the bottom of the vertical vessel. The filtrate passes from the outside to the inside of the tubes and into a filtrate chamber at the top or the bottom of the vessel. The sohds form a cake on the outside ofthe tubes with the filter area actually increasing as the cake builds up, partially compensating for the increased flow resistance of the thicker cake. The filtration cycle continues until the differential pressure reaches a specified level, or until about 25 mm (1 in) of cake thickness is obtainea... 

For a given slurry, the maximum filtration rate is determined by the minimum cake thickness which can be removed—the thinner the cake, the less the flow resistance and the higher the rate. The minimum thickness is about 6 mm (0.25 in) for relatively rigid or cohesive cakes of materials such as mineral concentrates or coarse precipitates like gypsum or calcium citrate. Sohds that form friable cakes composed of less cohesive materials such as salts or coal will usually require a cake thickness of 13 mm (0.5 in) or more. Filter cakes composed of fine precipitates such as pigments and magnesium hydroxide, which often produce cakes that crack or adhere to the medium, usually need a thickness of at least 10 mm (0.38 in). 

Pressure Drop Flow resistance depends on flame arrester channel arrangement and on a time-dependent fouling fac tor due to cor-... 

Slime masses or any biofilm may substantially reduce heat transfer and increase flow resistance. The thermal conductivity of a biofilm and water are identical (Table 6.1). For a 0.004-in. (lOO-pm)-thick biofilm, the thermal conductivity is only about one-fourth as great as for calcium carbonate and only about half that of analcite. In critical cooling applications such as continuous caster molds and blast furnace tuyeres, decreased thermal conductivity may lead to large transient thermal stresses. Such stresses can produce corrosion-fatigue cracking. Increased scaling and disastrous process failures may also occur if heat transfer is materially reduced. 

Figure 3.6.1 (Berty 1979) is a Sankey (1898) diagram, used in power engineering, where the bandwidth is proportional (here qualitatively only) to the flowing masses. This illustrates the calculation results for a rather extreme case of an NOx reduction problem. The case is extreme because the catalyst particle has a dp=0.2mm, i.e., 200 microns. Flow resistance is very high, therefore an L=1 mm deep bend is used only. Per pass concentration drop is still high, Ci-C=1.2ppm, or Dai=0.11. This was tolerated in this case, since it is between 11.2 and 10.00 ppm concentration, and nothing better could have been achieved.

For turbine mixers that the width of a baffle should not exceed more than one-twelfth of the tank diameter and, for propeller mixers, no more than one-eighteenth the tank diameter. With side-entering, inclined or off-center propellers, as shown in Figure 13, baffles are not required. Instead, shrouded impellers and diffuser rings may be used to suppress vortex formation. These devices contribute to flow resistance and reduce circulation by creating intense shear and abnormal turbulence... 

When solid particles undergo separation from the mother suspension, they are captured both on the surface of the filter medium and within the inner pore passages. The penetration of solid particles into the filter medium increases the flow resistance until the filtration cycle can no longer continue at economical throughput rates, at which time the medium itself must either be replaced or thoroughly cleaned. 

When the space above the suspension is subjected to compressed gas or the space under the filter plate is under a vacuum, filtration proceeds under a constant pressure differential (the pressure in the receivers is constant). The rate of filtration decreases due to an increase in the cake thickness and, consequently, flow resistance. A similar filtration process results from a pressure difference due to the hydrostatic pressure of a suspension layer of constant thickness located over the filter medium. 

Equation 46 states that when complete pore blockage occurs, the intensity of the increase in the total resistance with increasing filtrate volume is proportional to the square of the flow resistance. 

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

Capacity Minimum net flow area Certified flow resistance, Kj ASME UD code symbol... 

The problems experienced in drying process calculations can be divided into two categories the boundary layer factors outside the material and humidity conditions, and the heat transfer problem inside the material. The latter are more difficult to solve mathematically, due mostly to the moving liquid by capillary flow. Capillary flow tends to balance the moisture differences inside the material during the drying process. The mathematical discussion of capillary flow requires consideration of the linear momentum equation for water and requires knowledge of the water pressure, its dependency on moisture content and temperature, and the flow resistance force between water and the material. Due to the complex nature of this, it is not considered here. 

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