Flow rate to pressure drop

Capillary Flow Rheometry Next we examine the experimentally obtained results with the capillary flow rheometer shown in Fig. 3.1, which are directly relevant to polymer processing flows, since the attainable shear rate values are in the range encountered in polymer processing. The required pressure drop AP does not increase linearly with increases in the volumetric flow rate Q, as is the case with Newtonian fluids. Rather, increasingly smaller increments of AP are needed for the same increases in Q. The Newtonian Poiseuille equation, relating flow rate to pressure drop in a tube, is linear and given by... 

The equation relating the volumetric flow rate to pressure drop is similar to that for the orifice. The only difference is that the coefficient Co is replaced by the Venturi coefficient, Cv This coefficient approaches 0.99 in. large pipes at high Reynolds numbers. Figure 6.7 illustrates the variation of C as a function of pipe diameter and Reynolds number at the throat. 

Manufacturers of valves in North America have developed a valve coefficient to relate flow rate to pressure drop as C, which is defined as ... 

Although it has been common practice to specify the pressure loss in ordinary valves in terms of either equivalent length of straight pipe of the same size or velocity head loss, it is becoming more common to specify flow rate and pressure drop characteristics in the same terms as has been the practice for valves designed specifically for control service, namely, in terms of the valve coefficient, C. The flow coefficient of a valve is defined as the volume of Hquid at a specified density that flows through the fully opened valve with a unit pressure drop, eg, = 1 when 3.79 L/min (1 gal /min) pass through the valve... 

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 ... 

The channel spacings can be different on each side to match the flow rates and pressure drops of the process design. The spacer studs are also adjusted in their pitch to match the fluid charac teristics. 

Another important objective which must be considered is to provide adequate cyclone capacity for the application. The volume of feed slurry that a given cyclone can handle is related to the pressure drop across the cyclone. The relationship between flow rate and pressure drop for several different sizes of standard cyclones is shown in Figure 56. As shown, the flow rate increases as the pressure drop increases. In order to utilize this graph, the pressure drop used for calculating the separation is used to determine the flow rate for the cyclone diameter which was... 

H type columns must be used at a flow rate and pressure drop below maximum values listed in Tables 4.12-4.16. Standard flow rates are also listed in these tables. They are flow rate range recommendable for long-term usage in tetrahydrofuran at 25°C and vary with temperature. H type columns can be operated at a higher flow rate at elevated temperatures. They also vary with solvent depending on the viscosity. They are approximately inversely proportional to the solvent viscosity. The maximum pressure drop listed in the tables is for one column. When some columns are used in series, the total maximum pressure drop is a summation of values of all columns. 

The filtration, or superficial face, velocities used in fabric filters are generally in the range of 1 to 10 feet per minute, depending on the type of fabric, fabric supports, and cleaning methods used. In this range, pressure drops conform to Darcy s law for streamline flow in porous media, which states that the pressure drop is directly proportional to the flow rate. The pressure drop across the... 

Conventionally, the sample is initially saturated with one fluid phase, perhaps including the other phase at the irreducible saturation. The second fluid phase is injected at a constant flow rate. The pressure drop and cumulative production are measured. A relatively high flow velocity is used to try to negate capillary pressure effects, so as to simplify the associated estimation problem. However, as relative permeability functions depend on capillary number, these functions should be determined under the conditions characteristic of reservoir or aquifer conditions [33]. Under these conditions, capillary pressure effects are important, and should be included within the mathematical model of the experiment used to obtain property estimates. 

The maximum distance the styrene must travel horizontally is around 300 ft. The total distance traveled inside pipes is 390 ft. If a pressure drop of 2 psi per 100 ft is assumed, the pressure drop due to friction will be about 8 psi (20.5 ft of styrene) and that due to elevation is 90 ft. The total pressure drop is 110.5 ft. Usually for normal flow rates the pressure drop due to the change of velocity is ignored. 

To have a better appreciation of the utility of these representations let us first consider the laws that govern flow rates and pressure drops in a pipeline network. These are the counterparts to KirchofTs laws for electrical circuits, namely, (i) the algebraic sum of flows at each vertex must be zero (ii) the algebraic sum of pressure drops around any cyclic path must be zero. For a connected network with N vertices and P edges there will be (N — 1) independent equations corresponding to the first law (KirchofTs current... 

Power input per unit mass of the system is equal to the rate of energy dissipation per unit mass of the liquid and it is estimated by considering the permanent pressure head loss across the orifice. The rate of energy dissipation due to eddy losses is the product of the head loss and the volumetric flow rate. Frictional pressure drop at downstream of the orifice can be calculated as,... 

In 1883, Osborn Reynolds conducted a classical experiment, illustrated in Fig. 6-1, in which he measured the pressure drop as a function of flow rate for water in a tube. He found that at low flow rates the pressure drop was directly proportional to the flow rate, but as the flow rate was increased a point was reached where the relation was no longer linear and the noise or scatter in the data increased considerably. At still higher flow rates the data became more reproducible, but the relationship between pressure drop and flow rate became almost quadratic instead of linear. 

In the case of an unknown flow rate, the pressure drop across a given orifice is measured for a fluid with known properties, and the flow rate is to be determined. 

When a flow sensor is installed for accurate accounting measurements of the absolute flow rate, many precautions must be taken, such as providing a long section of straight pipe before the orifice plate. For control purposes, however, one may not need to know the absolute value of the flow but only the changes in flow rate. Therefore pressure drops over pieces of equipment, around elbows or over sections of pipe can sometimes be used to get a rough indication of flow rate changes. 

Hot oil from the base of a distillation column is used to reboil two other distillation columns that operate at lower temperatures. The design flow rates through reboilers I and 2 are 100 and 150 gpm, respectively. At these flow rates, the pressure drops through the reboilers are 20 and 30 psi. The hot oil pump has a flat pump curve. 

Film thickness is predicted more closely from film flow rate and pressure drop, than is film flow rate from film thickness and pressure drop. This improvement results from the fact that the film flow rate is approximately proportional to the square of the thickness. 

The rigor of this development requires that all fluid-flow data6 follow the conventional / = 16/Nr, relationship in the laminar-flow region. Accordingly, deviations from the theoretical curve in this region are due entirely to errors in measurement or calculation the figures show that these errors were always low except at the lowest Reynolds numbers, where both the flow rates and pressure drops were extremely difficult to determine accurately. 

For rheological measurements the flow through the tube must be laminar no orifices or other restrictions may be present (as they would induce turbulence), and the flow rate (or pressure drop) must be variable. Apparently very few commercially available instruments meet these requirements, but it is often readily possible to build such equipment. Severs (S8) has discussed these factors in some detail. A recent develop-... 

While the object of this chapter is to introduce readers to the science of polyurethane design, it is best to begin with definitions of terms. When physical requirements are to be addressed, quality system disciplines dictate that a system of analysis be established to monitor compliance with the design. For instance, if a device is to allow the flow of water through a foam, a system that can be validated to indicate flow rate or pressure drop must be established. 

Among the many complications of structural testing of membranes is the variety of approaches to membrane stack design proposed by different groups working in the field (1, 8). The necessary service conditions of a membrane are determined not only by the membrane itself but also by the type of spacer employed with it, the flow rate and pressure drop across the face of the membrane, pressure differences which can exist either permanently or temporarily from one side of a membrane to the other, the ease and frequency of disassembly and assembly of the stack, and the way in which it is supported. 

Blowers, fans, and vacuum pumps can be used as gas movers to provide necessary energy to transport the solids. In a negative-pressure conveying system, the vacuum pump is located downstream of the material collection device. In the positive-pressure conveying systems, the blowers or fans are installed upstream of the solids feeding equipment. The selection of a gas mover is primarily based on gas flow rate and pressure drop requirements for the successful transport of solids. 

P 44] Pumping for determination of the highest flow rates and pressure drops was realized using a normal water conduit (28 mm copper pipe with 1 inch ball valve), a water meter customary in trade (metering precision up to 5000 1 h ) and a stopwatch [130], The pressure drops were determined using a simple analog... 

The dall flow tube is available in medium to very large sizes. In the large sizes, the cost is normally less than that of a venturi flow tube. This type of flow tube has a pressure loss of about 5%. Flow rate and pressure drop are related as shown in Equation 4-3. 

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