Pressure drop Velocities

Maynes and Webb (2002) presented pressure drop, velocity and rms profile data for water flowing in a tube 0.705 mm in diameter, in the range of Re = 500-5,000. The velocity distribution in the cross-section of the tube was obtained using the molecular tagging velocimetry technique. The profiles for Re = 550,700,1,240, and 1,600 showed excellent agreement with laminar flow theory, as presented in Fig. 3.2. The profiles showed transitional behavior at Re > 2,100. In the range Re = 550-2,100 the Poiseuille number was Po = 64. 

Stepped-diameter pipelines to minimize pressure drop, velocity, wear and power consumption. 

Many attempts have been made to obtain general expressions for pressure drop and mean velocity for flow through packings in terms of voidage and specific surface, as these quantities are often known or can be measured. Alternatively, measurements of the pressure drop, velocity, and voidage provide a convenient way of measuring the surface area of some particulate materials, as described later. 

The Richardson-Zaki equation has been found to agree with experimental data over a wide range of condifions. Equally, if is possible fo use a pressure drop-velocity relationship such as Ergun to determine minimum fluidization velocity, just as for gas-solid fluidizafion. An alternative expression, which has the merit of simplicify, is fhaf of Riba ef al. (1978)... 

Ratio of wake volume to bubble volume Constant in pressure drop-velocity relationship, Eq. (101) Constant in pressure drop-velocity relationship, Eq. (102) Constant in pressure drop-velocity relationship, Eq. (101) Constant in pressure drop-velocity relationship, Eq. (102) Proportionality constant in Eq. (31)... 

When converged, the user has complete access to all information such as temperature profiles, pressure drop, velocity profiles, mass and species distribution if the model is appropriate and the model inputs were correct, and the cells are sufficiently small the likelihood of an accurate simulation is very good. 

Hydraulic calculations such to match allowable pressure drop, velocity of fluids, and residence time. 

He assumed that since the pressure drop, velocity and density of the vapour greatly influence the efficiency of a packed column the calculation should be based on these parameters. By analogj with a well-known equation for the pressure droj) in pipes, he formulated a flow factor f as follows ... 

A typical pressure drop-velocity plot for a free-flowing powder is shown in Figure 4.1. The superficial gas velocity corresponding to the intersection of the sloping packed bed line and the constant pressure line is called the minimum fluidization velocity, Vmt- Even though few processes operate at V u a knowledge of that critical velocity is essential since it is one of the important parameters used to characterize fluidization. 

For fine particles the pressure drop-velocity relationship will be given by the Carman-Kozeny equation, which will take the following form for incipient fluidization ... 

Note that for n = 1 and k = /i, Equations (4.7) and (4.8) reduce to the familiar Hagen-Poiseuille equation which describes the pressure drop-velocity relationship for the laminar flow of a Newtonian fluid. 

Knowlton and Bachovchin (1975) have studied gas-solid pressure-drop velocity at the choking conditions. Their study was performed on coal at high pressures of 482 to 3319 k N/m. Multiple regression analysis was performed on the variables to determine a correlation for the choking velocity ... 

Viscosity is measured in poise. If a force of one dyne, acting on one cm, maintains a velocity of 1 cm/s over a distance of 1 cm, then the fluid viscosity is one poise. For practical purposes, the centipoise (cP) is commonly used. The typical range of gas viscosity in the reservoir is 0.01 - 0.05 cP. By comparison, a typical water viscosity is 0.5 -I.OcP. Lower viscosities imply higher velocity for a given pressure drop, meaning that gas in the reservoir moves fast relative to oils and water, and is said to have a high mobility. This is further discussed in Section 7. 

Oil viscosity is an important parameter required in predicting the fluid flow, both in the reservoir and in surface facilities, since the viscosity is a determinant of the velocity with which the fluid will flow under a given pressure drop. Oil viscosity is significantly greater than that of gas (typically 0.2 to 50 cP compared to 0.01 to 0.05 cP under reservoir conditions). 

For a single fluid flowing through a section of reservoir rock, Darcy showed that the superficial velocity of the fluid (u) is proportional to the pressure drop applied (the hydrodynamic pressure gradient), and inversely proportional to the viscosity of the fluid. The constant of proportionality is called the absolute permeability which is a rock property, and is dependent upon the pore size distribution. The superficial velocity is the average flowrate... 

Centrifugal demister or cyclone) devices rely on high velocities to remove liquid particles and substantial pressure drops are required in cyclone design to generate these velocities. Cyclones have a limited range over which they operate efficiently this is a disadvantage if the input stream flowrate is very variable. 

The second mechanism can be explained by the wall liquid film flow from one meniscus to another. Thin adsorptive liquid layer exists on the surface of capillary channel. The larger is a curvature of a film, the smaller is a pressure in a liquid under the corresponding part of its film. A curvature is increasing in top s direction. Therefore a pressure drop and flow s velocity are directed to the top. 

Pig. 22. Schematic representation of typical pressure drop as a function of superficial gas velocity, expressed in terms of G = /9q tiQ, in packed columns. O, Dry packing , low Hquid flow rate I, higher Hquid flow rate. The points do not correspond to actual experimental data, but represent examples. 

Horizontally Mixing Aspirator Aerators. An aerator using a horizontally mixing aspirator has a marine propeller, submerged under water, attached to a soHd or a hoUow shaft. The other end of the shaft is out of the water and attached to an electric motor. When the propeller is rotated at high velocity, at either 1800 or 3600 rpm, a pressure drop develops around the propeller. Air is then aspirated under the water and mixed with the water, and moved out. This type of aerator, shown ia Figure 3g, is very efficient ia mixing wastewater. 

Venturi scmbbers can be operated at 2.5 kPa (19 mm Hg) to coUect many particles coarser than 1 p.m efficiently. Smaller particles often require a pressure drop of 7.5—10 kPa (56—75 mm Hg). When most of the particulates are smaller than 0.5 p.m and are hydrophobic, venturis have been operated at pressure drops from 25 to 32.5 kPa (187—244 mm Hg). Water injection rate is typicaUy 0.67—1.4 m of Hquid per 1000 m of gas, although rates as high as 2.7 are used. Increasing water rates improves coUection efficiency. Many venturis contain louvers to vary throat cross section and pressure drop with changes in system gas flow. Venturi scmbbers can be made in various shapes with reasonably similar characteristics. Any device that causes contact of Hquid and gas at high velocity and pressure drop across an accelerating orifice wiU act much like a venturi scmbber. A flooded-disk scmbber in which the annular orifice created by the disc is equivalent to a venturi throat has been described (296). An irrigated packed fiber bed with performance similar to a... 

Motionless inline mixers obtain energy for mixing and dispersion from the pressure drops developed as the phases flow at high velocity through an array of baffles or packing in a tube. Performance data on the Kenics (132) and Sul2er (133) types of motionless mixer have been reported. 

The specific cake resistance is the most troublesome parameter ideally constant, its value is needed to calculate the resistance to flow when the amount of cake deposited on the filter is known. In practice, it depends on the approach velocity of the suspension, the degree of flow consoHdation that the cake undergoes with time, the feed soHds concentration, and, most importantly, the appHed pressure drop Ap. This changes due to the compressibiHty of most cakes in practice. often decreases with the velocity and the feed concentration. It may sometimes go through a maximum when it is plotted against soHds concentration. The strongest effect on is due to pressure, conventionally expressed as ... 

The basic concepts of a gas-fluidized bed are illustrated in Figure 1. Gas velocity in fluidized beds is normally expressed as a superficial velocity, U, the gas velocity through the vessel assuming that the vessel is empty. At a low gas velocity, the soHds do not move. This constitutes a packed bed. As the gas velocity is increased, the pressure drop increases until the drag plus the buoyancy forces on the particle overcome its weight and any interparticle forces. At this point, the bed is said to be minimally fluidized, and this gas velocity is termed the minimum fluidization velocity, The bed expands slightly at this condition, and the particles are free to move about (Fig. lb). As the velocity is increased further, bubbles can form. The soHds movement is more turbulent, and the bed expands to accommodate the volume of the bubbles. 

Good gas distribution is necessary for the bed to operate properly, and this requites that the pressure drop over the distributor be sufficient to prevent maldistribution arising from pressure fluctuations in the bed. Because gas issues from the distributor at a high velocity, care must also be taken to minimize particle attrition. Many distributor designs are used in fluidized beds. The most common ones are perforated plates, plates with caps, and pipe distributors. 

Design Considerations. For a perforated plate, the pressure drop across the distributor should be at least 30% of the bed pressure drop when operating at the lowest expected gas velocity. The number of holes in the distributor should exceed 10 per square meter. The pressure drop, AP, across the distributor is given by... 

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